Distribution Categories:Physics-Atomic and Molecular

(UC- 34A)Chemistry (UC-4)

ANL-82-88

ANL--82-8 8

DE83 010693

ARGONNE NATIONAL LABORATORY9700 South Cass Avenue

Argonne, Illinois 60439

Proceedings of theWORKSHOP ON THE INTERFACE BETWEEN

RADIATION CHEMISTRY AND RADIATION PHYSICS

Held atArgonne National Laboratory

September 9-10, 1982

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither the United States Government nor any agency thereof, nor any of theiremployees, makes any warranty, express or implied, or assumes any legal liability or responsi-bility for the accuracy, completeness, or usefulness of any information, apparatus, product, orprocess disclosed, or represents that its use would not infringe privately owned rights. Refer-ence herein to any specific commercial product, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof. The viewsand opinions of authors expressed herein do not necessarily state or reflect those of theUnited States Government or any agency thereof.

March 1983

NOTICEPORTIONS OF THIS REPORT ARE ILLEGIBLE.It has been reproduced from the bestavailable copy to permit the broadestpossible availability.

A major purpose of the Techni-cal Information Center is to providethe broadest dissemination possi-ble of information contained inDOE's Research and DevelopmentReports to business, industry, theacademic community, and federal,state and local governments.

Although a small portion of thisreport is not reproducible, it isbeing made available to expeditethe availability of information on theresearch discussed herein.

Introduction

At many conferences, including a succession of the Department of Energycontractors' meetings, numerous papers have been presented by radiationchemists and also by physicists who model systems closely related to thosetreated by chemists. An observer, unfamiliar with the topic, might havebelieved that physicists and chemists were talking about two entirelydifferent branches of radiation research.

At a recent DOE contractors' meeting in Gettysburg (Ref. 1), thereevolved the idea of a meeting devoted to areas of interest common to bothradiation chemistry and radiation physics. The proposed conference became the,orkshop on the Interface Between Radiation Chemistry and Radiation Physics,held at Argonne National Laboratory on 9-10 September 1982. We are verygrateful to Dr. Robert W. Wood and Dr. Frank P. Hudson of the Office of Healthand Environmental Research of DOE for providing us with funds on shortnotice. The list of participants is attached as Appendix A.

The workshop proved to be both timely and enlightening. It demonstratedthat, except for a difference in emphasis, physicists and chemists share afairly common view of gas and liquid phase radiolysis. Thus, chemists tend tooperate in a time domain where chemical reactions can be observed and todeduce therefrom initial G values. Meanwhile, physicists naturally focusconsiderable attention on initial energy deposition events and performcalculations which should predict the same initial yields.

Formal presentations at the workshop were kept to a minimum to allowsufficient time for short, informal presentations and subsequent

discussions. All participants were encouraged to submit writtencontributions, comments, and even afterthoughts. As is clear from the

contributions included in this report, the topics of interest to the workshopparticipants are diverse, reflecting the nature of radiation research. Yet,there is a unifying theme underneath; we are all trying to understand theinteraction of radiation with matter in terms of basic physical and chemicalprocesses.

We grouped the contributed papers and remarks according to the subjectsdiscussed only in a very broad sense. We strongly urge you to browse throughthe contributions because they contain many candid ideas and comments that canbe found only in informal documents as this report. The program of theworkshop is reproduced in Appendix B, and the author index is included asAppendix C.

The workshop answered some questions, raised more, and pointed to futurepossibilities. We will attempt to enumerate some of these here.

I. Main Issues and Accomplishments of Workshop

a. Theorists and experimentalists became more aware of each other'saccomplishments. The instances available for comparison of theory withexperiment in aqueous systems became clear. The need to identify adjustable

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parameters in the theory and test the effects of variations in such was alsosuggested. Also, the ability to simulate energy deposition events brought upthe question as to whether the older, more intuitive concepts of spurs arestill valuable in guiding our thinking. Discussions at the workshop and some

contributions included in this report clearly indicate that, in trackstructure modeling, the quality of input cross section data is a more crucial

problem than the bookkeeping of the energy transport processes. Furthereffort is needed, however, to develop theory to predict more diverse,experimentally verifiable results.

b. There were presentations to indicate that the gas-liquid differenceis becoming better understood, particularly with respect to the initial energydeposition. At present, however, no general theoretical methods exist tocorrelate gas phase data with liquid phase data and vice versa. Althoughprimary events that involve large energy transfers, such as the production(but not the fate) of delta rays, should be independent of target phase, morestudy is desirable on the utility of gas-phase data in simulating condensed-phase events.

c. Many comments were directed tj6the lacl1 2of knowledge concerningevents occurring in the time range 10 to 10 second. The study ofphysico-chemical events during this time range should get more attention,particularly in the radiation chemistry of condensed media.

II. Suggestions for Future Efforts

Discussions both formal and informal converged to the followingsuggestions:

a. Choose some molecule (other than water) and measure yields andkinetics over a large pressure range for the gas (including the criticalregion, if possible) and also for the liquid. Both the validity of variousmodeling codes and the use of gas phase data can then be properly assessed.

b. Although the energy deposition events are calculable given thenecessary cross sections, the exact nature of the primary chemical species andhow they change at early times is still unknown. Workshop participants wereundecided as to whether new experimental tecpgiques jI the near future (10years) will allow time resolution in the 10 - 10 second range to see,for example, how the solvated electron in water forms.

c. Can theory be useful in this time range? For example, in the case ofcondensed media there is a need to know about the motion and reactivity ofcollective excitations. Initial yields and spatial distributions of reactantsderived from such knowledge can then be used as initial input for calculatingtime-dependent kinetics.

d. The degradation of slow electrons (<10eV) undoubtedly depends on thephase of the target medium as well as the shape of target molecules, becauseslow electrons have long de Broglie wavelengths extending over manymolecules. For instance, the formation of transient negative ion states maysubstantially alter the diffusion and localization characteristics of theseelectrons. Most of the modeling codes currently available do not treat the

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degradation of slow electrons in sufficient detail. More theoretical studieson the fate of slow electrons may lead to a better understanding of thetransition from the physical to the chemical stage.

e. More attention should be paid to nonpolar solvents, particularly withrespect to the process of geminate-ion-recombination and its relationship tothe energy deposition events.

f. Some theoretical and experimental effort should be invested in theradiation chemistry of mixtures. Investigations of this sort provide anopportunity to observe reactions between radiolytically produced transients ofmixture components. Also, important questions about the partition of initialenergy deposition in liquid mixtures have yet to be answered. For example,how valid is it to assume that energy deposited in a mixture component isproportional to its electron fraction?

g. Complete sets of energy loss cross sections (for elastic andinelastic scattering of projectiles and secondary electrons generated by them)should be measured and compiled for a few selected substances. These shouldbe used initially to calculate track structure in order to determine whethersuch detailed knowledge is required in predicting important consequences inradiation chemistry. A secondary objective would be to utilize thesystematics of the measurements and use them to interpolate for molecularsystems where complete data are not available.

h. In general, cross sections for the interaction of photons with mediaare better known than those for the interactions of charged particles such aselectrons and heavy ions. Under certain conditions, the two types ofinteractions are related. Yet no systematic method has been developed tocorrelate cross sections for charged particle interactions with those forphoton interactions except for the cases where the first Born approximation isapplicable. Further exploration of this possibility is desirable to make useof more abundant, and often more reliable photoionization and photoexcitationdata. Success in this direction, coupled with the success in relating gasphase data to liquid phase data described earlier, will open up new horizonsin radiation physics and chemistry.

i. Photoionization of liquids should be further investigated toelucidate the mechanism of ion pair formation and separation. In this area,development of high-repetition rate picosecond lasers with photon energies 5eV and higher should allow substantial progress to be made in the area ofphotoionization in liquids. The observation of ions and their reactions onshorter time scales than was generally possible previously will be feasible.

Reference

1. The biological effects of ionizing radiation: Radiological physics, 15thContractors Meeting, Office of Health and Environmental Research, Officeof Energy Research, Department of Energy. 4-6 May 1982, Gettysburg,Pennsylvania.

Editorial Committee

M. A. Dillon Y.-K. KimR. J. Hanrahan M. C. Sauer, Jr.R. Holroyd L. H. Toburen

V

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Contributed Papers

Page

I. SUMMARIES

Summary: Radiation ChemiEtryE. J. Hart . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Concluding RemarksM. Inokuti . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

II. PRESENTATIONS AND COMMENTS DURING THE WORKSHOPMeasurements of Physical and Chemical Properties

Several Interfaces Between Radiation Physics and Chemistry That CculdPleasure Each Other More

G. R. Freeman . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Comments During the WorkshopG. R. Freeman . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Inelastic Cross Sections for Electron Interactions in Liquid WaterR. N. Hamm, R. H. Ritchie, J. E. Turner, and H. A. Wright . . . . 32

Excitation Processes in Irradiated Aqueous SolutionsE. J. Hart .-..... . .. . . . . . . . . . . . . . . . . . . . 37

Range and Linear Ionization Rates of Low Energy ElectronsG. G. Meisels and T. Fujii . . . . . . . . . . . . . . . . . . . . 40

Optical Properties of Molecular LiquidsL. R. Painter and R. D. Birkhoff . . . . . . . . . . . . . . . . . 44

Interaction of 0-20 eV Electrons with Thin Solid Films at CryogenicTemperatures

L. Sanche . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Track Structure Modeling

Some Analysis Techniques and Results of the Monte Carlo Simulation ofProton and Electron Tracks

D. J. Brenner and M. Zaider . . . . . . . . . . . . . . . . . . . 58

Spatial Aspects of Radiological Physics and ChemistryA. E. S. Green and D. E. Rio . . . . . . . . . . . . . . . . . . . 65

Modeling Early Events in the Radiation Chemistry of Dilute AqueousSolutions

J. H. Miller and W. E. Wilson . . . . . . . . . . . . . . . . . . 73

Recent Calculations Modeling Data from the Pulse Radiolysis and GammaRadiolysis of Water and Aqueous Solutions

C. N. Trumbore and W. Youngblade . . . . . . . . . . . . . . . . . 82

Effects of Phase on Electron Transport in WaterJ. E. Turner, H. G. Paretzke, R. N. Hamm, H. A. Wright,and R. H. Ritchie . . . . . . . . . . . . . . . . . . . . . . . . 91

Track Modeling by Monte Carlo TechniquesW. E. Wilson. . . . . . . . . . . . . . . . . . . . . . . . . . . 101

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Page

Early Physical and Chemical Events in Electron Tracks in Liquid WaterH. A. Wright, J. E. Turner, R. N. Hamm, R. H. Ritchie,J. L. Magee, and A. Chatterjee . . . . . . . . . . . . . . . . . . 106

Computational Details of the Monte Carlo Simulation of Proton andElectron Tracks

M. Zaider and D. J. Brenner . . . . . . . . . . . . . . . . . . . 113

III. COMMENTS AFTER THE WORKSHOP

Spurs and Track Structure

Comments on Tracks and Delta RaysR. Katz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Tracks, Spurs, Blobs and Delta RaysJ. L. Magee and A. Chatterjee . . . . . . . . . . . . . . . . . . 121

What Is a Spur?C. N. Trumbore . . . . . . . . . . . . . . . . . . . . . . . . . . 123

The 10- 1 6 - 10-12 Second Region

The Physico-Chemical Stage: 10-16 - 10-12 SecondJ. L. Magee and A. Chatterjee . . . . . . . . . . . . . . . . . . 126

Comment on the Possibility of Securing Experimental Data for VeryShort Times and the Determination of Initial Yields

W. Primak, C. J. Delbecq, and D. Y. Smith . . . . . . . . . . . . 129

Comments on Subexcitation Electrons

R. J. Hanrahan . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Others

A Selection of Problems in Radiation Physics and ChemistryD. A. Douthat . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Comments After the WorkshopG. R. Freeman . . . . . . . . . . . . . . . . . . . . . . . . . . 137

How Radiation Chemistry Can Help Understand Primary Processes in theEnergy Deposition Process

C. D. Jonah . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Is the Fricke Dosimeter a 1-Hit DetectorR. Katz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

The Special Nature of WaterC. N. Trumbore . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Appendix A: List of Participants . . . . . . . . . . . . . . . . . . 145Appendix B: Workshop Program . . . . . . . . . . . . . . . . . . . . 149

Appendix C: Author Index . . . . . . . . . . . . . . . . . . . . . . 151

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SUMMARY: RADIATION CHEMISTRY

Edwin J. Hart*

Elegant tools, but mainly electron accelerators, computers and a vastarray of instruments useful for detecting transient species have aided theradiation chemist in basic studies of the chemical changes induced in solids,liquids and gases by ionizing radiations. The present status of these

accomplishments were expertly summarized by Dr. Freeman. He placed specialemphasis on primary events such as non-homogenous spur reactions, primary andsecondary recombination of ions and electron solvation. The problems are farfrom being solved but considerable progress has been made in understanding the

nature of these initial reactions and in establishing yields of the primaryspecies. Now, with picosecond pulse radiolysis and flash photolysis, thechemists is able to identify and measure products formed at times in the rangeof 10~ s in aqueous solutions and possibly to shorter times in non-polarliquids, solids and gases. It was recogni d that a gap in our knowledge ofthe processes occurring exists between 10 s, the time for energy deposition,

and 10~11s, the time for electron solvation. Hopefully, theoretical andexperimental physicists will be able to contribute significantly to ourknowledge of phenomena occurring in this sub-picosecond time zone.

Liquid water, because of its biological importance, was widely discussedin all sessions. Chemical reactions taking place in irradiated aqueoussolutions have been investigated extensively for the last 50 years. As aresult primary yields of H, eaq , OH, H2 and H202 have been documented for avariety of radiations by scavenger techniques; initial yields of eaq and OH

have also been measured for electrons by picosecond pulse radiolysis. Theseresults have been fruitfully applied by the physicist in modelling energy lossparameters in liquid water and in calculations of chemical yield for electronsand heavy ions. ratifying agreement has been obtained between observed and

experimental G(FeJ+) for 3H20. This work could be profitably extended to 6 0Co

y-rays, a widely used radiation with a well known yield.

A shortcoming of the use of G(Fe3+) in these studies is that it measuresonly the total effect of free radicals and molecular products. A morecritical test of the assumptions made in these modelling experiments would beto match the products formed in the HCOOH + 0 dosimeter. In this system theprimary yields, g(H), g(OH), g(H2) and g(H202) are independently obtained byseparate measurements of H2, H202 and CO2 formed and by the 02 decrease.

These yields are known for a variety of radiations.

Everyone seems to have their own definition of a spur. However, one

exists in liquid water since there is unquestionably an initiUl heterogenousdistribution of radiolysis products. No one disagreed with the Magee conceptof spur, blob and short track. In the average spur with an initial diameter

* Consultant, Chemistry Division, Argonne National Laboratory

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of 2 x 10-8 cm, 40 eV of energy has been deposited. Experimentally this

heterogenous distribution of primary species manifests itself by the"molecular products," H2 and H202 in irradiated water. G(mp) increases with

increasing density of ionization and approaches a maximum for fission

particles where remaining free radicals are practically zero.

At best, the radiation chemist's concept of molecular product formationin liquid water is vague. It is usually assumed that H2 and H202 form by the

pairwise recombination of H and/or ea and by two OH radicals,respectively. However, from the singlet and triplet excited states of thewater molecule, H2 and H202 may form by the following reactions:

MO Mode of Decomposition

3b1 H + OH*

3a1 H2 + 0

1b2 hot H + OH or H2 + 0*.

Molecular H2 and H202 may then form as follows:

hot H + H20 + H2 + OH

OH* + H20 + H202 + H

0* + H20 + H202 .

A theoretical treatment of water vapor has been made. Help from the

physicist is needed in assessing the importance and validity of these

reactions in irradiated liquid water. In alkaline solutions, H202 forms by

the reaction:

OH + 0 + HO2

But diversion of some of the OH radicals to O(3P) formation is possible by thereaction:

OH + O0 + O( 3 P) + OH

The important question of the ratio of cross-section (a) for ionization

to excitation (aion)/(aion + Oexc) was calculated theoretically. For highenergy electrons this ratio is 0.95. Useful for the chemist would be a

knowledge of this ratio for commonly used radiations such as y-rays, 2-, 4-,and 16-MeV electrons. Excitation cross-sections of solute molecules relativeto that for water are of great importance as the concentration of solutebecomes of the order of one molar. Under these conditions the product yields

from excitation processes may approach those of the ionization processes. Andsince the excitation products differ appreciably from those induced byionization, there is a need for continued research in this field. Inbiological systems that are outside the dilute solution range, excitationprocesses are probably important and should be studied. Chemical

investigations of excitation processes will apply to biological effects just

2

as chemical studies of ionization processes have.

Should the radiation chemist select other systems for study? Thisquestion was raised since a preponderant amount of the research discusseddealt with theoretical and experimental studies on aqueous systems. Becauseof its polar nature, the water molecule might not be the ideal one for studiesdesigned to understand the processes taking place at times shorter than10-1 s. Would a molecule with a low molecular weight such as ethane orpropane be better suited for this study? Possibly so for this limited goal,but over the long run, much still must be learned about the water moleculeincluding D2 0. Because of its applications in power reactors, in chemical andbiological systems and in atmospheric chemistry, much research with aqueoussystems is still required. As discussed abov:' H 2 is a decomposition productof water radiolysis. Since H2 is viewed by many as the ideal non-pollutingfuel of the future, methods of increasing G(H 2 ) has been sought by radiationchemists for many years. And since G(H2 ) increases with incrasing density ofionization, it is possible that the intense irradiation cot:ditions availablefrom fusion reactors might be useful for the production of H2 by Shedecomposition of water. Thus a study of the behavior of D2 0 and H20 by highfluxes of epithermal neutrons, ultraviolet light, y-rays and electrons at hightemperature water vapor should be considered. Environmental chemistry, too,would benefit by further studies of the effects of ionizing radiations onwater vapor containing pollutants such as SO2 , H2SO 4 , NO, NO2 and organiccompounds.

3

CONCLUDING REMARKS

Mitio InokutiArgonne National Laboratory, Argonne, Illinois 60439

I was literally pleased to listen to the discussion in the past two days

and to participate in it. When I say "literally pleased" I really mean it,rather than using a cliche of empty pleasantry. I was pleased because Irecognized a great deal of progress since the late 1950's, when I beganworking on some of the topics treated here such as electron collision crosssections, electron-degradation spectra and the total ionization yield. Atthat time I felt severely hampered by the lack of basic data and also wasdepressed with the scarcity of colleagues with whom I could share interest.To take an example, in the 1950 Oberlin Symposium (about which I know through

the published proceedings) only), Platzman stressed the need for mapping outthe oscillator-strength spectra of molecules over the vacuum-ultraviolet andx-ray regions as the most fundamental data in radiation physics. In the early1960's, when I joined him in the effort toward analyzing primary physicalevents in radiation action, there was no single measurement of a secondary-electron spectrum for an ionizing collision of any particle with any atom; allthe data I could find in books such as the book by Mott and Massey were

theoretical and were dubious in reliability.

In part owing to a continued campaign3 led by Platzman, Fano, and others,

a large volume of data on the oscillator-strength spectra and on thesecondary-electron spectra came along. This was largely attributable to theprogress in experimental techniques and instrumentation including vacuumtechnology, electron optics and analysis, and development of light sources

such as electron synchrotrons and storage rings; at the same time, there wereadvances in atomic-collision studies including theoretical work. By the 1972

Airlie Conference 4 the impact of the progress in physics on radiation researchbegan to be visible, but remained somewhat limited in scope. Now after adecade, I witness in the present Workshop discussion on the sarie general topicbut more advanced, more detailed, and richer in substance than ever before.

The progress in the understanding of early physical and chemical stagesof radiation action owes much to support for over three decades by certainbranches of AEC, later ERDA, and now DOE. In particular, the offices ofR. W. Wood and R. J. Kandel are the most important in this respect. I ampointing this out not merely as an expression of my personal appreciation butalso as an excellent example of a major role played by government agencies incertain special areas of science. Let me paraphrase this below. The primarybeneficiary of radiation research, especially as it relates to the health

effects of radiation, is the general public, although radiation research alsocontributes materially to nuclear industry and to some areas of chemical andmaterials industry. The benefit to the general public is a good reason for

* Work performed under the auspices of the U.S. Department of Energy.

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support by The government. In addition, there is another reason related tothe nature oi work in radiation research. It is multidisciplinary, rangingfrom physics and chemistry to biology and medicine, and it is addressed to aunifying goal, i.e., the full elucidation of radiation actions on matteri ncluding the man and his environment. Research of this kind goes beyond thetraditional scope of academic institutions, and may not appear attractive tothose whose interest is purely academic; it also requires sustained effortsover a long period. Therefore, it is best done in government laboratories orin universities under government support. It is indeed a result of greatwisdom and penetrating foresight that continued government support has been

given to our areas of research, i.e., to the most fundamer .al part ofradiation science; as a consequence, the U.S. maintains a leading position inthese areas.

Let me turn to the heart of our business. As I see, the elucidation ofthe earliest physical and chemical stages demands good knowledge in thefollowing four major categories.

1. Spectroscopic data, i.e., the knowledge of energy levels of atoms,molecules, and condensed matter.

2. Cross-section data for initial processes.

3. Rates of reactions among initially produced species.

4. Analysis of cumulative consequences of elementary processes, i.e.,transport theory and kinetics.

Following are some commentaries on the four categories. The importanceof category 1 is all too obvious; without that, no serious analysis canbegin. The only reason I have listed it above is to remind you that ourcurrent knowledge of excited states of polyatomic molecules, even of simplerones such as H20, is far from satisfactory.

Category 2 refers to the knowledge of the probability of each elementaryprocess in which radiation energy is delivered to matter. The most typical ofthe data of this kind concern cross sections for electron collisions with agiven molecule resulting in specified values of energy transfer and inspecified set of products, e.g.,

e + H20 + e + H20(E), (1)

1i20*(E) + H20+(v) + e, (2)

or H + OH(v) + e, (3)

or H + OH(v), (4)

and so on, where H2 0*(E) means an excited state of the water moleculecharacterized by excitation energy E, H20+(v) represents a vibrationallyexcited state of the H2 0+ ion, which is stable in isolation, but rapidlyhydrates in the liquid. Likewise OH(v) signifies a vibrationally excitedstate of OH. The above exposition is extremely sketchy; to be completely

5

precise, one must specify the kinetic energies and the internal energies ofall the product species. On an earlier occasion,5 I discussed the status ofthe cross-section data from a reasonably wide perspective; a more generaldiscussion about the role of physics in radiation chemistry and biology wil beseen in a forthcoming article.6

In category 2, the first task is the mapping of the distribution of theprobability of each energy transfer E, viz., the energy-loss spectrum for theprocess (1). The mapping has been carried out for many molecule s andsolids. Moreover, the same spectrum for fast charged particles is intimatelyrelated to the photoabsorption spectrum, which has been extensively studied.Thus, the probability distribution has been fairly well documentd. Inaddition, we have now begun to understand the influence of the molecularaggregation in condensed phases on that probability distribution, as we heardhere from L. R. Painter. In sharp contrast, the relative probabilities ofalternative processes that an excited species, say H20 , at a fixed E mayundergo have been poorly mapped out so far. These relative probabilites,which may be called branching ratios, fcr processes (2)-(4) are known asfunctions for E only for high-energy electron collisions and forphotoabsorption, even for an isolated water molecule in the gas phase.Corresponding information is unavailable for condensed phases in general, andis an object of educated guesses at best with an aid of scanty and fragmentaryindications. Here at the present Workshop we saw in the work by L. Sanche thbeginning of efforts toward the understanding of the branching ratios insolids; however, we await for a breakthrough in both experiment and theory inthis area.

Category 3 concerns the central theme of the present Workshop, i.e., thebridge between chemistry and physics. None of the products (i.e., the primaryspecies) on the right hand sides of Eqs. (2)-(4) is stable unless left invacuum. For example, the electrons slow down through multitudes of collisionswith medium molecules (in both gas and liquid phases, though at radicallydifferent rates), and eventually become solvated in the liquid phase orrecombine with a parent ion or a foreign ion. Other product species alsocollide with medium molecules and often undergo chemical reactions. It is theprimary concern of radiation chemists to elucidate the chain of processessketched above by use of various kinetic techniques. Certainly a large volumeof rate-constant data has been amassed, and their systematics seem to befairly well understood. For instance, in the joint work of the Oak Ridge andLawrence Berkeley groups on liquid water, which J. E. Turner and R. N. Hammdescribed, I was most impressed at that part which concern chemistry and

diffusion of the primary species. The results of the work appear to agreewell with experimentally measured chemical yields, and seem to indicate thatthe major part of the chemistry in the particular case of that treatment isunderstood.

We have also heard about several other aspects of the chemistry work fromG. Freeman, C. Trumbore, E. J. Hart, and G. Meisels (listed in the temporalorder of their presentations). Perhaps, the latter of the greatest interestis the behavior of slow electrons in liquids, i.e., the subject Freemantreated. As M. C. Sauer pointed out, non-polar liquids present especiallychallenging problems because one cannot simply interpret data in terms ofhydration or solvation as one does in polar liquids. It happens that slow-electron interactions with individual molecules is a topic in which physicists

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have accomplished major advances in the past decade, and it is probably timelyfor some of us to devote efforts toward systematic interpretation of thosephenomena of the kind discussed by Freeman.

Work in category 4 presumes sufficient knowledge and data of categories1-3, and aims at theorizing full consequences of many elementary processes.In the present Workshop, topics of category 4 wcre treated by J. H. Miller, W.E. Wilson, H. A. Wright, M. A. Zaider, D. J. Brenner, J. E. Turner, and R. N.Hamm (listed in the temporal order of their presentations). A crucialquestion here is, "Does one have sufficient knowledge and data aboutelementary processes?" What is sufficient depends on what specific purposeone sets out to fulfill. For instance, to predict the total ionization yieldto a given certainty, one must know the cross sections for ionization and

excitation to some accuracy. Because our knowledge of elementary processeswill never be absolutely complete, this question will remain with us forever,

and its answer is a matter of strategy and priority requiring mature

judgement.

To take an example, the Monte-Carlo simulation work on the electron

degradation in liquid water by the Oak Ridge group is certainly impressive inthe degree of details of treatment. Yet, as the workers certainly know, manyof the input data are provisional; in particular, the branching ratios foralternative products resulting from a fixed energy transfer are not reallyknown from direct experimental evidence, and are assumed on the basis of dataon gases and of certain theoretical ideas. I fully recognize that the workersprobably do the best anyone can do at present. At the same time, it remains

debatable whether the present status of the cross-section data justifies thedetailed treatment of the Oak Ridge group, and how much of the results aretruly realistic. In this respect, I want to make a plea to all workers in thekinetics or transport studies: they should document in their report all theinput data in all the possible details and with utmost clarity, so that futureworkers may know precisely how to reproduce the results and to build up on

them. Without full documentation of the input data, it is often difficult to

assess the significance of the work.

Here in the Workshop we heard much about the Monte-Carlo simulation.However, there is another approach to the transport analysis, i.e., methods oftransport equations as exemplified by the Spencer-Fano theory of electronslowing-down. Sometimes, the two approaches, viz., Monte-Carlo methods andtransport-equation methods, are viewed as mutually exclusive competitors. Istrongly disagree with this view; I believe that the two approaches aremutually complementary and they jointly contribute to the eventual fullunderstanding of transport and kinetics. On one hand, Monte-Carlo methods areapplicable to complicated situations, for example, those which involvedetailed spatial distributions of various events (viz., track structures).But results of Monte-Carlo calculations are in the form of large amounts ofnumbers, and require some suitable summary for interpretation of the physicalsignificance. On the other hand, transport equations are solvable only forsimplified situations, and even then often approximately. Nevertheless,analytic results derived from transport equations are much more amenable tophysical interpretations and 6 cneralizations, and often provide an importantguide for analyzing Monte-Carlo results. Perhaps, an eventual optimalapproach to transport problems will be some hybrid of analytic methods andMonte-Carlo methods.

7

Finally, I want to point out an important problem in electron

transport. Most of the results we have heard about concern electrondegradation in a chemically pure medium. In almost every problem of practicalsignificance, the medium contains more than one chemical species. An extreme

example is the biological cell, which contains water and a multitude oforganic molecules and has spatially inhomogeneous structures. Even a liquid

sample used in a radiation-chemistry experiment is often a chemical mixture,which may be deliberately prepared or may have resulted from incompletepurification. In any case, one wishes to know how a quantity describingelectron slowing-down, e.g., the electron degradation spectrum as defined bySpencer and Fano, depends upon the chemical composition of a mixture medium.In general, the dependence of such a quantity on the composition must benonlinear. How large the nonlinearity is and under what circumstances it isso are extremely important questions in many contexts, e.g., in the evaluation

of intermolecular energy-transfer effects and of scavenging or quenching ofchemically reactive species. As far as I know, questions of this kind havebeen left unanswered.

It is my impression that the Workshop has helped us all in seeing clearlythe gaps in our knowledge. One of the most obvious gaps concerns the physico-chemical stage involving events that take place between 10-16 sec and 10-12sec, as we have heard many times. I am hopeful that coming years, perhaps ina decade, will see considerable progress in this matter, although I cannotpredict it precisely. In experiment, some new technique of following the

early events in condensed phases will be crucial. In theory, the centralobject of consideration will be the coupling of electronic motion withrotational and vibrational degrees of freedom and the resulting relaxation ofelectronic energies. Some of the key elements of the understanding are comingalong in certain specialized contexts, e.g., predissociation and pre-ionization near an ionization threshold contexts, e.g., in simpler molecules,

relaxation of inner-shell hole states of atoms, and dissipation of electronic

energies in simple semiconductors.

REFERENCES

1. J. J. Nickson, ed., Symposium on Radiobioloy, Oberlin College 1950 (JohnWiley & Sons, Inc., New York, 1952).

2. N. F. Mott and H.S.W. Massey, The Theory of Atomic Collisions, SecondEdition (Oxford at the Clarendon Press, 1961).

3. U. Fano, Radiat. Res. 64, 217 (1975).4. R. D. Cooper and R. W. Wood, eds., Physical Mechanisms in Radiation

Biology. Proceedings of a Conference Held at Airlie, Virginia, 1972USAEC Report CONF-721001, (U. S. Atomic Energy Commission, 1974).

5. M. Inokuti, in Electronic and Atomic Collisions. Invited Papers andProgress Reports, XIth International Conference on the Physics ofElectronic and Atomic Collisions, Kyoto, Japan, 1979, edited by K.Takayanagi and N. Oda (North-Holland Publishing Company, Amsterdam,Netherlands, 1980) p. 31.

6. M. Inokuti, Radiation Physics as a Basis of Radiation Chemistry andBiology, in Applied Atomic Collision Physics. Vol. 4. Condensed Matter,

edited by S. Datz (Academic Press, New York) in press.7. K. H. Tan, C. E. Brion, Ph. E. van der Leeuw, and M. J. van der Wiel,

Chem. Phys. 29 299 (1978).

8

Several Interfaces Between Radiation Physics and Chemistry That Could

Pleasure Each Other More

Gordon R. Freeman

Chemistry Dept., University of Alberta, Edmonton, T6G 2G2, Canada

INTRODUCTION

Myran Sauer has kindly asked me to give an overview of currently activeareas in Radiation Chemistry that may be pertinent to what Radiation Physicistscan calculate. I am not clear about what can be calculated, but there are cer-tain things that it would be highly desirable to try to calculate. Measurementsprovide a superficial understanding of a system, and modeling is needed to seekmore deeply into it.

To give an extensive overview would take longer than an hour. It seemsbest to largely avoid areas to be covered by Miller and Turner. There are majoromissions of works by Magee, Mozumder, Chatterjee, and others. However, I willbegin with an overlapping topic, the nonnomogeneous kinetics of reactions inspurs. I will then speak about electron thermalization distances and thermalelectron mobilities in fluids, electron scattering in gases, and finally,a possible new approach to calculating the energies and shapes of the opticalabsorption bands of solvated electrons.

The problems I will discuss have been around a long time. It would be ahappy event to learn during this meeting that some of them have been solved al-ready.

Those of you who look up the references will find that the mathematicsin our early work was clumsy, though effective. Much of the math has sincebeen made more elegant by theoreticians, and the rest probably could be improvedwith a little effort.

NONHOMOGENEOUS KINETICS OF REACTIONS IN SPURS

Experimental studies in this area are of three types: product yieldsmeasured as functions of scavenger concentration, free ion yield measured as afunction of applied electric field strength, and the yield of an intermediatespecies measured as a function of time. Relatively little experimental work isbeing done on the first two types these days, but a great deal remains to be donewith their modeling. Track structure calculations, such as those by Paretzke(1,2) are relevant to the modeling of radiolysis reactions in dense fluids (3-6).They could be used to improve the models for the work I will report. They giveinformation about the initial spacial distribution of energy deposited in thesystem. They do not, however, give information about the spacial distributionof thermalized electrons in spurs, because thermalization ranges of electronsare largely dependent on the scattering behavior at energies below 1 eV. Scatteringat these low energies is strongly affected by subtleties of the liquid structure,in ways that are only partly understood.

The word spur is not used in a uniform manner by all workers in our field.I find it simplest to let the one word spur represent all sizes and shapes ofzones of reactivity, including what some others call blobs and short tracks. Inour terminology a spur is a grouping of reactive intermediates in which there isa significant probability that some of the intermediates will react with each otherbefore they can diffuse into the bulk medium. A spur might be a single radical

9

pair or ion-electron pair, or it might be the entire track of a heavy particle.In a given radiolysis system there is a distribution of spur population numbersand densities. For example, in the y radiolysis of a liquid about 60% of allspurs initially contain only one ion-electron pair and about 13% contain morethan two pairs (7,8).

a) Product Yields as Functions of Scavenger Concentration

The compound that has been studied most is water, which is characterizedby a high dielectric constant. As a consequence of the high dielectric constant,most of the spurs that initially contain only one ion-electron pair are dissi-pated by diffusion, without reaction. Essentially all of the reaction between primaryintermediates in irradiated water occurs in spurs that contain more than onepair. Extensive kinetics modeling has been done for the radiolysis of water andit continues at a relatively sophisticated level. I would like to briefly dis-cuss modeling for low dielectric constant liquids, for which the coulombic inter-action between the ion and electron tends to dominate their behavior even insingle pair spurs. Calculations have mainly been done with single pair spurmodels, which are in great need of improvement (9-11).

Consider the radiolysis of a pure compound in the liquid state:

(1) M -AA-- [M+ + e~]

(2) [M+ + e_] M* (geminate neutralization)

(3) [M+ + e ] - M+ + e (free ions)

(4) M+ + e --- M* (random neutralization)

The square brackets indicate that the species inside them exert an appreciablecoulombic force on each other, that is, they are in a spur. The coulombicattraction tends to draw the ion and electron back together to undergo geminateneutralization. Random thermal motion tends to separate the ion and electronto make them freely diffusing species. The free ions, usually at a much latertime, undergo neutralization with free ions that originated in other spurs.

Now consider a liquid that contains a certain concentration of electronscavenger S. The free ions are long-lived at usual radiolysis dose rates andare scavenged by very low concentrations of scavengers. Thus all the free ionsare usually scavenged under conditions where scavenging in the spurs is important.The concentration dependence of electron scavenging in spurs is described below.

As the ion and electron drift towards each other in the solution, thereis a finite probability that the electron will encounter and react with a solutemolecule before encountering the positive ion. The task is to calculate theprobability.

(5) [e-+ S] --. [S]-

(6) [S (+M+)] - products

To calculate the scavenging probability one must estimate the number of moleculesthat an electron encounters after its energy has been reduced to near thermal ,..dbefore it becomes neutralized.

10

The number of molecules met by an electron before it undergoes geminateneutralization is equal to the product of the number n of diffusive jumps madeby the electron and the number b of new molecules that it meets per jump. Thenumber of diffusive jumps is taken as the ratio of the geminate neutralizationtime to the time required for one jump, which are related to the initial separa-tion distance y between the thermalized electron and ion, and to the diffusioncoefficients D and jump distances A of the various species. After a number ofapproximations and manipulations one may obtain the following expression for theprobability $e that an electron will be scavenged by S before being neutralizedby the counter ion (9):

(7) $e = 1-(l - fNs)V

where f is the encounter efficiency of the e + S reaction, N is the mol fractionof S and

(8) =( e,g + -, (up + 1 e)1

e s

where the subscripts e, s and p refer to the electron, scavenger and positive ion,respectively, and u is the mobility, while

(9) v = 1.39 x 10 cy3

where c is the dielectric constant of the medium. The value of c is time dependentin alcohols and other polar systems and has been taken into consideration ( 11).The scavenging probability is strongly dependent on y, other things such as f inequation 7 being equal.

The values of b and A in equation 8 are related but are not known, so 8is uwed as an adjustable parameter in the calculations.

By adding the fraction of free ions fi one obtains the total probability

me that an electron will react with a solute molecule:

(10) me = $fi+ + 0e -fi)

where

(11) *0fi = exp(-C2/ckTy)

where C is the electronic charge, k is Boltzmann's constant and T is the temperature.

In any given system there is a distribution of thermalization distances.The final scavenging yield G(S ) is obtained by averaging_4e over the distributionF(y)dy and multiplying by the total ionization yield G(e )tot'

(12) G(S) = G(e~)totf eF(y) dy

0

If a physicist, or almost anybody, looked through the details of what Ihave presented he could find many places to improve.

11

The form of the distribution function F(y) is not exactly known, soapproximate functions have been devised. Two functions that each give thecorrect free ion yield in liquid ethane at 183K are shown in Figure 1 (9,12).

Nitrous oxide scavenges electrons to form nitrogen:

(13) e + N20 -+ N2 + 0

Nitrogen yields from the y radiolysis of nitrous oxide solutions in ethane at183K (12) are shown in Figure 2. Yields calculated from equation 12 usingthe delta distribution function YD did not agree with the experimental results.The distribution that gave best agreement with the measured yields was thepower function YP:

(14a) F(y) = 0 , y <42 x 10-8 cm

(14b) F(y) = 4.1 x 1010 y-2.5 y >42 x 10-8 cm

Equation (14b) is of the form

(14c) mF(y) = xyminy min

A single parameter, three dimensional Gaussian distribution functiondid not provide as good agreement as did YP between between equation 12 andthe experimental yields (9).

The foregoing model contains the assumption that there is only oneion-electron pair per spur. Inclusion of multipair spurs would increase theestimated values of the thermalization ranges y at the low range end of thedistribution.

A fresh approach to stochastic and Monte Carlo treatments of spur re-action kinetics has been made recently by Pilling and coworkers (13). So farthey have only treated neutral radicals, but they hope to try ions in thenear future. The project is still some distance from comparison with experiment.

b) Electric Field Effect on Free Ion Yields

Free ion yields in irradiated liquids are often measured by sweepingthe charges out of the liquid with an applied electric field and collectingthem on a capacitor. The yields measured in this way increase with increasingf eld strength (Figure 3) (14). The field dependence of the free ion yieldG. is a function of the electron thermalization range distribution F(y). Int single pair spur model the field dependence may be represented by the modifiedOnsager equation 15 (15):

(15) GEfi = GtotJ fiF(y)dy0

where n-lj+l

(16)0fi $E + e26y (2Qy) E (n-j) (jr/)

(n+l)! j=0

where $fi is given by equation 11, r = E2/ckT and 8 = (EE/600 kT).

12

If the field effect model and the previously described chargescavenging model were exact, the same F(y) distribution would be used inboth systems. However, exact models would include multipair spurs, amongother things, so the same F(y) distribution will not fit in the two kindsof single pair spur model. When YP distributions of form 14c were used inscavenging yield calculations the best value of x was 1.5, whereas in thesefield effect calculations the best value of x was 2.5.

A crude multipair spur model of the electric field effect on freeion yields in X irradiated liquids was tested briefly (16), but much remainsto be dcne. It was found that when the properties of the liquid and fieldare such that more than about 10% of the total ions become free ions, themultipair spur model requires a larger mean thermalization range than doesthe single pair spur model to provide agreement with experimental yields.When less than 10% of the ions escape the spurs the effect of the multipairsis buried so deeply that it is not noticeable in the calculations. However,a systematic study has not been made to find the effect on the best valueof x in a YP distribution.

A valuable project would be to improve the scavenging and fieldeffect models to the extent that similar F(y) distributions would give satis-factory results in both. Comparison of the two models should give insightabout each. Track structure calculations would provide information for theproject.

A problem that cannot be convincingly solved until the preceding pro-ject has been completed is the calculation of the lifetime distribution of thespecies that react in the spurs. In the meantime, valuable experiments arebeing made with time resolution in the picosecond range.

ELECTRON THERMALIZATION DISTANCES

Secondary electron thermalization distances in many liquids have beenestimated by fitting equation 15 to experimental free ion yields (14-18). Thecalculated temperature and field dependences of the free ion yields aredependent on the form of the distance distribution function F(y). With a singleform of F(y) in the single pair spur model it has been possible to fit boththe field and temperature dependences of the experimental free ion yields indozens of dielectric liquids (15). The function has a Gaussian body and apower tail, and is designated by YGP (Figure 4):

(17a) F (y) = (3.84y2/ir b P)exp(-y2/bGP) , y < 2.4bGP

(17b) F2(y) = F1(y) + 0.48(b P/y3) , y > 2.4bGP

where b is the dispersion parameter and is also the most probable value of y.The deviation from the simple Gaussian occurs only for the outermost 7% of theelectrons. The power tail presumably refers to the ion-electron separation dis-tance in the last surviving pair in a multipair spur. The tail is thereforean artifact of the single pair spur model.

Other things being equal, electron ranges b P are inversely proportionalto the liquid density d. We therefore normalize th ranges by using theproduct bGPd.

The density normalized ranges of the secondary electrons in liquidsare dependent on the molecular structure. The range increases with increasing

13

degree of sphericity of the molecules (Figure 5). The range varies inverselywith the rate of transfer of energy from the electrons to the molecules of theliquid. For C1 to C3 hydrocarbons the rate of energy loss by the electrons

correlates roughly with the anisotropy of polarizability of the molecules. Thisindicates that rotational modes of the molecules are a major energy sink forthe electrons in the energy range that governs their thermalization range (15).Mozumder and Magee (19) had come to the same conclusion earlier on theoreticalgrounds. Most of the range is attained when the electron energy is below thevibrational threshold, _0.2 eV, because the magnitudes of excitation crosssections generally increase in the order rotational << vibrational << electronic.

For hydrocarbons containing more than three carbon atoms correlationsare more complex (15), because the electron interaction with a molecule appar-ently penetrates effectively only two carbon-carbon bonds in series (20).There is no time to do much more than point out that molecular structure effectsare large and only partially explained. One outstanding example is the effectof substituting the hydrogens on acetylene by methyl groups (Figure 5). The C-Hbonds in acetylene are rather polar, with the H being positiv . Replacing thepolar C-H groups y C-CH3 groups increases bgpd from 21 x 10 g/cm in acetyleneto 67 x 10-8 g/cm in dimethyl acetylene (15), a factor of 3. The triple bondin dimethyl acetylene appears to be an al: ost inert sphere to the epithermalelectron, whereas we had expected it to show an affinity for the electrons andtherefore be an efficient energy sink by way of transient anion states.

The problem of thermalization ranges is related to that of mobilities,which will be discussed next.

THERMAL ELECTRON MOBILITIES IN DIELECTRIC LIQUIDS

There is a loose correlation between the previously discussed thermaliza-tion ranges of secondary electrons and the mobilities of thermal electrons inliquids (21,22). It is not surprizing that the behavior of thermal electrons(-0.03 eV) is more sensitive to properties of the liquid than is that of epi-thermal electrons (.O.1 eV). Thermal electron mobilities in dielectric liq-idsmay differ by factors up to 107, while thermaliz tion distances in the same setof liquids differ by factors up to about only 10 (Figure 6). The correlation is

somewhat dependent on molecular structure (23). For example, in liquid hydro-carbons at 294K a thermal electron mobility of 0.10 cm /Vs correlates witha thermalizatign distance of about 44 x 10-8 cm in the alkyl benzenes, and toabout 72 x 10 cm in the n-alkanes (Figure 7). Energy is transferred fromelectrons to benzenes more readily than to alkanes, presumably by way oftransient anion states.

The reason for the approximate correlation between thermalization range andthermal electron mobility is that the potential fluctuations represented schemati-cally in Figure 8 affect both (23). The magnitude of the potential fluctuationsdepends on the nature of the liquid and can be a few meV up to a few tenths of an eV.The magnitudes of the energy loss steps in Figure 9 are apparently related tothe magnitudes of the potential fluctuations. Furthermore, the energy losscross sections (cm-1) are probably related to the magnitudes of thepotential fluctuations. Since most secondary electrons begin with energies ofthe order of 10 eV, the thermalization range bGp is inversely related to themagnitude of the potential fluctuations. Now, the mobility p of thermal electronsis also inversely related to the magnitude of the potential fluctuations. Ifthe fluctuations are small compared to kT the electrons remain quasifree and hav'a high mobility. If the fluctuations have magnitudes DV kT the electrons spendpart of their time in localized states and have u a exp(-AV/2kT). The 2 in theexponent indicates that the electron cannot sit in the bottom of the well. If therelaxed, solvated state has AV > 2kT, as it does in hydroxylic solvents, theelectron has a low mobility similar to that of a heavy ion.

14

A theoretical problem is to calculate a realistic potential fluctuationcurve such as that in Figure 8 for an electron in a real liquid. The pathwould be three dimensional, energy dependent, and momentum transfer (directionchange) collisions would probably occur more frequently than energy loss colli-sions. Energy loss calculations would lead to curves similar to those inFigure 9.

Electron localization occurs when an energy loss collision allows theelectron to drop into a potential well from which it lacks the energy to escape(end of path in Figure 9). Once the localized state is formed it relaxes tothe solvated state on a timescale similar to that of the librational motionsof the molecules in the liquid (24 and Figure 10). The dipole orientation isassisted by the torque of the charge-dipole interaction. The settling of thestate into deeper levels causes a shift in the optical absorption spectrum tolower wavelengths.

Thermal electron states can be partially characterized by the a eragemobility displayed by the electrons. Quasifree electrons have u >10 cm /Vs. Inliquids that have a viscosity near 1 cP localized electrons have U 10-3 cm2/Vs,similar to that of an anion. Mobilities intermediate between quasifree and anionicvalues are usually interpreted through transitions between localized and delocalizedstates or through a hopping mechanism.

The mobility of quasifree electrons in dense media is usually interpretedby way of the Cohen-Lekner model or some modification of it (25-28). The modelstill needs work, for example to refine the interpretation of the change of signof the electron-molecule scattering length on increasing the fluid density in theliquid range (29). The liquids to which the model applies are composed ofspherelike, nonpolar molecules that do not capture electrons to form anions.

A larger problem is the interpretation of mobilities intermediate betweenthose of quasifree electrons and those of anions. There are hopping models andpercolation models, but those most commonly used involve transitions betweenlocalized and delocalized states.

(18) e loc edeloc

The distribution of excitation energies E is usually taken to be a Gaussiancentered about Eo and with a dispersion a:

(19) N(E) = r 1oexp[-(E-E0)2 2

The measured mobility is the average of the mobilities in the two states, takenover the respective residence times.

(20) =XPdel + (l-X)uloc

where X is the fraction of electrons in the delocalized state at a given instant,

(21) X = N(E)[1+ exp(-E/kT)]YdE

and

(22) Uloc = Woc exp (-Eloc/kT)

where * uocand E10 are the pre-exponential factor and activation energy for mobilityof the localized sate (30).

Equation 21 involves the assumption that localized states can exist bothabove and below the delocalized level. This assumption might be poor and could

15

easily be changed. Both Eo and a in equation 19 are temperature sensitive and moretheoretical work is needed to determine the best way of handling the variationswith temperature. The model we use was built by analogy with optical absorptionspectra of solvated electrons:

(23) E0 = E(O) - aT

(24) a = o(O) + bT

If the model were reworked it might be better to tie a to E in some way. To proceedwith the model at hand, the mobility in the delocalized state is taken to besensitive to the fluid density n and temperature:

ref~ rf\2Te(25) del ~delk n 2 / T

Mobilities measured in the isomeric butenes at temperatures from theirmelting points to their critical points have been fitted by equations 19-25(30 and Figure 11). The parameter values are listed in Table 1. The greatlydifferent behavior in cis- and trans-butene-2 shows up mostly in the temperatureu2pendence of o, within the restrictions of the model. A possible interpretationof the temperature independence of a in trans-butene-2 might be that the localizedstate in this liquid is an anion, rather than a solvated electron. However, moremodeling should be done, for example by using Eo/o as a parameter rather thanallowing the two to vary independently. In the present model the magnitude of aand its variation with temperature are not basically understood. We tried relatingo to the thermal energy fluctuations, through the heat capacity of the liquid inthe Schiller and Jortner fashion (23), but it did not withstand the test oftemperature variation from the melting point to the critical.

The mobility of electrons in each of the butene critical fluids is near10 cm2/Vs (Figure ll) which is in the quasilocalization regime. Near the normalboiling points, -270K, the mobilities differ by up to 70 fold. The greatestdifference is between cis- and trans-butene-2; the difference is in the directionopposite to expectation from the molecular dipole moments (Table 1). The behaviorcorrelates with the physical shape of the molecules; the mobility near the normalboiling point is greater when the molecules are more spherelike. The liquidstructure has a great influence on the magnitude and dynamics of the potentialfluctuations shown schematically in Figure 8.

When a mobility model has been devised that rationalizes, in more detailthan presently enjoyed, the differences in behavior of electrons in the C1 to C3hydrocarbons, it can be fine tuned through treatment of the cis- and trans-butene-2systems.

MOLECULAR SHAPE AND DENSITY EFFECTS ON ELECTRON SCATTERING IN GASES

In a low density gas, where an electron interacts with one molecule ata time, thermal electron mobility p is inversely proportional to the gas densityn. The product un is therefore independent of n, but it depends on the natureof the gas and on the temperature. This has been known for 60 years or more, butwhat is new is that there is a molecular shape effect that is the inverse of theone in the liquid phase. In the liquid phase, the electron mobility is greaterwhen the molecules are more spherelike, as shown by the values of pn in theisomeric pentanes at n > n (31 and Figure 12). Although a good theory remainsto be developed, the behavior has been rationalized in terms of molecularorientational disorder and anisotropies of polarizabilities, and the effects ofthese on the potentials depicted in Figures 8 and 10. In the low density gas, theelectron mobility is lower when the molecules are more spherelike (Figure 12). Thecause is that the momentum transfer cross sections at electron energies below 100

16

meV are larger for the more spherelike isomer (32 and Figure 13). The reasonfor this is not yet known. One may speculate about transient anion statesthat involve spherical Rydberg type orbitals, but nothing quantitative hasbeen done. Several theoreticians have been consulted, all of whom thought theproblem to be trivial at first sight. One at Cal Tech said he'd give theproblem as an assignment in his undergraduate course! But the shape effectturns out to be a tricky problem for reasons that none have explained to me.(Backlash from their early overconfidence?). Perhaps multipoles are involved.The molecular models have to be severely simplified (a base ball, a tennisball can and a hockey puck). Perhaps someone here will have a helpful ideaabout the problem.

Now let us briefly examine the behavior in dense gases. In n- andiso-pentane at densities greater than about 10% of the critical the value ofun decreases (Figure 12). There would be a similar effect in neopentane butit is compensated by the beginnings of conduction band formation, which dominateselectron behavior at n > n (Figure 12). In all of the gases, including neopentane,the temperature coefficient of mobility at constant density increases with in-creasing density at n > 0.1 nc (Figure 14). Similar behavior has been observed inevery substance studied, including argon, methane, ethane, dimethyl ether (33) andammonia (34). The Arrhenius temperature coefficient increases to about 60 kJ/molin the critical region, then decreases again in the liquid phase (Figure 15). Thelarge temperature coefficient exists only close to the vapor liquid coexistencecurve; it decreases quite rapidly as the vapor is heated away from the curve(Figure 14). The effect is attributed to quasilocalization of electrons by therelatively large density fluctuations (van der Waals quasidroplets) that existin the dense coexistence vapor. Heating the vapor at constant density decreasesthe magnitude of the fluctuations (increases the compressibility factor).

The proposed mechanism is:

(26) medium - site

(27) e~qf + site eqf - ql

where "site" represents a density fluctuation of sufficient amplitude andappropriate breadth, while &f and &l represent the quasifree and quasilocalizedelectron, respectively.

Heating the vapor to remove it from the coexistence region decreases theconcentration of sites. The overall enthalpy and entropy of activation ofprocesses 26 and 27 are large and negative (35). Most of the enthalpy andentropy changes have been attributed to the quasicondensation equilibrium 26.However, within the 10- s time resolution of the apparatus the enthalpy changeof process 27 in ethane could be as much as 30 kJ/mol, which would be 30% of thetotal at the critical density. (10-7/10-12 : exp(30,000/8.3 x 300)).

Theoretical calculations could be done that test the reasonablenessof the quasilocalization model and to work out details. It has also been suggestedthat the large temperature coefficient of mobility in the dense vapor near thecoexistence curve is simply due to enhanced scattering by the clusters and thetemperature dependence of the cluster sizes. One could make theoretical estimatesof the cluster populations and see in what way the larger scattering crosssections differ conceptually from quasilocalization-

17

NEW APPROACH ro OPTICAL ABSORPTION SPECTRUM OF SOLVATED ELECTRONSSolvated electrons have a broad, asymmetric optical absorption spectrum,

without fine structure. The spectrum shifts strongly in energy and width ongoing from one type of solvent to another (Figure 16). Values of the ratio

W /EAmax range from 0.5 to 1.0 on going from water or ammonia to 2-butanol. The

asymmetry factor Wb/Wr ranges from 1.4 to 2.3 in the same solvents (36-38). Thusa greater band width is caused mainly by increasing the width of the highenergy side (Figure 16).

Theoretical interpretations of the energies of the optical absorptionmaxima have employed many models over the past fifty years. In 1933 Ogg useda particle in a bubble box (39). In 1962 Jortner did an SCF treatment of anelectron in a bubble in a polarizable continuous dielectric medium (40). Semi-continuum models employed short range interactions with a first shell ofpolarized solvent molecules arranged symmetrically around the edge of a sphericalcavity, and a long range polarization interaction with a continuum beyond thefirst shell (41,42). The molecules in the first shell were assumed to havepoint dipoles and to have isotropic polarizabilities. Medium rearrangementenergies (dipole-dipole repulsion in the first shell, cavity creation, longrange orientation of the permanent dipoles, and so on) are estimated to determinewhether the model can provide a stable localized state of the electron. Itusually can, but it is difficult to see a pattern in the change in parametervalues from one type of solvent to another. The main shortcoming is thatthe calculated band shape, obtained by introducing Boltzman distributions ofdipole orientations and cavity radii, is too narrow.

Inclusion of molecular vibrations, and both localized bound-bound andhopping transitions provides a better band shape (43,44). The calculationspossess so many parameters that one cannot assess them. Furthermore, it hasbeen shown experimentally that the absorption energy is dominated by the detailedstructure of the liquid, and it has not been possible to take this into accountin any model so far. Another major shortcoming might be that multibody inter-actiorns are handled as sims of pair interactions.

Evidence for the effect of liquid structure on the optical absorptionenergy of solvated electrons is obtained by comparing optical absorptionenergies with the Kirkwood structure parameter gK. The Kirkwood parameter isrelated to the way in which polar molecules orient relative to each other inthe liquid (45 and Figure 17). If the molecules line up in such a way thattheir dipole moments tend to counteract each other, gK < 1.0. If the structureis random, gK = 1.0. If the alignment tends to enhance the dipole moment, gK >1.0.The values are calculated from those of the static dielectric constant Ds, themolecular polarizability a and the liquid phase molecular dipole moment u(Onsager cavity model, neglects spacial and optical anisotropies of molecules,could be refined). Oster and Kirkwood suggested that as a basis for classificationof 'iquids according to their thermodynamic behavior, the correlation parameter9K is more significant that the molecular dipole moment (45).

The values of gK for water and a series of n-alcohols at 296K are in therange 2.7 - 3.3 (Table 2). The dielectric constants vary four fold, from 79 to20. The optical absorption energies EAm x are similar, 1.7 - 1.9 eV. Bycontrast the values of gK for ammonia ana n-amines are 1.3 - 1.6, half of thehydroxy compound values; the EAmax for solvated electrons in these liquids areabout 0.65 eV, about a third of the values in the hydroxy solvents (Table 2).The correlation of EAmax with gK, and the lack of correlation with dielectricconstant and dipole moment, indicate that the details of liquid structure have adominating influence on the energy levels of solvated electrons.

In theoretical treatments of electrons in liquids the spacial and opticalanisotropies of the molecules have largely been ignored. The ground state of a

18

solvated electron is not s-like, because the volume occupied by the electronis not spherical in shape; it is many-branched and irregular (Figure 18).Fluctuations in molecular density and orientation about the electron sites canbe envisioned to have a great influence on the energies of the electron states,and therefore on :he optical and transport properties of electrons in dielectricliquids.

I would like to suggest a different quantum statistical mechanical approachthan that made by Simons (43), although a great deal can be learned from hiswork. One could begin by a consideration of the liquid structure in theabsence of the electron. One could perhaps calculate the gK factor bystatistical mechanical methods and adjust the model parameters until the correctvalue of gK was obtained. (The manner in which the molecules orient with respectto each other in the liquid depends strongly on the external shape of themolecules). One could then insert an electron at a site that seemed suitable, dueto accidentally favorably oriented and spaced molecules, and allow the chargeto perturb the liquid structure in its vicinity. The perturbation would probablyextend about three molecular layers into the liquid, beyond which it would havefaded into the normal liquid structure. One could then use this relaxed electronsite and the thermal (translational, rotational and vibrational) fluctuationsin it to calculate the optical and transport properties of the electron. Thedifferences between optical and transport transition energies might be largelydue to the Franck-Condon restriction on the former.

A test of the new model would be to have rationalizable changes inparameter values on going from one solvent to another. A disadvantage of it isthat the number of parameters that can be adjusted is likely to be large.

REFERENCES

1. H. G. Paretzke, in Advances in Radiation Protection and Dosimetry inMedicine, R. H. Thomas and V. Perez-Mendez (eds.), Plenum PublishingCorp., New York, 1980, p.51.

2. G. Burger, D. Combecher, J. Kollerbaur, G. Leuthold, T. Ibach and H.G.Paretzke, in Seventh Symposium on Microdosimetry, Oxford, 1980.

3. A. K. Ganguly and J. L. Magee, J. Chem. Phys. 25, 129 (1956).

4. J. L. Magee and A. Chatterjee, J. Phys. Chem. 84, 3529 (1980).

5. J. H. Miller, Radiat. Res. 88, 280 (1981).

6. D. R. Short, C. N. Trumbore and J. H. Olson, J. Phys. Chem. 85, 2338 (1981).I mention this work good naturedly in spite, of the fact that Conrad stillhasn't paid off the two bets he lost.

7. A. Ore and A. Larson, Radiat. Res. 21, 331 (1964).

8. H. A. Schwarz, J. Phys. Chem. 73, 1928 (1969).

9. G. R. Freeman, Int. J. Radiat. Phys. Chem. 4, 237 (1972).

10. (a) W. P. Helman and K. Funabashi, J. Chem. Phys. 66, 5790 (1977).(b) R. J. Friauf, J. Noolandi and K. M. Hong, J. Chem. Phys. 71, 143 (1979).

11. K. N. Jha and G. R. Freeman, J. Chem. Phys. 51, 2839 (1969).

12. M. G. Robinson and G. R. Freeman, J. Chem. Phys. 55, 5644 (1971).

13. P. Clifford, N. J. B. Green and M. J. Pilling, J. Phys. Chem. 86, 1322(1982).

14. J.-P. Dodelet, P.G. Fuochi and G. R. Freeman, Can. J. Chem. 50, 1617(1972). See ref. 16 for less awkward equations describing the field effect.

15. J.-P. Dodelet, K. Shinsaka, U. Kortsch and G. R. Freeman, J. Chem. Phys.59, 2376 (1973).

19

16. J.-P. Dodelet and G.R. Freeman, Int. J. Radiat. Phys. Chem. 7, 183 (1975).

17. G. R. Freeman, J. Chem. Phys. 39, 1580 (1963).18. W. F. Schmidt and A. 0. Allen, J. Chem. Phys. 52, 2345 (1970), and

several others.

19. A. Mozumder and J. L. Magee, J. Phys. Chem. 47, 939 (1967).

20. J.-P. Dodelet and G. R. Freeman, Can. J. Chem. 50, 2667 (1972).

21. J.-P.Dodelet, K. Shinsaka and G. R. Freeman, J. Chem. Phys. 59, 1293 (1973).

22. G. R. Freeman, Radiation Research: Biochemical, Chemical and PhysicalPerspectives, eds. 0. F. Nygaard, H. I. Adler and W. K. Sinclair, AcademicPress, New York, 1975, p.367.

23. (a) J.-P. Dodelet, K. Shinsaka and G. R. Freeman, Can. J. Chem. 54, 744,(1976)(b) J.-P. Dodelet and G. R. Freeman, Can. J. Chem. 55, 2264 (1977).

24. G. R. Freeman, Radiation Research 1966, ed. G. Silini, North-HollandPubl., Amsterdam, 1967, p.113.

25. M. H. Cohen and J. Lekner, Phys. Rev. 158, 305 (1967).

26. J. Lekner, (a) Phys. Rev. 158, 130 (1967); (b) Phil. Mag. 18, 1281 (1968);(c) Phys. Lett. 27A, 341 (1968).

27. S. Basak and M. H. Cohen, Phys. Rev. B, 20, 3404 (1979).

28. S.S.-S. Huang and G. R. Freeman, Phys. Rev. A, 24, 714 (1981).

29. J. A. Jahnke, N. A. W. Holzwarth and S. A. Rice, Phys. Rev. A, 5, 463(1972).

30. J.-P. Dodelet and G.R. Freeman, Can. J. Chem. 55, 2893 (1977).

31. I. Gyorgy and G. R. Freeman, J. Chem. Phys. 70, 4769 (1979).

32. G. R. Freeman, I. Gyorgy and S. S.-S. Huang, Can. J. Chem. 57, 2626 (1979).

33. N. Gee and G. R. Freeman, J. Chem. Phys. (in press).

34. P. Krebs and M. Heintze, J. Chem. Phys. 76, 5484 (1982).

35. N. Gee and G. R. Freeman, Phys. Rev. A, 22, 301 (1980).

36. F.-Y. Jou and G. R. Freeman, J. Phys. Chem. 83, 2383 (1979); 85, 629(1981).

37. F.-Y. Jou and G. R. Freeman, Can. J. Chem. 57, 591 (1979).

38. A.-D. Leu, K. N. Jha and G. R. Freeman, Can. J. Chem. 60, 0000 (1982).

39. R. A. Ogg, Phys. Rev. 69, 243 (1933).

40. J. Jortner, Mol. Phys. 5, 257 (1962), Rad. Res. Suppl. 4, 24 (1964).

41 D. Copeland, N. R. Kestner and J. Jortner, J. Chem. Phys. 53, 1189 (1970).

42. K. Fueki, D.-F. Feng and L. Kevan, J. Phys. Chem. 74, 1976 (1970);J. Am. Chem. Soc. 95, 1398 (1973).

43. A. Banerjee and J. Simons, J. Chem. Phys. 68, 415 (1978).

44. K. Funabashi, J. Phys. Chem. 85, 2734 (1981).

45. G. Oster and J. G. Kirkwood, J. Chem. Phys. 11, 175 (1943).

20

TABLE 1

Parameter values for equations 19-25 and Figure

Solvent

ci4 -butene-2

4 o -butene

butene-1

-t'an -butene-2

a

(meV/K)

0.98

0.86

0.96

1 .08

a(o)

(meV)

0

8

49

117

b

(meV/K)

1.08

0.97

0.35

0

Eo/o-at 300K

0.9

1.2

2.0

2.4

11.0

I270K(cm2/Vs)

1.6

0.89

0.038

0.025

Db

(D)

0.3

0.50

0.34

0.00

. e= 30 cm2/Vs at Tref = 295K, E(0) = 600 meV, Myc = 0.12 cm2/Vs,

Ec = 65 meV. The values ref and E(0) are not unique, but have

been placed at slightly larger than the minimum required for butene-l.

Reference 30.

b. Electric dipole moment.

TABLE 2

Solvent Properties and Electron Excitation Energies, 296K

Solvent

H20CH3OHC2H5OHn-C3H70H

NH3CH3NH2C2H5NH2n-C3H7NH2

a. electricformula

b.C.

Pt ( D )0

2.322.142.162.15

1.811.611,481.42

D5b

7933.424.520.1

17.39.46.55.3

9KC

2.72.93.03.3

1.31.51.61.6

EAmax (eV)

1.721.951.801.95

0.680.650.640.65

dipole moment, liquid phase, Onsager

static dielectric constantKirkwood molecular correlation factor.

21

v v 0 y . . W. r "

I I I I *I

100

y (10-8 cm)

FIGURE 1 Two different thermalization range distributions thatfree ion yield in y irradiated liquid ethane at 183K.corresponds to y = 150 x 10- cm. The power function14. Data from references 9 and 12.

Nz

5

4O

3-

2/-YP/YD

solo 0000-.5 -4 -3

Log NN20-2

would give the correctThe delta function YD

YP represents equation

-1

FIGURE 2. Nitrogen yields G(N2) from y irradiated solutions of nitrous oxide in ethaneat 183K, plotted against the mol fraction of nitrous oxide NN 0. The curveswere calculated from equation 12, using the indicated F(y) distributions fromFig. 1. The Experimental points are from reference 12.

22

1000

100

LM'

0

10

10

co

YP YD

-I-

-I-

I -' -

1000

I I I I I ---

-1---1-11'111 . _ .1 1 1 1 1 11 1 1 1 1 1 111 1

I I I I

0.41

0.3

W50D

02

0. 1--

0 4 8 12 16 20 24 28

E (kV/cm)

FIGURE 3. Electric field dependence of the free ion yield in liquid propane at 183K.,, experimental, reference 14. The curves were calculated from equation 15.

0

d.0

0.0

a0

I A1 r 4 6 10 2

FIGURE 4. Thennalization range distribution function YGP of secondary electrons in yirradiated liquids. F(>y/bGp) YF(y/bGp)d(y/bGp); bGp is the dispersionparameter. The simple Gaussia '' function YG1 is shown for comparison.Reference 15.

23

1_

"S

dI

2 YG1 YG P

i~ ' ii i/

YG1- X = 4.5 -

- e X = 2.5~

X = 1.5-

ww w wII

2100CNI

oA.O

o *+

Q ti

A )-C

"}-,o-0 f-<

00

O^.- O"n. O

A-

0.

r^ .O /

0.. a y

1 2 3 4 s 6 7 6 9

NUMBER OF CARBONS

FIGURE 6. Correlation between thermal electronmobility we and the most probable thermali-zation distance bGp of secondary electronsin irradiated liquids. References 21 and22.

FIGURE 5. Effect of molecular structure on thedensity normalized thermalizationranges of secondary electrons in liquidhydrocarbons. 0, alkane or cyclo-alkane;A, alkene;O, diene; 0, alkyne.Reference 15.

120

100 1-

E

60

40

20

10.000

1000-

100

10

E

V

" [r

011-

@10"A

rctd

.i."M CM@ 1

" - -1114 IMP

D C-.---- 0

- S n-CaMa- 0

"NM 1

-- C -C3M

- A g

7 --

" C14 5 0w

0.1

001

0001

24

00 1000nnnn L

inn --

10

N. 1

GV

00.1

001

0.001

40 60 80 100

bGP

120 140 160

200

150

100 NE

50

0290 370 450 530

T (K)

(a) Correlations between thermal electron mobilities ue and secondary electronthermalization distances bGp in organic liquids at 294 + 2K. " , unsaturatedhydrocarbons; o , saturated hydrocarbon; , ether. Reference 23a. (b) Cor-relations between temperature effects on the density normalized ranges bGpd(filled points) and thermal electron mobilities u (open points) in neopentane(circles) and n-pentane (squares). The vertical dashed lines mark thecritical temperatures. Reference 23b.

25

T 1 1 1 1 1 I I ?IOr121 2.5 0

(a

0A

4 0

/O- "

-S I ,i i i i i

200

150

(b)

no-NE

o

-a

100

50

0

FIGURE 7.

"........ v

interstitial positions

Fluctuations of V in space due tofluctuations in moleculardensity and orientation.

DISTANCE ALONG PATH

FIGURE 8. Qualitative representation of the variation of the potential energy V of anepithermal quasifree electron near the end of its thermalization path. Theheights of the potential fluctuations range from a few meV to a few tenthsof an eV, depending on the liquid. Reference 24.

}DwzwW

WHr

E

E=T+V

'" E decreases through" " "inelastic scattering

T '

."

DISTANCE ALONG PATH

FIGURE 9. Qualitative representation of the variation of the potential energy V,kinetic energy T and of E " (T + V) of an electron along the last part of itsthermalization path. The heights of the potential fluctuations and the sizes ofthe steps in E range from about a meV to about an eV, depending on the natureof the liquid. If the potential fluctuations are small relative to kT theelectron does not become localized. Reference 24.

26

V

A

4

A

w

w

-1!

Tra

Ele

II I --I-13

LOG t (s)

-12 -11

SolvatedElectron

n-C6H14

~P3

H20

-10

FIGURE 10. Qualitative representation of the variation of the potential energy V of anelectron as a function of time after the localization event. Reference 24.

500 400 300

10

~Eu

v1 0%

0 01

o.oo

T(K)200 150

3 4 5

looo/T (K)6 7

FIGURE 11. Mobilities of electrons in liquid cia-butene-2 (o), isobutene (i), butene-1(O) and trans-butene-2 ("). The lines were calculated from equations 19-23using the parameter values listed in Table 1. -.- ", approximate mobilities ofanions in each of the liquids, taken as 0.7 (u- + u,) averaged for the fourliquids. Reference 30.

27

5 -14

ippedctron

\ \--/ _

- -

00 K

1021

103Eu.

Ec

1021 1

1020 1021n(molecules / cm3 )

FIGURE 12. Effect of density on the density normalized mobilities of thermal electronsin the coexistence vapor and liquid of the pentane isomers. nc = criticaldensity. A thermal electron feels the shape of an alkane molecule.Reference 31.

1000

L

0

EV

b

3

100

6

3

10

6

.59

0.01

v(107 cm/s)1.03 1.88

3 6 01

E(eV)

3.25

3

FIGURE 13. Electron momentum scattering cross sections v for the isomeric pentanemolecules, as functions of electron velocity v and energy E.... , 1010X Maxwel ian Iiand v distribuion2at 400K,F * (1.36 x 10- 7 v /T- 1)exp(-3.3 x 10- v2/T). The Maxwellian has beenmultiplied by 1010 to fit the scale. Reference 32. XMCCAIe ee.,.P.

28

10'9 1022

.JI 1 1 11 11111 1 1I

-A

- 1

x

31 I _I 1 1 1 1 1 1 1 1 1 1 _

024 -I ~

-. nc

_j10221

Li

10'

N~E

u

102

102.0 2.5 3.0 3.5

1000/T(K)

FIGURE 14. Arrhenius plots Qf thermal electron mobilities in n-pentane vapor at differentdensities. n(l019 molecule/cm): v , 2.25; A , 9.93; y , 29.8; [3, 81.0;0, 116; A, 156; o, 198 (critical). * , coexistence vapor. Reference 31.

05 I 3 05 1

B

OA"T e

0 a

0/

0/A-- ..

05 01 03 005 01

n/nc

3 0.5

C

- /

/6-

/

05

K

100

50

10

5

FIGURE 15. Arrhenius temperature coefficients of electron mobility in vapors at constantdensity, a few degrees from the vapor/liquid coexistence curve. The eighteencompounds include methane (A,O), n-butane (A,0D), cis-butene-2 (B,0O),n-hexane (B,A), dimethyl ether (CA) and xenon (C, X). Reference 33.

29

tTc

001 005 01100

50

E

ti10

5

0/

s~o

/0

O01 a 005 011 T 1 f t 11 a 11 f l" 1 1 l 1 11

d

.IA

'

1 2 3 4 5

E (.V)

02 . : O

yr J ,l"o1,' yi _ 0FIGURE 16. Optical absorption spectra of solvated electrons in n-propanol, water and

tetrahydrofuran. Data of F.-Y. Jou , this laboratory.

1.0(CH3)2C0

>1.0

C3H7OH

(D -1)(2D +1)M 4wN g, 29Ds d 3 3kT

FIGURE 17.

Kirkwood structure parameters 9K forpolar liquids.

0r -+ O-

-+ +

FIGURE 18.Schematic of a solvated electron,illustrating that the volumeoccupied by the charge distribu-tion is many-branched andirregular.

30

1.0

Pr OH

-0

- HOH

-

AAmax

0.2

0

9K <1.0C6H5CN

08-

0.6-

04

5

Friday, September 10, 1982, PM

G. R. Freeman (communicated):

It was encouraging to hear of the progress that has been made in theMonte Carlo treatment of radiolysis track structures in water, and in theapplication of those structures to the calculation of product yields.Differences in yields for different types of radiation having the sameL.E.T. have been successfully interpreted. More detailed information aboutthe solvated electron distribution will require input from an independentsource. A Monte Carlo treatment of 1 MeV electron track structures in liquidhydrocarbons could be used to develop a multipair spur model for thoseliquids. By fitting the model to measured product yields as a function ofelectron scavenger concentration, and to measured free ion yields as afunction of applied electric field strength, more accurate informationabout electron thermalization distances could be obtained. Experimentaldata are abundantly available. The model could then be extrapolated toalcohols and water through scavenging yield data alone to obtain betterinformation about the solvated electron distributions in spurs in thoseliquids.

Following the remarks this afternoon it might be worthwhile to give areminder that electron thermalization distances are strongly affected by thestructure of the fluid. In general, the dynamics of processes that occur ina system are strongly influenced by the structure of the system (Figure 1is a slide from my talk that is not in the manuscript). That statement mightseem trivial at first sight, but its full significance is not yet widelyappreciated. The significance is illustrated by the fact that the mobilitiesof thermal electrons in two isomeric pentane liquids at 295K, the spherelikeneopentane and the zigzag n-pentane, differ by 500 fold; the mobilities inthe isomeric cis- and trans-butene-2 at 278K differ by 50 fold. The mobilitiesare larger in the liquids of the more spherelike molecules. The molecularshapes govern the way in which the molecules pack together in the liquid andstrongly influence the polarizability tensor.

The radiolytic response of dilute aqueous solutions will be quite differentfrom that of highly structured biological cells. The response of concentratedaqueous solutions will be at least quantitatively different from both. Thestudy of micellar and vesicular systems seems to be a more fruitful approachto modelling the radiolytic response of biological cells.

Structuredsystems

l1

FIGURE 1

... havespecial

dynamics

31

INELASTIC CROSS SECTIONS FOR ELECTRON INTERACTIONS IN LIQUID WATER*

R. N. Hammn, R. H. Ritchie, J. E. Turner, and H. A. Wright

health and Safety Research Division

Oak Ridge National LaboratoryOak Ridge, Tennessee 37849

Our task is to develop a set of cross sections for electron inelastic

processes in water in the liquid phase suitable for use in a Monte Carlo

transport calculation. This has been described in much more detail

elsewhere1 and will only be summarized here. Very little of the experimental

data available pertain to liquid water, and it is thus necessary to use

some vapor data in arriving at consistent cross sections for the liquid. One

of the basic differences between gaseous and condensed media is theexistence of collective electronic modes in the latter. We take collectiveexcitations into account implicitly by starting with -Im(l/E) = + /,(C E+the so-called energy loss function for charged particles. For a gas,-Tm(l/E) and E2 are essentially identical. However, for the condensed

phase, the -Im(l/c) peak shifts to higher energies. This is illustratedby the model calculation shown in Fig. 1.

ORNL-DWG 74-318i

2 - "0.0 5

201~--------. . .

. . -0.2

0- I I I12 i I I I

T -

-00

-4 I I

0 10Alw (eV)

20

Fig. 1. Dielectric functions c1(---)and c , (-) and energy-loss fun ction

-Im(17E)(- - -) for a single oscillatorhaving hw1 = 8 eV, h 1 = 2 eV, and f 1 -1.0 for various densities p.

30

*Research sponsored by the Office of Health and Environmental Research,U.S. Department of Energy, under contract W-7405-eng-26 with the UnionCarbide Corporation.

32

The total differential inverse mean free path (DIMFP) for any kindof inelastic interaction may be written

dp=1 f- Im ~1 (1)dw iE q q c (q,w) '

where E is the primary electron energy, w the energy loss, and q arethe kinematic limits on momentum transfer (all quantities are in atomicunits).

Optical measurements on liquid water by Heller et al. 3 have determinedL(w,o) up to w = 26 eV. These data are combined with those on themolecule,4, 5 constrained by sum rules on the total oscillator strength.These data are shown in Fig. 2. In order to extend c into the w-qplane, we make use of the fact that for large q the electron shouldbehave as if initially free and at rest (the Bethe ridge). We fit theoptical data using a sum of derivative Drude functions in the form

2fn n3w 3

2 (w,o) * 02 [(E2 - w 2)2 + y2w 2 2 ,(2)

n n n

where the "resonance energies" En, the damping energies Yn, and the oscil-lator strengths fn are taken to be fitting parameters. The plasma energy,

= 21.5 eV for liquid water. We then let En + En + q2/2 for the partof 12 corresponding to ionization. We assume the part of E2 whichcorresponds to excitations does not disperse, but varies with q in amanner similar to the variation of the generalized oscillator strengthof the water molecule.6 Figure 3 shows a plot of Im(-l/c) versus w forseveral values of q. Figure 4 displays the quantity w2dp/dw versus wfor various values of electron energy as computed from Eq. (1). Theoryshows that for large w, the quantity du/dw should approach Zw 2/4Ew2

asymptotically, corresponding to the response of nearly free Electrons.For water this asymptotic value is given by 0.1556/Ew2 in atomic units.

0oeL-00 v.0 0Fig. 2. Optical constants of

ocac rcTFUMCntS or uowo WTER water as a function of photon- -energy w.

ft /

do (W..01

t0 =0 !o 40 5o 60 70

I G6Y TUAMLAE 6 w - WI

33

."0

DIELECTC REPNSE IV PCTY

OF LI~uJS WATER

I

I 1

Iv iii

Ia /b ' i10w IsV) -EMERY TRANSFER

Fig. 3. The energy loss function,-l

Im[ I plotted against w fore~,q)

three different values of q.

-3

lo'

10,0 100 200

S-ENERGY LOSS ("V)

Fig. 4. Energy transfer squaredtimes the DIMFP for all processesversus energy transfer w for threedifferent primary electron energies.The horizontal arrows mark theasymptotic value for each energy.

(j)The partitioning of E2 into the E2 (w,o) fractions is accomplishedby using data on the molecules together with information on the way inwhich threshold energies for various excitations and ionizations shiftfrom those for the isolated molecule to those for the condensed state.Vacuum UV photoemission experiments with amorphous ice7 and with H20multilayers adsorbed on gold surfaces at low temperatures8 indicate thatthe threshold energy for exciting an electron from the least tightlybound state to the vacuum level is 8.7 1 eV, corresponding to a bandgap of approximately 8 eV. This corresponds well with measured ESCAspectra from ice,9 which show a broad threshold at 47-8 eV. For thepresent purposes we take the lowest energy required to ionize electronsin water to be 48 eV. We take partitioning of the ionization probabilityamong the various interband transitions in the liquid to be similar tomeasured partitioning between the four molecular orbitals in the moleculeswhich merge to make up the valence bands of the liquid.

(j)Figure 5 shows the partial IMFPs, py (E), which are obtained from

Eq. (1) by replacing E2(w,q) by E 2(i)(w,q) in hj numerator of the inte-grand and then by integrating the resultant d 3 /dw over w after makingapproximate allowance for exchange and relativistic effects. In obtainingthe breakdown shown in Fig. 5, we initially made the assumption that

34

ORML DWG 7O-0M$

DWUEMTIAL *WV ME N PU/ATM OF CLCT M$ NOLXM WTD

1 i '

fragmentation is similar to that which occurs in the molecule. At presentwe assume that all the ionization channels give H20+, since in the condensedphase the vibrational energy is shared with neighboring molecules beforedissociation can occur.

Figure 6 shows the total IMFP, p(E), plotted as a function of E.On the same plot we have shown the stopping power of water, -dE/dx, asa function of primary electron energy. The open squares show values of-dE/dx recommended by the ICRU.1 0 The cross sections developed here,which obviously contain many uncertainties, are subject to continuedrevision as new data become available.

ORNL-DW 74-10)70IOr 1

PARTIAL IMFP's OF ELECTRONSIN LIQUID WATER

H20'

OH'

ALL EXCITATIONS

0'

K-SHELL

( IpI I I

103

E- ELECTRON ENERGY (iV)

LIQUID WATER

- (Mev/cm )

a ocRu(-:)Mo

S I I i

Fig. 5. Partial IMFPsversus electron energy.

b+4

ORNL DWG 78S-10337

Fig. 6. The curve markedIMFP shows the variationin the total IMFP with

primary electron energy.The other curve shows ourresults for the stoppingpower of water for electronsof energy E. The pointsshown represent valuesrecommended in ICRU Report16 for the stopping powerof water.

1 90 10 10 Ids 10

ELECTWW ENERGY (iV)

35

102 _

1.

WI

2.

10

SL

10

101 r

,0= r

10'

1. / 11 .I 1 1

REFERENCES

1. R. H. Ritchie et al., Sixth Symposium on Microdosimetry, Brussels,Belgium, May 1978, EUR6064 DE-EN-FR, pp. 345-354.

2. M. W. Williams et al., Int. J. Radiat. Phys. Chem. 7, 95 (1975).

3. J. M. Heller, Jr. et al. , J. Chem. Phys. 60, 3483 (1974)

4. K. H. Tan et al., Chem. Phys. 29, 299 (1978).

5. See, e.g., the references in G. D. 'eiss et al., Radiat. Res. 63,64 (1975).

6. See, e.g., A.E.S. Green and J. H. Miller, in "Physical Mechanismsin Radiation Biology," CONF-721001, Proceedings of a conferenceheld at Airle, Virginia, October 1972, p. 68.

7. B. Baron, D. Hoover, and F. Williams, J. Chem. Phys. 68, 1997(1978).

8. C. R. Brundle and M. W. Roberts, Surface Science 38, 234 (1973).

9. K. Siegbahn et al., "ESCA of Free Molecules," North-Holland Publishing

Co., Amsterdam (1969).

10. W. K. Sinclair et al., "Linear Energy Transfer," ICRU Report 16.

36

EXCITATION PROCESSES IN IRRADIATED AQUEOUS SOLUTIONS

Edwin J. Hart*

Experimental differentiation between chemical effects resulting from

ionization and excitation of the water molecule is difficult to assess indilute aqueous solutions since eaq and/or H and OH are the dominantintermediate free radical species of both processes. However, in manymolecules and ions the reaction products of these species with solutes aredifferent from those of excitation.

Excitation processes are revealed, however, as the concentration of

solute increases to a point where "direct action effects" may be detected.The bromate, perchlorate and formate ions are examples of species thatdissociate into products not obtained by their reaction with eaq , H or OH.In the case of Br0 3 the free radical reactions are':

Br03 + eaq~(H) + H20 + Br02 + 20H~ (1)

Br03 + OH + BrO3 + OH~. (2)

Whereas the excitation reactions are:

Br03 + hv + Br02~ + O(3P) (3)

Br03 +hv + Br02 + O. (4)

The perchlorate ion, C104j, is completely inert toward eaq~, H and OH, butdoes dissociate on irradiation at 184.9 nm and by "direct effects" in y-ray

irradiated solutions.2 One of the reactions is:

(CR04-) + hv + C03~ + O(3P) (5)

O(3P) also forms ij small yields in irradiated water. And in the pH range11.0 to 12.5, G(O( P)) doubles in value. Formic acid (HCOOH) and the formateion (HCOO~) are additional examples. Their free radical reactionsproduce H2 and C3 2 4whereas the excitation processes yield CO as oneof the products.

HCOOH + H, OHf+ H2 + CO2 + H2 0 (6)

HCOOH(HCOO) + hv + CO + H20(0H~). (7)

The results of these studies are summarized in Tables I and II. Thesedata have been useful in assessing the relative importance of ionization and

excitation processes in irradiated solutions. In Table 1, f(e) gives the

fraction of Y-ray energy directly absorbed by the solute at Conc.(M);

* Consultant, Chemistry Division, Argonne National Laboratory,

Permanent address: 2115 Hart Road, Port Angeles, WA 98362

37

G(Prod.)/f(e-) measures the effectiveness of the "direct" action effect.Table 2 gives the quantum efficiencies for the production of 0(3P) atoms orCO. Note that this yield is zero for water and the OH~. From these resultswe conclude:

(1) The effect of water subexcitation electrons is negligible if not zeroeven in concentrated aqueous solutions. A number of papers dealing withconcentrated solutions attributes part or all of the yields observedto participation by the sub-excitation electron (es ). (See literaturecited in Ref. 1). For example, the high yield of 0?35) from OH- in alkalinesolutions (22.2 of Table 1) was originally attributed to ese . Later,however, it was found that this high yield exceeded by a factor of 13 theyield of o(3P, observed in the efficient excitation process of Br03 *Therefore, O( P must form by a different mechanism at pH's above 11.Subsequent work on the formate ion confirmed this conclusion. Formatesolution irradiated in the presence and absence of I~, display identicalG(CO)'s. This result faults the ese mechanism since G(CO) should vanish, 2

in the presence of I.

(2) Energy rich secondary electrons directly excite th 9 Br03 , CZ04~ andHCOO ions to states producing the dissociation products, 0 3P) and CO. Theresults supporting this conclusion appear in Tables 1 and 2. Table 2 showsthat o(3P) forms on photolysis of the Br03 and CL04 ~. And CO forms onphotolysis of HCOO~. As noted above, these excitation products are not formedby H, eaq or OH. Details of the method of 0(3P) measurement and t'"emechanism of 0(3P) formation may be found in the references cited.

(3) O(3P) formed in alkaline solutions is produced by a non-excitation

process, very possibly by the reaction:

0 +0OH +0(3P) +0OH (8)

Reaction 8, if it took place in only 10% of the 01 and 0 encounters,would explain the high yield of 22.2 in Table 1. Work is in progress to testthe validity of this reaction.

Radiation chemists have thoroughly investigated the roles played by the

free radicals, ean , H and OH, dominant in the irradiation of dilutesolutions. Now tile time is ripe to identify the excitation products formed inconcentrated solutions. These products generally differ from those found indilute solutions. Such a study will provide sound basic research for thechemist and also furnish a more realistic picture of actual processesoccurring in biological media where "direct" effects may be dominant.

REFERENCES

1. E. J. Hart and W. G. Brown, Radiat. Phys. Chem. 15, 163 (1980).2. E. J. Hart and W. G. Brown, J. Phys. Chem. 84, 2237 (1980).3. E. J. Hart, J. Phys. Chem. 56, 594 (1952).4. E. J. Hart, J. Am. Chem. Soc. 81, 6085 (1959).5. W. G. Brown and E. J. Hart, J.Phys. Chem. 82, 2539 (1978).

38

Table 1. O(3P) and CO Yields in Y-ray Irradiated Solutions

Species Conc.(M)

H20

OH~

Br03

BrO 3

Ct04

HC00

HCOO

HCOO

55.5

0.01

0.01

2.00

1.00

0.50

1.00

1.50

Product

0(3P)

0(3P)

0(3P)

0(3P)

0(3P)

CO

CO

CO

G(Prod.)

0.006

0.004

0.017

0.252

0.236

0.052

0.078

0.109

f(e-)

1.00

0.00018

0.01075

0.183

0.0845

0.02045

0.0409

0.06135

G(Prod.)/f(e')

0.006

22.2

1.63

1.38

0.28

2.54

1.91

1.78

Table 2. Quantum Yields in Photolyzed Aqueous Solutions

(nm)

184.9

184.9

184.9

253.7

184.9

184.9

184.9

184.9

184.9

Product (Product)

0( 3 P)

0( 3 P)

0( 3 P)

0( 3 P)

0(3P)

0(3P)0( 3 P)

CO

CO

0.00

0.00

0.00

0.35

0.50

0.96

1.04

0.126

0.126

39

Species

H20

OH~

OH~

Br03

BrO3

C204

C904 ~

HCOO~

HCOO

Conc.(M)

55.5

0.001

0.010

0.100

0.010

1.00

2.00

0.010

0.100

RANGE AND LINEAR IONIZATION RATES OF LOW ENERGY ELECTRONS

G. G. Meisels and T. FujiiUniversity of Nebraska, Lincoln, NE 68588-0312

Abstract. A semiempirical method for estimating the range of low energy

electrons (100 to 600 eV) in water vapor using measurements in other gases hasbeen developed and suggests that ranges are near the upper limit of earliertheoretical estimates.

Low energy electrons (less than 1 keV) lead to most radiation chemicalchange. For heavy particles the range of these electrons determines theinitial spatial distributions of reactive intermediates or "trackstructure."1 Yet few experimental measurements of range and ionizing

properties of low energy electrons have been reported, and theoreticalcalculations are uncertain. An alternate approach, presented here, is themeasurement of the spatial distribution of ion formation for a collimatedelectron beam. Such measurements yield "linear ionization rates" di/dx. Thedistance within which 97% of the ionization occurs gives the "ionizationrange" R(i), which is formally similar to the usual range.

We have previously reported on the design and use of an ion source whosemain features are the coaxial electron entrance and ion exit apertures.2 The

electron gun is pulsed for ca. 100 nsec and the arrival time distribution(ATD) of the mass analyzed ions is determined by delayed coincidencetechniques. At very low electron energies (Eel < 20 eV) all ions are formedat the electron entrance aperture. The resulting drift time distribution(RTD), obtained from the ATD by subtraction of the flight time through themass analyzer, can be fitted by drift-diffusion equations of the appropriategeometry with the diffusion coefficient as the only adjustable parameter. Asthe electron energy increases the distribution becomes broader and is shiftedto shorter times, reflecting the deeper penetration of electrons into thesource and the formation of ions nearer the exit slit.3 To obtain di/dx, 10equally spaced RTDs, calculated for zero-dimensional ion formation points, areconvoluted with trial spatial distributions until the best fit is obtained.Integration of each curve to 97% of total ionization leads to the ionizationrange. Measured ionization ranges for the rare ga es and nitrogen arecomparable to those reported for air and plastics.

Of greater practical interest to radiation chemists are the electronranges in materials where chemistry follows ion formation. Figure 1summarizes experimentally observed arrival time distributions for CH5+ inmethane at two electron energies, while Fig. 2 shows the linear ionizationrates di/dx wh' h are derived from such data for two representative energies

using the fitti.g process described above. The curves for di/dx arecharacterized by a nearly linear decrease with penetration and a long tailextending to about twice the range one would estimate by extrapolation of thelinear segment. The ionization ranges derived from such curves for nitrogen,methane and isobutane are shown in Fig. 3. It is clear that these ranges arenearly linearly dependent on electron energies and are precisely inverselyproportional to density (Fig. 4) for these simple gases.

40

There is extensive interest in the stopping properties of water, however,the present method cannot readily be applied because RTDs show a complexdependence on temperature and pressure for this substance. This is a resultof ion clustering reactions4 which make the effective diffusion constants andmobilities for each ion dependent on the extent to which equilibrium has beenapproached.5 However, the range of electrons in water can be estimated fromdata on other gases on the basis of the following approach.

The linear ionization rate is proportional to the ionization crosssection o(E) at energy E and to the gas density n:

di/dx = o(E).n (1)

It is clear that the energy loss dE/dx is related to di/dx through W(E), theenergy required to form an ion pair. Thus

dE/dx = W(E).di/dx = W(E).a(E).n (2)

and range is given by the integral over dE/[W(E).a(E)]. If the integral canbe separated into an energy dependent component which is the same for allsubstrates, and a proportionality factor which is charateristic of the gas,then ranges can be estimated for other substrates from those in whichmeasurements have been made. The proportionality factor can be estimated bythe product of a(E) at a given energy, such as 70 eV, and W(E) at energies > 5keV where W is independent of E.

Figure 5 shows the result of this semi-empirical approach for water. 6Also shown is a comparison wkth calculated range-energy relationships by Lea,Mozumder et al., and Seitz. The ionization range appears to agree best withthe largest range calculated on the basis of various models.

This may well be a result of the experimental arrangement which must givea maximum for the ionization range. Our measurements provide not di/dx, but aquantity which is related to it by a geometry function peculiar to ourinstrumentation which must take into account that ions produced off-axis are

collected with reduced efficiency. Thus we obtain something which is betweenrange and path length, the furthest distance an undeflected electron wouldpenetrate (i.e., the straightened path length of the electron). Instrumentalmodifications which will eliminate this complication are underway. It shouldbe noted that tLh use of W(E) in applying Eq. (2) and developing Fig. 5 isonly an approximation since one should really use the differential dW(E)/dErather than W(E) measured for complete stopping of an electron of energy E.

Acknowledgements. This investigation was supported in part by the U.S.Department of Energy under contract DE-ASO2-76ER02567, for which we are deeplygrateful.

41

References

1. For example, see A. Mozumder, in Advances in Radiation Chemistry I, M.Burton and J. L. Magee, Editors; Wiley-Interscience, New York (1969).

2. A. J. Fillies and G. G. Meisels, Anal. Chem. 52, 325 (1980).

3. G. G. Meisels and A. J. Fillies, Anal. Chem. 53, 2162 (1981).

4. P. Kebarle, in Ion-Molecule Reactions, J. L. Franklin, Editor, Plenumpress, New York 1972; chapter 7.

5. G. G. Meisels, G. J. Sroka, and R. K. Mitchum, J. Amer. Chem. Soc. 96,5045 (1974).

6. D. E. Lea, Actions of Radiations on Living Cells, McMillan, New York(1949).

7. A. Mozumder and J. L. Magee, Radiation Res. 28, 203 (1966).

8. F. Seitz, Phys. Fluids 1, 2 (1958).

50 100 - 150Time, psec

.0

0.00

200

Fig. 1. Normalized arrival time dis-tributions of CH5+ in methaneat two electron energies.

2Penetration, cm

Fig. 2. Relative probabilities forionization (di/dx) normal-ized at the point of entryinto the source for CH5 + inmethane at two electronenergies.

42

H5

20 eV

320 eV

0

C

C

CH5

120 eV

320 eV

1 l

L

100 200 300 400Electron Energy,eV

500 600

1.:

1.0

0.8F

Fig. 4. Effect of temperatureand density on the ionizationrange of low energy electronsin methane.

v.v

0.6

ac0.4

0.2

Zoow

160k

120

40r-

OL0

M,

/d

p'

100 200 300 400Electron Energy, eV

500

OL0 100 200 300 400

Electron Energy,eV500

Fig. 5. Range-energy relationship inwater estimated from ionization rangesin hydrocarbon gases. --- This estimate;I Lea, Ref. 6; II Mozumder et al., Ref. 7;III Seitz, Ref. 8.

43

1.0-

2'I

Ela

o 0.6-

0 0.4

0.2F-

OL0

CH4

N2

--C4 H 1 0

CH 4

n 0.3 Torr,298K

o 0.5 Torr,298K

o 0.7 Torr,298K

o 0.5 Torr,410K

I I 1I t

i

1 1 1

s i

Fig. 3. Ionization range (dis-tance within which 97% of ioni-zation occurs) for nitrogen,methane, and isobutane at sev-eral electron energies; rangesnormalized to a pressure of onetorr at: 298 K.

-

-

/'

Optical Properties of Molecular Liquids*

Linda R. Painter and R. 0. BirkhoffDepartment of Physics

University of TennesseeKnoxville, Tennessee 37996-1200

I NTRODUCT ION

At the time studies were initiated on molecular liquids in the late60's, considerable data had been accumulated on the vacuum IV electronicproperties of solids but comparable data on liquids was scarce. Usefultheories had been formulated in the fields of solid state and molecularphysics to describe both the electronic structure of solids, which inmany cases have long range order, and gases, which are completely disor-dered. Because liquids have only short range order and no rigid struc-ture, it is difficult to specify the interaction of the molecules inorder to describe the liquid state. Over the last decade we havestudied some 20 liquids. There is still no existing liquid theory forinterpretation of experimental results.

In spite of this, there is considerable interest in the optical proper-ties of liquids, particularly in the vacuum ultraviolet region, which isthe region of maximum absorption for molecular liquids. Such knowledgehas direct biological application to understanding radiation damage toliving material, radiotherapy, radiodosimetry, problems in cell biology,to the calculation of adhesive interactions between cells and betweencells and artificial material. Several groups have done modifiedLiftshitz calculations on forces between biological cells. Most of thestudies we have done have been on pure insulating liquids of biologicalinterest. The interaction of radiation with these liquids provides aclose simulation to the interaction of radiation with biological systemsas far as primary processes are concerned1 . This paper will focus onliquid work performed at the University of Tennessee in collaborationwith H. Wright's group in HSR) of ORNL.

*Research sponsored in part by the Office of Health and EnvironmentalResearch, Office of Environment, U.S. Department of Energy, undercontract DOE-DE-ASO5-77EV03861.

44

The optical properties of liquid are specified when n and k, the real andimaginary parts, respectively, of the complex index of refraction, n, areknown as a function of frequency. We examine the absorption spectrum ofa liquid over an extended energy range. This yields the energies ofsingle-electron excitations. We interpret these as interband tran-sitions if we apply solid state theory or as molecular excitations if weconsider each molecule as only slightly perturbed by the surroundingmolecules in the liquid.

From n and k, the real and imaginary parts of the complex dielectricconstant, E, and the energy loss function, -Im(1/E), can be calculated.This function is proportional to the spectrum of energy losses sufferedby a fast charged particle which experiences no angular deflection ininteracting with the liquid. That is, optical measurements in thevacuum UV give information similar to that obtained by measuring thedistribution of energy losses experienced by a fast electron in goingthrough a thin layer of matter. So the calculated loss function can becompared with the characteristic electron-energy-loss spectrum for theliquid. Furthermore, analysis of the optical data enables the modes ofenergy deposition in the liquid to be identified for the electron-energyloss-spectrum in terms of single and collective electron excitations.'For the molecular state, n + 1, E 2k, and, for smell k, -Im(1/E) + 2k- k'/2. Thus, structure in -Im(11c) is associated with structure in kor k'. There is no structure due to collective effect in a gas.

METHODS

Several methods have been developed for studying liquids. Basically,optical properties are determined from reflectance and transmissionmeasurements. The energy region of interest to us extends from the

visible well into the vacuum UV, generally to ~25 eV. In thetransmission method a cell is formed of thick planar slabs separated byas little as 500 A of liquid, with sample thickness limited by polish onthe window.2 This method cannot be used beyond -10 eV, the limit of win-dow transparency. A second closed cell technique, also limited to theregion below -10 eV, is the semicylinder method.3 This method featuresthe possibility of employing reflection at angles around the criticalangle and of avoiding optical absorption in the vapor.

In the open-dish method light reflected from the surface of a liquid ismeasured while the liquid is in equilibrium with its vapor. For highvapor pressure liquids, it is difficult to maintain the liquid in aquiescent state under near vacuum conditions. Even for HMPT, a lowvapor pressure organic solvent, the surface was observed to be going

45

down at the rate of 3000 A/sec. Although the partial absorption of thelight by the vapor is a problem, the open-dish method is the only onecapable of being used at energies beyond -10 eV. Unfortunately, lowvapor pressure liquids amenable to open dish studies are very viscousand difficult to admit to the transmission cell by capillary action. Amore recently developed open-dish method is the double ionizationchamber method.5 ,6 In open-dish methods, absorption in the vapor is aproblem. In the photoio ization method, use is made of this absorption.The ionization in the vapor or added gas adjacent to the liquid is usedto monitor the photon beam strength before and after reflection. Theratio of ion currents is related to the reflectance. Measurements arelimited to energies above the ionization potential of the gas in thechamber. Argon, nitrogen, oxygen and benzene are used as added gas.Renzene has a low ionization potential (9.3 eV) which is comparable tothe upper energy limit of closed cell techniques.

Supplementing techniques for studying liquids through measurement ofreflectance and transmission is the photoemission method.7 All liquidswe have studied to 25 eV have been shown to have broad maxima in theenergy-loss function at about 21 eV. Although the optical data indi-cated collective oscillations should occur, it does not provide directobservation of their existence, for photons cannot directly stimulatethese oscillations. There is no maximum in k, the absorptive(imaginary) part of the index of refraction at this energy. The abso-lute photoemission yield of the liquid provides a more direct indicationof their existence. Photoemission studies have been useful in revealingdetails of electronic structure for many metals, semiconductors andinsulators. Prior to our measurements, no photoemission data existed onliquids in the energy region from 10-25 eV where collective oscillationscan be excited. The apparatus for measuring reflectance by photoioniza-tion was modified so that electrons ejected from the liquid by UV pho-tons could be observed. It uses the double ionization principle ofSamson. The choice of argon for filling gas was based on the essentialassumptions of Samson's method that in argon every photon lost to thebeam in the gas produces an argon ion. Argon has an ionizationpotential of 15.68 eV, which limits photoemission measurements toenergies above 16 eV.

The photoemission results are actually indirect evidence for existenceof collective effects since the photon must first produce a photo-electron before the latter loses energy to stimulation of collectiveoscillation. For direct evidence of collective oscillation in an orga-nic liquid, electron bombardment measurements are made. C. J. Powellhas published a series of papers on the reflectance of electrons fromliquid metals. 8 His experiments showed that reflected electrons had

46

generally lost energy to both the surface plasmon excitations describedby Ritchie9 and to volume plasmons, with the proportion allocated toeach being a strong function of the angle between the incident andreflected electrons. We have directed a beam of low energy electrons ata liquid surface and measured the energy loss distributions of theelectrons reemerging.

LIOIJIDS STUDIED

The spectra of several liquids representative of those we have studiedusing these techniques are examined along with the rationale for theirselection. The first reported measurement of the reflectance of a non-metallic liquid beyond 10 eV was on water. 10 All biological materialsabsorb energy most strongly in the vacuum IV region. Since water ispresent in all living matter, an understanding of the properties ofwater in this region is important. Analysis of these reflectance datayielded the optical and dielectric functions (Figs. 1 and 2).

CALCULATED WATERW. --KERR

-THIS STUDY /

W.04

02

- THIS STUDY16 -SOWERS

C-1A

~0.6 k l

4 0.4

10.20n

0-2 4 810-12 14.16.1.20 22 24 26PHOTON ENERGY (eV)

Fig. 1. Normal incidence reflectanceand optical functions of liquid water.

47

2 WATER

2A

1.6 1

1.2

0.8

0.4

1.0

0.

0.2

00 2 4 6 8 10 12 14 16 18 20 22 24 26PHOTON ENERGY (eV)

Fig. 2. Dielectric functions andenergy-loss function for liquid water.

Structure in e2 is seen at 1Nw 1=8.2 eV, A1=9.8 and N1=13.5 eV. Thestructure at 8.2 eV has been attributed to n+a* (observed in the vaporat 7.5 eV) and that at 9.8 eV to o+a* excitations. Structures in theenergy loss function, -Im(1/e), at 8.8 and 10.0 eV have been interpretedas due to the corresponding molecular excitations at 8.2 and 9.8 eV,respectively, while structure in -Im(1/) at 21 eV is associated withthe maximum in E2 at 13.5 eV. This displacement was cited as evidencefor the existence of collective absorption at the higher energy in thisliquid. In a paper by Williams et al. on Collective Electron Effects inMolecular Liquids' there is a discussion on conditions necessary for theexistence of collective electron effects in molecular liquids and thecollective behavior associated with a single oscillator and with acollection of oscillators is compared with the behavior of a free-electron gas. The separation in the energy between the peak in 2 at161, and the calculated peak in -Im(1/) is shown to be a measure of thedegree of collective behavior that the system exhibits. Except in thefree-electron-like limit this collective behavior should not rightly betermed a plasma resonance.

48

The liquid spectra of water are compared with those of gas" andsolid in Fig. 3. in the gas phase, where k is small, e2 + 2k and -Im(1/E) + 2k. The peak in E2 at 8.2 eV in liquid corresponds to the n +a* excitation observed in the vapor at 7.5 eV. This peak is shifted tolower energies in going from solid to liquid to gas. In -Im(1/E), thereis no structure for the vapor at 21 eV (plotted as 2k in 62)

corresponding to structure for the condensed state at this energy andassociated with the maximum in 62 at 13.5 eV.

X10-3

2. -VAPOR (right scale) 1.0-WATER

1.6 ICE 0.8

NL1 Q6

0

1.

04 rQ2

0C6 8 10 12 14 16 18 20 22 24 26PHOTON ENERGY (eV)

Fig. 3. Comparison of dielectric functionsand energy-loss functions for water insolid, liquid and vapor state.

Over a dozen organic liquids have since been studied beyond 10 eV andall liquids exhibit a broad maxima in the loss function similar to theone in water displaced from the peak in 62 or k. The loss function forseveral of these are compared in Fig. 4. Two widely used silicone pumpoils, DC-704 and DC-705, tetramethyltetraphenyltrisiloxane and tri-methylpentaphenyltrisiloxane, respectively, were studied not only toinvestigate the effects of these surface contaminants on optical com-ponents but to see if the properties could be understood in terms of theresponse of the individual molecular groups, i.e. methyl, phenyl, andtrisiloxane backbone.13 '1 Glycerol, like the silicone oils, is lowvapor pressure and more amenable to open dish studies than water. It isan essential ingredient of animal and vegetable oils. Since its pre-sence in a number of biological systems had been shown to give con-

49

1 ---- DC-704.-

.- DC-705,.-

O WATER1.0

J.4

O .2W

- C7H3--W -C

H 30

.4

.2.

PHOTON ENERGY (eV)

Fig. 4. Energy-loss functions of DC-704and DC-705, glycerol, water and thealkanes, tetradecane and heptadecane.

siderable protection against the effects of ionizing radiation, it wasfelt that knowledge of the electronic properties may be importantindetermining mechanisms responsible for this radioprotective capacity.Glycerol has only a electrons and thus shows no absorption until 1-7.5eV. Similarly, the linear alkanes, C1 4 H30 , normal tetradecane, andC17H36>, normal heptadecane are low vapor pressure at room temperature.The structure in these a-electron systems is compared to other alkanesfor systematic shifts and intensity changes in absorption peaks. InFig. 5, liquid tetradecane of this study is shown with spectra of liquidhexane, vapor octane and a solid paraffin for an indication of phaseeffects.

Recently we have determined the optical properties of four polycyclichydrocarbons, benzene, toluene, xylene, and trimethylbenzene in the 2 to10.2 eV region to characterize the spectra and investigate the effect ofsubstitution on these methylated benzenes.17 The electronic spectrum ofthe benzene molecule has been extensively studied. Inagaki has reportedthe absorption spectra of pure liquid benzene in the 4.1 to 7.4 eV

50

X16 6 C8 H1 82-

vapor1

0

3 C14 H30

C2 2. Iid

1C6H14

2 - C26H5

sold1-

06 8 10121416182022 24 26PHOTON ENERGY (eV)

Fig. 5. Comparison of imaginary part ofcomplex dielectric function for alkanes inthe solid, liquid and vapor state.

region at several temperatures. 1 Absorption bands in this region areassociated with w + w* singlet excitations. The absorption spectra ofliquid benzene were found similar to those of the solid phase at lowtemperature but differed from that of the vapor phase. This has beenattributed to a perturbation effect on the liquid molecule by neigh-boring identical molecules. The effect of methyl substitution on then + ir* molecular excitation of benzene as determined from our reflectancemeasurements is not appreciable (Fig. 6). There is evidence of a slightshift in peak value to lower energy in the k-spectra with an incre 3sirenumber of methyl groups consistent with gas-phase spectra. Thebroadening of bands with methylation reported for gas-phase data iscontrary to that observed in the ,r + lr* transition associated with thek-peak near 6.4 eV for the liquids studied. The absorption starting inthe region of 8 to 9 eV is associated with excitation of a electrons.The increase in absorption with addition of a-electron methyl functionalgroup is in agreement with the general observation that in nonconjugatedmolecules the effects of addtional functional groups are additive.

The spectra of liquid n20 and H20 have been compared for isotopiceffects.19 The principal difference observed was the contraction of the

n20 spectra due to the mass effect of the heavier isotope. There is a

51

3

- BENZENE-- - - TOLUENE.-...-.XYLENE-- TMB

2z0

2 4 6 8 10 12 14

E (eV)

Fig. 6. Optical functions of benzene,

toluene, xylene, and trimethylbenzene

as a function of photon energy.

contraction of the D20 spectra corresponding to a blue shift of r0.2 eV

at the low energy onset of absorption consistent with threshold electron

impact excitation spectra of molecular H2O and D20-

The first photoemission measurements for molecular liquids beyond 10 eV

were made on two low vapor pressure organic solvents, formamide,7, and

hexamethylphosphorictriamide (HMPT).21'2 Typical of a yield curve for

an insulating liquid is that shown in Fig. 7 for HMPT. The number of

photoelectrons per incident photon is given versus the photon energy.

The points represent experimental values and the lower curve was calcu-

lated using theoretical values for electron mean free paths and a three-

step model for the photoemission process. The upper curve was

calculated similarly but with electron mean free paths three times the

theoretical mean free paths. The yield falls from 9% at 16 eV to 5% at

25 eV. Such a falloff with increasing photon energy is expected from

theory. Plasmon formation is in competition with photoemission; with an

increase in one there must be a corresponding decrease in the other.

Conversely, electron mean free paths can he calculated from experimental

yields. For HMPT these data range from about 935 A at 16 eV to about

80 A at 24 eV. Tetraglyme shows photoemission comparable to formamide

and HMPT. However, squalane, squalene, and DC-705 show no photoemission.

52

Z00

CL

C

C

-JW~

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

Fig. 7. Yield of photoelectrons. The number ofphotoelectrons per incident photon is given as afunction of photon energy.

Electron bombardment measurements have been made on a single organicliquid. A beam of low energy electrons was directed at the surface ofDC-705 and thc energy-loss distributions of the electrons re-emergingwas measured. Fig. 8 shows the energy distribution for 50 eV electronsreflected from the oil. A sharp, elastically scattered peak at 50 eV isfollowed by an energy-loss maximum at about 37 eV with a shoulder about43 eV. These energy losses of m 7 and 13 eV are in reasonable agreementwith the optical data for DC-705 identified as due to ,r- and a-electronexcitation, respectively.

0 5 10 15 20

ELECTRON ENERGY LOSS IsV)

Hopefully, application ofthese basic physical tech-niques to studies of pureliquids and solutions willlead to some understanding ofelectronic energy levels inliquids which are excited bythe passage of ionizingradiation.

25 30

Fig. 8. Energy distribution of 50-eVelectrons reflected from DC-705 oil.

53

-S -

3xa

- -

- -

- _1 1, I I-

21 22 23ENERGY (eV)

16 17 18 19 20

PHOTOELECTRON24 25

0.4

.3[

0

-I I I

- 99gI99

9999I / I

gI I I

9 19IENERGY9 9 LOSS

1 9 19111119

11

\

-I-- 1

; I( l

i

References

1M. W. Williams, R. N. Hamm, E. T. Arakawa, L. R. Painter, and R. D.Rirkhoff, Int. J. Radiat. Phys. Chem. 7, 95 (1975).

2B. L. Sowers, M. W. Williams, R. N. Hamm and E. T. Arakawa, J. Chem.Phys. 57, 167 (1972).

3L. Robinson Painter, R. D. Birkhoff and E. T. Arakawa, J. Chem. Phys.51, 243 (1969).

4L. L. Robinson, L. C. Emerson, J. G. Carter, and R. D. Birkhoff, J.Chem. Phys. 46, 4548 (1967).

5R. D. Birkhoff, L. R. Painter, and J. M. Heller, Jr., Appl. Opt. 16,2576 (1977).

6R. D. Rirkhoff, L. R. Painter, and J. M. Heller, Jr., J. Chem. Phys.69, 4185 (1978).

7R. 1). Birkhoff, J. M. Heller, Jr., L. R. Painter, J. C. Ashley, and H.H. Hubbell, Jr., J. Chem. Phys. 76, 5208 (1982).

8C. J. Powell, Phys. Rev. Lett 15, (22) 852 (1965); Adv. Phys. 16, 1203(1967); Health Phys. 13, 1265 (1967); Phys. Rev. 175 (3), 972 (1968).

9R. H. Ritchie, Phys. Rev. 106, 874 (1957).

10J. M. Heller, Jr., R. N. Hamm, R. D. Birkhoff, and L. R. Painter, J.Chem. Phys. 60, 3483 (1974).

11See references in G. D. Kerr, R. N. Hamm, M. W. Williams, R. D.Birkhoff, and L. R. Painter, Phys. Rev. 5, 2523 (1972).

12j0 Daniels, Opt. Commun. 3, 240 (1971).

138. L. Sowers, M. W. Williams, R. N. Hamm, and E. T. Arakawa, J. Appl.Phys. 42, 4258 (1971).

14G. D. Kerr, M. W. Williams, R. D. Birkhoff, and L. R. Painter, J.Apple. Phys. 42, 4258 (1971).

15R. D. Birkhoff, L. R. Painter, and J. M. Heller, Jr., J. Chem. Phys.69, 4185 (1978).

54

16j. M. Heller, Jr., R. D. Birkhoff, and L. R. Painter, J. Chem. Phys.62, 4121 (1975).

17j. S. Attrey, R. D. Birkhoff, and L. R. Painter, accepted for publica-tion in J. Apple. Phys.

18T. Inagaki, J. Chem. Phys. 57, 2526 (1972).

19J. M. Heller, Jr., R. D. Birkhoff, and L. R. Painter, J. Chem. Phys.67, 1858 (1977).

20J. M. Heller, Jr., H. H. Hubbell, Jr., L. R. Painter, and R. 0.Birkhoff, J. Chem. Phys. 71, 4641 (1979).

21R. 0. Birkhoff, J. M. Heller, Jr., H. H. Hubbell, Jr., and L. R.Painter, 1. Chem. Phys. 74, 200 (1981).

22R. 0. Birkhoff, H. H. Hubbell, Jr., J. C. Ashley, and L. R. Painter,accepted for publication in J. Chem. Phys.

55

INTERACTION OF 0-20 EV ELECTRONS WITH THINSOLID FILMS AT CRYOGENIC TEMPERATURES

L. Sanche, MRC Group on Radiation Sciences

C.H.U., University of SherbrookeSherbrooke, Qu6., Canada

Part of our program in the Radiation Sciences at the University of Sher-brooke involves the study of the interaction of low-energy electrons (0-20 eV)with condensed matter; more particularly, organic and molecular solids, andsimple solids of biological interest (e.g., H20, 02). The main objective isto obtain a better understanding of how, in irradiated systems, the energy istransfered from the high-energy primary particles to ionic, electronic and vi-brational states through the action of transient intermediate species, themost important of which is the electron. We are particularly interested to

determine the mechanisms of slow-electron scattering in condensed phases andthe absolute values of the elastic and inelastic mean free paths (MFP).

To date, interesting results have been obtained from ETS (electron trans-mission spectroscopy) and HREELS (high-resolution electron-energy-loss spec-troscopy). These experiments can be briefly described as follows. A well-collimated monochromatic electron beam (.01 to .04 eV FWHM) impinges on a film

(10-30008) grown from a gas or a vapor on a metallic substrate attached to the

cold end of a variable temperature cryostat (17-300K). In ETS, the total cur-rent which traverses the film is measured on the metal substrate as a functionof electron energy (1). The structures in the current-vs-voltage curves areinterpreted in terms of electron interactions occurring in the film (1-8).Furthermore, measurements of the absolute value of the transmitted current asa function of thickness can be used to determine elastic and certain inelasticMFP (8). In HREELS, electrons emerging from the film are analysed in energy

and angle with respective resolutions of 5 meV and ~20 FWHM. Energy-loss mea-surements can be performed either in the constant-final-energy or constant-ini-tial-energy mode. Measurements of excitation functions are also possible. Ab-

solute values of the cross sections cannot be determine with this system butrelative amplitudes of energy-loss processes can be calibrated on the transmis-sion data. The substances studied to date include aliphatic and alicyclic hydro-carbon films (1-5), diatomic molecular solids (9-11) (e.g., N2, 02, NO, CO),triatomic solids (H20, C02), rare gas solids (7,8) and DNA basis (6).

Specific advances which resulted frai experiments with these systems maybe summarized as follows:

1) Measurement of vibrational (10,11), vibronic (9) and electronicenergy losses (5,8,9) in solid films;

2) Derivation of a theoretical model to extract from ETS the elasticand inelastic MFP (9);

3) Observation of structural and thermal disorder effects in thin films(1,4,9);

56

4) Observation of shapes resonances in diatomic molecular solids (10,11);5) Observation of sharp features in ETS which can be explained by the

existence of electron-exciton complexes (1-5).

1. L. Sanche, J. Chem. Phys. 71, 4860 (1979).

2. L. Sanche, Chem. Phys. Letters 65, 61 (1979).

3. L. Sanche, J. Phys. C 13, L677 (1980).

4. G. Bader, L. Caron, and L. Sanche, Sol. State Comm. 38, 849 (1981).

5. L. Sanche, G. Bader, and L. Caron, J. Chem. Phys. 76, 4016 (1982).

6. L. Sanche and G. Leclerc, "Transmission of 0-20 eV electrons throughthe DNA basis" (in preparation).

7. L. Sanche, G. Perluzzo, G. Bader, and L. Caron, J. Chem. Phys. (to appearin September 1982 issue).

8. G. Bader, G. Perluzzo, L. Caron, and L. Sanche, Phys. Rev. (in press).

9. L. Sanche and M. Michaud, Chem. Phys. Letters 80, 184 (1981).

10. L. Sanche and M. Michaud, Chem. Phys. Letters 84, 497 (1981).

11. L. Sanche and M. Michaud, Phys. Rev. Letters 47, 1008 (1981).

57

SOME ANALYSIS TECHNIQUES AND RESULTS OF THE MONTE CARLO SIMULATION

OF PROTON AND ELECTRON TRACKS

D. J. BrennerLos Alamos National LaboratoryLos Alamos, New Mexico 87545

and

M. ZaiderRadiological Research Laboratory

Columbia UniversityNew York, New York 10032

1. Introduction

As described in a companion paper (Zaider and Brenner, 1982), in

response to the need for detailed data on energy deposition in micron and

sub-micron sites, the code PROTON has been developed to transport protons

and electrons on an event-by-event basis in water vapor. The electrons are

currently transported down to sub-electron-volt energies, making the

results a suitable starting point for radiation chemistry studies.

This report describes the details of some techniques we use to analyze

the large amount of data produced by the code. In particular, we shall be

concerned here with lineal energy distributions (lineal energy, y, is the

energy deposited in a specified volume by a passing particle and its

secondaries, divided by the mean path length through that volume). Such

distributions are used as input to theories of radiation action. In the

present context, however, the fact that lineal energy spectra can be

measured using microdosimetric techniques offers a useful opportunity for

comparing Monte-Carlo-based predictions with experimental data.

2. Techniques For Calculating Lineal Energy Distributions

The calculation of lineal energy distributions proceeds as

follows: consider a track, i.e., the positions and energies of all

non-elastic interactions (hereafter referred to as events), we need to

"throw" repeatedly spheres (or other volumes) of the size of interest

58

randomly onto the track and after each throw tally the total amount of

energy or, to compare with experiment, the number of ionizations inside the

volume. Crucial to this is Lea's concept of associated volume (A.V.) (Lea,

1940): if we consider spheres of the size of interest centered on every

event in the track, the union of these spheres is the A.V. of the track.

The A.V. is thus the geometric locus of the centers of all the spheres,

which have at least one event inside, and if we throw a sphere outside the

associated volume, it has zero probability of having an event inside it.

For efficient computation, particularly for small volumes, it is necessary

to take advantage of this idea rather than the alternate "box" technique in

which spheres are thrown into a cuboid containing all the points in the

track as, in this latter case, many throws will yield zero events, a

situation of no interest. Computationally, the A.V. is simulated by

randomly choosing a point in the track, considering a sphere of the

diameter of interest centered at this point, then choosing a point randomly

within this sphere to be the center of the sphere in which events are to be

tallied. This procedure gives a biased estimate of the distribution and it

is thus necessary to assign a statistical weight to each value so obtained

inversely proportional to the number of events in that sphere. This is

because each sphere has a selection probability proportional to this

number.

Thus in terms of successful throws, the A.V. method will always be

more efficient than the box method, by a factor "a"(>1), which is the ratio

of the box volume to the A.V. However,.in a stochastic computational

problem of this nature the ultimate aim is to achieve the best possible

"figure of merit" (FOM = 1/a2t, where a2 is the variance of the mean of the

calculated quantity and t is the computer time). To clarify this idea, we

consider, as an example, a calculation of p, the mean number of events in a

sphere. We let x be a random variable denoting the number of ionizations

in a sphere and f(x) its probability density function with variance a2.

In the "box" method, following analysis of n spheres yielding

x ,.....xn, we obtain an estimator of p, which is simply

nx = - xi

n i11

59

with

E(x) = y , V(i) = c2/n (1)

where E and V respectively denote expectation value and variance.

The A.V. method results in a biased or weighted density function of

x-values:

fw(x) =x(

and here, after analyzing n spheres, we obtain a different estimator of u:

n

i=1

1 n 1Xi (=V -)xi i-1 xi

n 1= n/ E (-)

i=1 xi

and one can show, for this estimator

E(1) =i,%, w

V( ) =1 [!E(!) -L.

w n p x p2

Tc first order, the variance is then

1-4 1 1)V(xw) ~ -E(_)f--1.

n p x u2

(2)

Thus, Eqs. (1) and (2) can, in principle, be used to determine the

relative number of spheres, N, to be thrown, using each method, to obtain

equal accuracy in the estimation of p. While no general solution exists to

this problem, a few examples were worked out and typically the A.V. method

required a factor of N Q 3 more throws for equal variances of the mean.

Hence, our relative FOM for the two techniques may be estimated by a/N,

60

where a is the ratio of the volumes, defined above. Typically for small,

nanometer, volumes, a )N and the A.V. calculation is much preferred, but

for large site sizes this may no longer be the case.

3. Results For Protons

Fig. 1 illustrates the results of our calculations for 1.5-MeV protons

for three different site sizes. The representation of the data is such

that the ratio of the area between any two values of y to the total area is

the fraction of the dose deposited in that range of y. In each case the

dashed histrogram represents the lineal energy distribution due to ionizing

events only, while the full histograms are the results of also including

all excitation events. (Experimentally, only ionization events can be

detected; however, the role of excitation events in biological systems is

currently not known.) From the results it is clear that at the very small

site sizes that are believed to be of importance in radiobiology (< 10 nm,

e.g., Brenner and Zaider, 1982 and Goodhead and Brenner, 1982) there is a

significant difference depending on whether or not excitations are

considered. This difference is even more marked for x rays (not shown

here).

4. Techniques For Combining Lineal- Energy.Spectra

Photons and neutrons deposit their energy through a spectrum of

secondary charged particles. Given calculated lineal energy spectra for

any possible given secondary, we demonstrate how to combine them to yield

the lineal energy spectrum of the primary radiation. The problem is also

frequently complicated by the incident radiation having a spectrum of

energies.

We consider photons (though the analysis also applies to neutrons)

with energy fluence N (E ), then the number of events in the detector will

be

EYN(E )u(EI)/p(3f FEY) dE (3)

where the numerator is the total dose deposited (y(E )/p being the mass

61

energy absorption coefficient) and the denominator, the normalized first

moment of the lineal energy distribution for photons of energy E [i.e.,

f (y,EY)], is the average dose deposited per event. Thus the lineal energy

distribution will be

f(y) = fEYN(E)(Ey)/P f( E d

yF(Ey) Y

Using similar reasoning it can be shown that

(4)

fN(

f(y,E ) =-

where N (Ee,E )

energies, Ee, for

energy spectrum

quantity that can

be shown that

Ee

(EE)F e f(yEe)dEe

E

fN(EE) e dEeJe'y YF(Ee)

(5)

is the normalized distribution of secondary electron

a given value of E1, and f(y,E ) is the normalized lineal

for a monoenergetic beam of electrons, energy Ee - a

be calculated with the track structure code. Thus it can

Eef N(EeE )- -- (yEe)dEe

f(y) fEN(EY)(E)/p( YF edE .

fN(EeE )EedEe

(6)

As an example some calculated spectra for 250 kVp x rays are shown in

Fig. 2, together with some results for monoenergetic low energy x rays,

for a variety of site sizes.

62

5. References

Brenner, D. J. and Zaider, M. The soft x-ray experiment revisited - atheoretical approach. In Proc. Eighth Symposium on Microdosimetry,Julich, 1982 (In Press).

Goodhead, D. T. and Brenner, D. J. The mechanism of radiation actionand the physical nature of biological lesions. In Proc. Eighth Symposiumon Microdosimetry, Julich, 1982 (In Press).

Lea, D. E. Size of viruses and genes by radiation methods.137 (1940).

Zaider, M. and Brenner, D. J. Computational details of thesimulation of proton and electron tracks. This symposium.

10' c1(Pdfy (kev/ym)

I -

0.9 -

0.6-

0.4-

02-

04I

~'0

Nature 146,

Monte-Carlo

icy (key/Mm)

id

d=1000nm

-- - -

idy (kev/sm)

Fig. 1. Calculated lineal energy distributions for 1.5 MeVdifferent site sizes.

protons for

63

0 .

0.7-

0.6 -

0.5 -

0.4-

0.3 -

02-

0.1-

d=100nmd=10nm...

1.4 r

12-

1-

0.8-

0.6-

0.4-

02-

T1 I V i '1f

=1n0V

- 1 ENERGY DEPOSITION IN SPHERESBY X-RAYS

1in

-I|

- L -

- I

I-Its

* i Cabo

-

1C

3nm nm101

i 250 0 .50 kkV

I3 I

Fig 2Eerydep pongsion ditriutionsfornerbn axgrayns (80eV),z

is plotted.

64

I

1F I

Spatial Aspects of Radiological Physics and Chemistry

Alex E. S. Green and Daniel E. RioDepartments of Nuclear Engineering Sciences and Physics

University of FloridaGainesville, Florida 32611

ABSTRACT

The spatial distributions of the early time yields of electrons, ions,excited atoms and molecules which follow deposition of low energy electrons inH20 vapor are first calculated using the spatial yield spectra methodology.These are used as source functions for the calculation of the effects ofdiffusion and kinetics upon the final distributions of neutral products.

I. Introduction and Background

Our work on electron energy deposition in H 0 dates back to a paper',entitled "Microdosimetry of Low Energy Electrons , presented at theInternational Atomic Energy Agency meeting on Biophysical Aspects of RadiationQuality, held in Lucas Heights, Australia in 1971. In this work, we assembledfrom the literature a detailed H20 energy level - process diagram shown inFigure 1. Then using certain semi-empirical modifications of the Zornapproximation developed in pursuit of auroral and airglow studies wegenerated a rather comprehensive set of electron impact cross-sections for theexcitations, ionizations, dissociations, and the other process illustrated inFigure 1.

We utilized reasonable extrapolations of high energy c oss sections intothe low energy region characteristic of secondary electrons ,5 for all typesof primary particles. These individual cross sections together with amodified form of continuous slowing-down approximation (MCSDA) enabled us toapportion the energy loss in a medium to all of the individual processes. Incontrast, sut rules for all cross sections together are used in Bethe's theoryof stopping. The final output of the Lucas Heights paper is given in Figure2. The ordinates give the efficiencies or the percentage of the total energyloss going into these individual processes for electrons starting at variousprimary energies. For example, 10% of a 1000eV electron's energy goes into

the production of OH+, 27% into the production H20+, etc.

My group haq also developed a simple model for electron energy depositionin liquid water. Figure 3 illustrates some of the results of this work.After one allows for the decay of the plasmon the results are not verydifferent from those for water vapor. We have also calculated efficienciesfor proton deposition in H20 vapor using a MCSDA and the results appear quitereasonable.

65

0+2H

H" + O~+H

20--

+H2 __ _ H'+ HH +OH

12

15 -- C

H(np)+ OH( 2HI)4-----------

4 - - - - - - - -

3------------

O' 'P) +H 2 ' 9g

A B D O(3S 0) + H 2( 9 -)-2 - - -- - - --

- n sa, npa npb

'B , 'A

nd

-------- I

4-

- 3-

4_-4-

3 _ 3

4 -

3-

H( 2 S)+OH(B 2 r.)r,

db

H( 2 S)+OH( 2 Z-) rb

BA'

B82

__ _A

2

3B,

3A

("P) +H 2 (ZEu) r5

H( 2 S)+OH(A 2.) r4

O('D)+H 2(X 'Z g r3

H(2S)+OH(XH) r2

O(3P) + H2(X'Z g)r,

VIBRATIONALSTATESXA

Fig. 1. Energy level and process diagram for H20.

66

25

'B

LUJ

10

5

0'

H +O+H

- 5 n

0+H+H -- _2B

.. _282

H (S) + OH(X ) _._2A- -

- - - - - - ,

3

0~ 2P) + H2(X '+g)- - ni

OH~('Z') + H( 2S)

H2 O

I---'IA2

100

LOW ENERGY .

'Adb. -OH

c D RYD

HI/DEO

-na b RYD

0"

/O DE

H2 .

E'0vcc

E revi)

w

C)

LLu

'

v

I 1 1 1 l

-I - - - -

it

101

PLASMON

OH ;t(3064- RYD (C +D)

HO (BALM:ER a)

0+

~ RYD (A+ B)

Hv( (BALMER 0)

H 4o1(8447)

I / I 1 1 1 1 111 I

E (eV)

Fig. 2. Efficiencies for electron energy

deposition in H20.

Fig. 3. Efficiencies for electron energydeposition in liquid water. Plasmonyield is predecay while all others arepost plasmon decay.

4-)-I

L-)ZU-U-O

v%

.3

iO

i i I I i I I I I I I I I I 1--

I- l

1

A)

L 410-1102

At the University of Florida we have also given attention to the discretenature of the 8low-down process using a variety of calculationaltechniques.9,' We finally found it most fruitful to systematize the discreteelectron yn gy loss in various substances in terms of their yieldspectra.1, These quantities U(E ,E) te physically uivalent to thedegradation spectra of Spencer and Fano, and Douthat, but have somewhatsimpler systematics with respect to the incident electron energy E0 and thetarget atomic number.

II. Spatial Aspects of Electron Deposition

The Monte Carlo technique15, 1 6 which is one of the techniques utilized inour discrete energy loss studies, appears to be essential to thegeneralization of yield spectra to incorporate spatial information. Beforesuch calculations can be carried out, it is essential to systematize thedifferential elastic scattering cross sections r1 ow energy electronsstriking the target medium. In our first works ' we used simple analyticforms to characterize the systematics of such cross sections. Thesecalculations led to a numerical four dimensional spatial yield functionU(r,z,E0 ,E) which is the spatial generalization of our two dimensional yieldspectra U(E ,E). This spatial yield spectra has the general featur of aplume and can, to a reasonable degree, be represented analytically. Thefour dimensional function can be used to generate the spatial yield of any ofthe products or spectral emissions. Figur1 94 gives examples of two spatialyields in N2 obtained by such calculation.

(a)

NK0.3 KeV

7 Ks

7.

5.0 KeV

-%

N \ N

NN

N\

/ //% //

/.

(b)

\

I,,/ ,/'/

,/ /

(I

//

/

/

//

Fig. 4. Isocontours for Ek = 0.3 and 5 KeV2fo (a) vibrational excitationof N2 ; (b) ionization leading to X 2gstate of the N2+ ion.

g

68

N

V1AL

1

N

III. Kinetics and Diffusion Following Initial Events

In our current work on kinetics and diffusion following electron energydeposition in H20 we were initially updating our 1971 H20 cross-section setbut we are now using the recently updated set of Zaider, Brenner and WilsonO.We are now generating the spatial yield spectra for electrons in H20 usingMonte Carlo. At very low energies we incorporate the condensed historytechniques pioneer by Berger et al.2 1 and developed for our purpose byKutcher and Green. From the spatial yield spectra, we generate the spatialyields of all of the initial products and spectral emissions illustrated inFigures 1 and 2. In the case of water vapor we have no experiments to checkthese results on initial yields. However, we have checked our results foremission in the case of N2 against measurements of fluorescent yieldsby Gran , Cohn and Caledonia , and Barrett and Hayes . The agreement givesus some confidence as to the correctness of our overall procedures.

Having obtained an initial set of yields for the important processes, weare treating the diffusion/kinetics problem using continuum procedures. Inthis, the poor man's approach, the early time spatial yield distributions areinserted into a partial differ gtial equation formulation somewhat similar tothat of Kupperman and Belford. We are using, however, a steady stateapproach so that we seek the solutions of the set of partial differentialequations

2 6CiD V2C + Y + I K C C = - = 0

where Di is the diffusion constant of the ith species. Ci is the thconcentration of the i species, Yi is the direct product of the i speciesproduced by incoming electrons and Ki. is the bimolecular reaction rate. Weare treating this multispecies kineti /diffusion problem in cylindricalsymmetry and apply suitable boundary conditions. The reactions that we areconsidering involve early time products e, H20+, H30+, H and othersillustrated in Figu s2 and 2. In addition, follow 8g earlier work onradiation chemistry and studies of H2-0 flames we include the neutralspecies H2, OH, 02, HO2, 0. Based upon preliminary calculations we expectfinal steady state yields to be something like that illustrated schematicallyfor H20+ in Figure 5. Because of the mathematical complexity of this two-dimensional diffusion kinetics problem, my group is pursuing two mathematicalpaths of solutions. Daniel Rio has built up a diffusion and kinetic codestarting with an International Mathematical Scientific Library (IMSL) two-dimensional partial different equation solver.

As a second, back-up approach, Paul Schippnic is attempting to adapt ahighly sophisticated hydrodynamic-combustion code to this problem. As anintermediate seep this combusion code will be applied to the prediction of thetemperature distribution and emission distribution of hydrogen-air diffusionflames. Here my group has experimental spatial and spectral data which, if itcan be explained by the model and code we are adapting would provide aconvincing basis for our further adaptation of the calculation to radiologicalproblems.

69

1.0

.5Z0

zwUZ00

-J

0

.2 .4 .6 .8 1.0

SCALED DISTANCE

Fig. 5. The solid curves are early time steady

state yields of H20+ relative toY(0,) = 3 x 10-8 3 . The dashed

cm -scurves are steady state concentrations of

H2 0+ for an illustrative electronbeam after allowing for diffusion andkinetics relative to C(0,0) = 5 x 10~moles

cm3

Fig. 6. Illustrative example of concentration

profiles of e-, H2 0+, H, H3 0+ aty = 0(z=0) for an illustrative electronbeam after allowing for diffusion andkinetics. The x coordinate is saled by

tan~1(r/r0 A) where r = 088 x 10-6 cmand A = 3 and for Ce?0,O) = C 1 x 10-22.

10-3N

.1

.3

H 2 0\0 \ H NHN

zi 0.5 .37

' I.1i1

. 5 /

/

/ 1.0

\'2\

\\

\ 11

//

0

-. 5

-1.0

,

10-,01

10-1 ,I

~

I

It is also our hope to adapt this poor man's approach to the liquidphase. Here we would use the Kutcher-Green method of relating liquid phasecross-sections to gas phase cross-sections. Of course, if the Oak Ridgeeffort is completed before then, we will undoubtedly be guided by theirresults in our future work.

3jo adapt our work to positive ions, we are following the Battelle,34 LRL-ORNL and the Los Alamos-Columbia3 6 efforts. The path which we are takingwill involve independent computing machinery and it would be encouraging if weall come up with similar answers.

This work was supported in part by the U.S. Department of Energy underContract DE-AS-5-76 EV03798.

References

la. A. E. S. Green, J. J. Olivero, and R. W. Stagat, Biophysical Aspects ofRadiation Quality, pp. 79-97. International Atomic Energy Agency,Vienna, 1971.

1b. J. J. Olivero, R. W. Stagat, and A. E. S. Green, J. Geophys. Res. 77,4797-4811 (1972).

2. A. E. S. Green and S. K. Dutta, J. Geophys. Res. 72, 3933-3941 (1967).3. A. E. S. Green and C. A. Barth, J. Geophys. Res. 70, 1083-1092 (1965);

72, 3975-3986 (1967).4. A. E. S. Green and J. H. Miller, Physical Mechanism and Radiation Biology

(R. D. Cooper and R. W. WOods, Eds.), 68-114. U.S. Atomic EnergyCommission, 1974 Conf. 731001. (Available from National TechnicalInformation Services, Springfield, VA 22151.).

5. A. E. S. Green, Radiat. Res. 64, 119-140 (1975).6. H. Bethe, Ann. Phys. 5, 325-400 (1930).7. G. J. Kutcher and A. E. S. Green, Radiat. Res. 67, 3 (1976).

8. J. H. Miller and A. E. S. Green, Radiat. Res. 54, 343-363 (1973).9. L. R. Peterson, Phys. Rev. 187, 1, 105 (1969).10. R. H. Garvey and A. E. S. Green, Phys. Rev. A, 14, 3, 946 (1976).11. A. E. S. Green, R. H. Garvey and C. H. Jackman,~Int. J. Quantum Chem.

Symp. 11, 97-103 (1977).12. A. E. S. Green, C. H. Jackman and R. H. Garvey, J. Geophys. Res. 82,

5104-5111 (1977).13. L. V. Spencer and U. Fano, Phys. Rev. 93, 1172-1187 (1954).14. D. A. Douthat, Rad. Res, 61, 1 (1975);~64, 141 (1975).15. M. J. Berger, Methods in Computational Physics (Academic, New York,

1963), Vol. I, p. 135.16. R. T. Brinkman and S. Trajmar, Ann. Geophys. 26, 201 (1970).17. C. H. Jackman and A. E. S. Green, J. Geophys.~Res. 84, 2715-2724 (1979).18. R. P. Singhal, C. H. Jackman and A. E. S. Green, J.~Geophys. Res. 85,

1246-1253 (1980).19. A. E. S. Green, R. P. Singhal, Geophys. Res. Lett. 6, 625-628 (1979).20. M. Zaider, D. J. Brenner and W. E. Wilson, "The Application of Track

Calculations to Radiobiology I. Monte Carlo Simulation of Proton Tracks",Los Alamos National Lab Report (1982).

21. M. J. Berger, S. M. Seltzer, and K. Maeda, J. Atmos. Terr. Phys. 32,1015-1045 (1970).

22. G. J. Kutcher and A. E. S. Green, J. Appl. Phys. 47, 2175-2183 (1976).

71

23. A. E. Grun, Z. Naturforsch 12a, 89-95 (1957).24. A. Cohn and G. Caledonia, J. Apple. Phys. 41, 3767-3775 (1970).25. J. L. Barrett and P. B. Hays, J. Chem. Phys. 64, 743-750 (1976).26. A. Kupperman and G. G. Belford, J. Chem. Phys. 36, 1412-1426 (1962).27. L. Monchick, J. L. Magee and A. H. Samuel, J. Chem. Phys. 26, 935 (1957).28. J. L. Magee and A. Chattergee, J. Phys. Chem. 82, 2219 91978); 84, 3529

(1980).29. A. Chattergee and John Magee, J. Phys. Chem. 84, 3737 (1980).30. J. A. Miller and R. J. Kee, J. Phys. Chem. 81, 2534 (1977).31. TWODEPEP, IMSL, Houston, Texas (1981).32. NASA Contractor Report 3075: A Computational Model for the Prediction of

Jet Entrainment in the Vicinity of Nozzle Boattails (The BOAT Code),S. M. Dash and H.S. Pergament (1978).

33. R. N. Hamn, H. A. Wright, J. E. Turner and R. H. Ritchie, Sixth Symposiumon Microdosimetry, Brussels, Belgium, ed. by J. Booz and H. G. Ebert,Vol. I, Harwood Academic Publishers Ltd., Commission of the EuropeanCommunities (1978).

34. J. H. Miller, et al., this conference.35. H. A. Wright, et al., this conference.36. D. Brenner, et al., this conference.

72

MODELING EARLY EVENTS IN THE RADIATIONCHEMISTRY OF DILUTE AQUEOUS SOLUTIONS*

J. H. Miller and W. E. Wilson

Pacific Northwest LaboratoryRichland, Washington 99352

ABSTRACT

The "beads on a string" model proposed by Ganguly andMagee (1) was generalized to allow Monte Carlo techniquesto be used in calculating the influence of track structureon the yield of free radicals at early times following en-ergy deposition by ionizing radiation in aqueous solutions.The results of the Monte Carlo calculations can be inter-preted in terms of an effective linear energy transfer (LET)that is significantly less than the stopping power of theradiation when the track structure has a diffuse radialdistribution due to energy transport by delta-rays. Byincorporating this effective LET for deuterons and alphaparticles into a one radical approximation, the model canaccount for the effect of track structure on the yield ofhydrated electrons measured by Sauer and co-workers (2).

INTRODUCTION

We have developed a stochastic model of trackstructure effects in radiation chemistry that allows usto use detailed information on the pattern of energydeposition events made available by Monte Carlo calcula-tions (3). Application of this model to liquid scintil-lators showed that fluorescence from dilute solutions ofbenzene in cyclohexane excited by alpha particles would bequenched significantly less than fluorescence excited byprotons of the same stopping power (4,5). In this paperwe describe how the model can be used to predict theeffect of track structure on the yield of radicals inaqueous solutions.

Figure 1 illustrates a segment of the track of ahigh energy charged particle at various times after en-ergy has been transferred to the medium (6). Our modelof the track at 10-16 sec. is a collection of ions andexcited water molecules represented by the dots in thepanel labeled A. The spatial distribution of these excita-tions and ionizations is calculated from cross sections

*Work supported by United States Department of EnergyContract DE-AC06-76RL0-1830.

73

Figure 1. Schematic illustration taken from Ref. (6) ofa particle track at various times after energy

transfer to the medium.

that describe the interaction of radiation with isolatedwater molecules in gas phase (i.e. no collective modes ofexcitation are included).

Panel B represents our model of the track at 10-11

sec, the boundary condition for the chemical stage ofradiation action. At this time the rapid solvationphenomena that precede material diffusion have modifiedthe initial products of energy deposition to yield hydratedelectrons and proton, OH radicals and hydrogen atom as wellas other minor constituents. We do not attempt to modelthe development of the track between 1-16 and 10-11 seconds.Rather we assume that the yield at 10-11 sec. of reactivespecies that develop from an initial energy deposition eventis proportional to the amount of energy transferred to themedium at that point. The spatial distribution of reactantsrelative to the initial inelastic collision is assumed to bea Gaussian with a width that will be referred to as the"initial cluster radius". We also assume that the

74

relaxation phenomena that occur between 10-16 and 10seconds are independent of radiation quality so that theprimary yields and initial cluster radii obtained fromanalysis of picosecond pulsed radiolysis with electronscan also be used for high LET radiation.

Panel C represents our model of the track at sometime during the diffusive relaxation of the medium. Thegoal of our research has been to investigate this phaseof the track evolution with a minimum number of assumptionsconcerning the spatial distribution of reactants at 10-11seconds. For example we do not introduce quantities likeblobs and short tracks that are designed to approximatecor.nonly occurring groups of inelastic collisions (7).

The first section of this paper develops the modelfor the simple case of a single radical species undergoingbimolecular recombination while reacting with a homogeneousscavenger. Generalization to the multi-radical system isobvious from the structure of our results. The next sectiondescribes the track structure calculations and compares re-sults for protons and alpha particles of equal stoppingpower. The final section compares the predictions of themodel with measurements of the yield of hydrated electronsin pulsed radiolysis with deuterons and alpha particles (2).

MODEL DEVELOPMENT

The concentration C(r, t) at position r and time t ofradicals undergoing simultaneous diffusion and reaction isassumed to satisfy the equation

rt-=DV2C - kRRC2 - kRSCSC (1)

where D is the diffusion coefficient, k is the radicalrecombination rate constant and kRS is He rate constantfor reaction with a homogeneous scavenger present in con-centration C5 . Integration of Eq. (1) over space coordi-nates and division by the total energy E absorbed in theliquid gives the result

= -kRR 1 fC2dr - k C g (2)E

75

where

g (t) = E C (r,t) dr (3)

is the mean radical yield per unit of energy absorbed.To evaluate the recombination term in Eq. (2) we assumethat the concentration of radicals is a sum of Gaussiandistribution functions

N ige (r-r)2 (4)C(r,t) = exp -

i=1 (/2n a) 3 2a 2

where c. is the energy transferred to the medium in theinelastic collision at position i and a2 is the varianceof the Gaussian that increases with time due to diffusion.In the prescribed diffusion approximation a2 is assumedto increase linearly with time; however, this approxima-tion can be improved by the definition (8)

l r2C(Ert)dr

a2 (t) = 1Jt(5)JC(rit)dr

Ganguly and Magee proposed an expression similar toEq. (4) for the concentration of radicals in the track ofa heavy ion.

N v. (p2+(z-z.)2)CGp,z,t) = 1 exp - 2 1 j (6)

G i=l (v2r' a)3 L22

This approximation is a sum of Gaussian distributionfunctions centered on the trajectory of the primary ion,that is assumed to be a straight line. Hence the Gangulyand Magee model has cylindrical symmetry. We relax thiscylindrical symmetry and allow the distribution functions

76

to be centered at the points r. where significant energytransfer to the medium has occurred resulting in elec-tronic excitation or ionization. This allows us to ac-count for the transport of energy away from the trajectoryof the primary ion by high energy secondary electrons(i.e., delta-rays).

When Eq. (4) is used in Eq. (2), the integral overspace coordinates in the recombination term can beevaluated analytically to yield the result

= - kRRg2d - kRS Cg (7)

where

N r + -)d(t) = exp - o-rir (8)

i=1 87Q3/2 4Q2

is the mean density of energy near a radical at time tafter energy has been transferred from radiation to themedium. The angular brackets < > in Eq. (8) denote anaverage with respect to ro, the position of radicals inthe track structure.

In this discussion each term in the sum over i ofEq. (8) will be referred to as a cluster and the widthparameter a will be called the cluster radius. As thecluster radius increases due to diffusion the number ofterms that make a significant contribution to the sumin Eq. (8) for a given r0 also increases. This partiallycompensates for the decrease in energy density of eachcluster as the radius increases. When the number ofclusters that overlap is large and their displacementfrom the trajectory of the primary ion is small, thedensity of energy near a radical reduces to

<e> + 1 dE (9)d =+-

GM_8w3/2 a3 4Qa2 dx

where <E> is the average energy transferred to themedium in an inelastic collision and dE/dx is the

77

stopping power of the primary ion. This result suggestthat it would be useful to plot energy density times thecube of the cluster radius as a function of the radius.

TRACK STRUCTURE CALCULATIONS

Monte Carlo computer codes developed by Wilson andParetzke (3) were used to calculate the position of in-elastic collisions in the slowing down of primary ionsand all generations of secondary electrons. These re-sults were used in Eq. (8) to obtain the average densityof energy near a radical as a function of time afterirradiation. Figure 2 compares the average density ofenergy near a radical produced in water by energy trans-ferred from ions with equal stopping power but differentvelocity and charge. As expected from the Ganguly andMagee model, our Monte Carlo results for the mean energydensity times the cube of the cluster radius are approxi-mately a linear function of the radius. Our results for

1500

0 1.5 MeV H +

> 040MeVHe++ui 0

-a + bSeff

j1000-

0

. -Seff = 19 KeV /pm

G 500- Seff = 14 KeV/ym

0 0200 400 600

CLUSTER RADIUS, A 0

Figure 2. Density of energy near radicals produced in

water by protons and alpha particles with

stopping power of 19 keV/um.

78

1.5 MeV protons in water plotted in this manner yield aline with a slope equal to the stopping power, but foralpha particles with the same stopping power as the1.5 MeV protons, this slope is significantly smaller.Alpha particles have a greater velocity than protons ofthe same stopping power. Hence they produce a moreenergetic delta-ray spectrum and a greater fraction ofthe energy deposited in the liquid is transported awayfrom the trajectory of the primary ion. The slope of ourMonte Carlo results when plotted in this manner will bereferred to as the "effective LET" of the radiation.

We have carried out thistype of track structure anal-ysis for protons and alphaparticles at various stoppingpowers between 5 and 50 keV/pmin both water and cyclohexane.These calculations are summa-rized in Fig. 3 were the openand closed symbols show theresults in water and cyclo-hexane respectively. In allcases we found that the ef-fective LET for protons isnearly equal to the stoppingpower and the effective LETfor alpha particles is about75% of the stopping power.

Figure 3.

50rE

>

m-aJ

UU.W

302

20

0 10 20 30 40

STOPPING POWER, keV/ m

Effective LET of protons and alpha particles inwater (open symbols) and cyclohexane (closedsymbols).

COMPARISON WITH EXPERIMENT

The results shown in Fig. 3 provide a basis for calcu-lating the effect of track structure on the yield of freeradicals produced by high LET radiation. Figure 4 showsthe data of Sauer and co-workers on the yield of hydratedelectrons at about 10 p sec after a pulse of deuterons oralpha particles (2). These data were obtained by probingthe beam at different penetration depths in the sample sothat the yield can be plotted as a function of the stoppingpower of the ions in different track segments. Thedeuterons in this experiment have velocity and charge inthe same range as the protons for which we have carriedout our track structure analysis. Hence we expect theireffective LET to be nearly equal to their stopping power.

79

- H+

/ He++

O

50v

2.5

M.C. Sauer, et. alRADIAT. RES. 70, 91-106 (1977)

2.0

1.5

V

o ONE RADICALE MODEL

1.0 -+"'f4He

0.5

5 10 50 100

dT- (keV/1m)

Figure 4. Yield of hydrated electrons in pulse radiolysiswith deuterons and alpha particles of variousstopping powers.

The solid curve in Fig. 4 that passes through the deuterondata is a fit obtained by varying the recombination rateconstant in the one radical model. The best fit was ob-tained with a recombination rate constant of 2 x 1010 1/mole sec. The solid line through the alpha particle datais the result predicted by the model with no additionaladjustment of parameters. The model predicts a higheryield of hydrated electrons for alpha particles than fordeuterons of the same stopping power because the effectiveLET of the alpha particles is only 75% of their stoppingpower.

80

We do not mean to suggest by these results that aone radical model adequately explains the chemical kineticsin pulsed radiolysis of water. The data of Sauer, et al.(2) should be analyzed by a multi-radical model making useof all the available data on diffusion and reaction ratesin dilute aqueous systems. Work in this direction is inprogress using computer codes that were kindly providedto us by Dr. William Burns at Harwell. The results ob-tained with the one radical model do show that the trackstructure effects that cause the yield of hydrated electronto be higher for alpha particles than deuterons of equalstopping power are the same order of magnitude as thatpredicted by our track structure analysis.

REFERENCES

1. A. K. Ganguly and J. L. Magee, J. Chem. Phys. 25,129 (1956).

2. M. C. Sauer,Jr., K. H. Schmidt, E. J. Hart, C. A.Naleway and C. D. Jonah, Radiat. Res. 70, 91 (1977).

3. W. E. Wilson and H. G. Paretzke, Radiat. Res. 81,326 (1980).

4. J. H. Miller, Radiat. Res. 88, 280 (1981).

5. M. L. West and J. H. Miller, Chem. Phys. Lett. 71,110 (1980).

6. A. M. Kellerer and D. Chmelevsky, Rad. and Environm.Biophys. 12, 61 (1975).

7. A. Mozumder and J. L. Magee, Radiat. Res. 28, 215(1966).

8. W. G. Burns and A. R. Curtis, J. Phys. Chem. 76,3008 (1972).

81

"Recent Calculations Modeling Data from the Pulse

Radiolysis and Gamma Radiolysis of Water and Aqueous Solutions"

Conrad N. Trumbore and Walter Youngblade

Department of Chemistry, University of Delaware, Newark, DE 19711

Abstract

A model employing a spur overlap feature, an electron probability distri-

bution which is displaced away from the center of the spur, and high and lowspur density regions has been used to fit, within experimental error, hydratedelectron decay data and the Fricke dosimeter G(Fe3+) value from studies on the

pulse radiolysis of pure water and aqueous solutions. The radiation source

employed to obtain the pulse radiolysis electron decay data used in these

studies was the Argonne 14 MeV Linac Accelerator. When the same model is used

to predict yields from cobalt 60 gamma radiolysis experiments, there is quanti-

tative agreement at low solute concentrations. At high solute concentrations,

molecular product yields are not predicted as accurately.

At a workshop similar to the present one, Kuppermann made an attempt to

reconcile the classical spur model with experimental results of subnanosecond

pulse radiolysis.1 Alterations in the model were necessary because the observed

hydrated electron decay rate during the time period 10-10 to 10-8 secondsfollowing the pulse was much slower than predicted by the classical spur model.2

We consider Kuppermann's alteration unsatisfactory because the average

spur energy was increased from 100 ev to 172 ev which is an adjustment away

from the 40 ev figure predicted by Mozumder and Magee.3 We believe the aspectof the classical model responsible for the problem is having the maximum inthe probability distribution of all reactive intermediates in the center ofthe spur. Our proposed solution to this was to move the maximum of the hydra-ted electron probability density function away from the center of the spur.This change in the model created more of an induction period for the hydrated

electron decay, and we were able to model within experimental error the dataof Jonah and coworkers on the early decay (10-10 to 10-8 seconds) of both thehydrated electron4 and the hydroxyl radical5 following exposure of pure waterto pulsed 14 MeV electrons from the Argonne Linac.

Using this new model, we attempted to fit the pulse radiolysis data forpure water obtained by Fanning6 using the same Argonne-pulsed electron source at

times greater than tens of nanoseconds. In order to fit these data, which gaveindications of a pulse dose dependence,7 we incorporated a spur overlap featureinto our model. Our first-order approximation8 to such overlap was to treatthe average spur of interest as being surrounded by a spherically symmetricsmear of radiolytic intermediates from other spurs overlapping at a sphericalshell (enclosing the spur of interest) with a shell radius half the calculatedaverage distance between spurs for the given pulse dose. The boundary conditionwas that the flux of material diffusing out through this spherical shell wasequal to the flux entering through the shell surface from other spurs. Using this

82

approximation, we were successful9 in fitting within experimental error pulseradiolysis data at fairly high dose rates (ca 80 Grays pulse-1) as illustratedin Figure 1. However, as the pulse dose decreased, the agreement between

6.0

5.0

OH Radical

4.0 Hydrated Electron

G Values3.0

2.0-

1.0-

I x 10- 12 1 x 10~'1 I x 10 1 0 1 x 10 9 1 x 10-8 1x10 7 1x10 6

Time, sec

Figue 1. CaYcuated and Expen imentae Hydrated E Lec t'on and Hydoxyl RadicaDecay Data bon Wa-en at pH 7. Hydated election data are {tnomn e. 4 (0) and6 (0) and OH iadicat data ae ()om red. 5. Sofid ewtce caue calcuLated asdescribed in text.

experimental and calculated results became increasingly poor. At pulse doses

of on the order of one Gray, preliminary calculations indicated there should belittle or no hydrated electron decay in the time period between 10~7 and 10-6

seconds. This was clearly contrary to experimental results in which there was

a significant decay during this time period.

An analysis of both computed and experimental data convinced us thiscontinued electron decay at low pulse dose at late times was not due to random

placement of isolated spurs, with resulting early overlap of the closest spurs,or to electron scavenging impurities. Instead, it was assumed1 0 that the decay

was due to spur overlap in regions of high spur density such as might be foundin regions designated "blobs" and "short tracks" by Mozumder and Magee.' 1 Wemade the approximation that these high LET regions were composed of high spurdensity regions and, following the ideas of Mozumder and Magee, incorporated afixed fraction of the total energy expended into these high spur density regionsin our calculations. Further, we assumed that the spur density in these highLET regions was equal to or greater than those created locally by an 80 Graypulse from the Argonne Linac. In other words, a constant fraction of the pulse

83

energy was used to create high spur density regions with a fixed spur densityand the rest of the energy was channeled into regions with a lower spur densitywhich varied with the pulse dose. Our calculations for the Argonne data pre-dicted that for all doses used in the Argonne Linac experiments, the low spurdensity regions could still be treated as randomly placed spurs since theestimated spur spacing along the high energy electron tracks were larger thanthe estimated average distance between tracks. Using this model, we thenperformed two separate calculations (for high and low spur density regions)for the hydrated electron decay kinetics and weighted the results of eachcalculation in terms of its energy fraction.

We have recently completed modeling nearly within experimental error allthe Argonne Linac pulse radiolysis data of James Fanning6 using the parameterslisted in Table 1. Typical fits between experiments and calculations are shown

TABLE 1

Values of Spur Model Parameters Chosen for Optimum Fit with Pulse

Radiolysis Data of Fanning6

Average energy per spur - 60 ev G = 4 .7aeaq

+ 0oRadius (1/e) for -OH and H+ distr. - 30 A G H = 6.0

GCH = 1.3 - 2xb

Maximum in e~ distr. - 40 A GH = xaq 2

0G4H202=*0

Avg interspur distance (high spur density region) - 300 AAvg interspur distance (low spur density region) 'L (Pulse dose)-1 /3

Fraction of energy deposited in high spur density region = 0.20

aG values assumed at t = 10-12 seconds.

bFor most work x = 0.25; results relatively insensitive to value of x chosen

between 0 and 0.25.

84

in Figure 2. The Fanning data6 coupled with the data of Jonah, et al,45span

3.00 2.004.00 s x 00

qg x

® x

3.00-

x

2.00 -

1.00-

0.001

Ix10~10 Ix10"9 1x10"8 1x10"7 1x10-6 1x10-5Time, sec

F iguLe 2. CaLcuated and Expe imenta Hydrated Eecton Decay Data ().om theP'tse RadIoysi oo Pune Wa ten and Aqueous Sowution. Soid &i e nane calcu-&azted and points aie expekvimentaJ data. A: 3320 tad puses, pure water at pH 7;B:2455 nad putses, pH 11 waeIL; C:770 tad puLsn, pH 7 water, 0.1 M 2-ptopanoe;D:709 tad putse, pH 11 waters, 0.1 M 2-p'opanot.

a range of two orders of magnitude in pulse dose, four orders of magnitude in

time, and include studies of pure water as well as solutions containing high

and low concentrations of scavengers of the precursors of the chief reactive

intermediates in the spur; namely the hydrated electron, the hydroxyl radical,and the hydronium ion. Thus, while there are in our model a number of adjustableparameters (listed in Table 1), we believe the model has been tested against avery wide range of experimental data. The adjustable parameters used to fit theJonah et.al. data4'5 for hydrated electron and hydroxyl radical decay have notbeen altered to fit the Fanning data at later times. At these later times onlytwo parameters were altered; namely, spur density of the high spur densityregions and the fraction of energy deposited in these regions. It should benoted also that both the average spur energy (60 ev) and the fraction of energy

85

(0.20) deposited in high LET regions (e.g., spurs and blobs) are in surprisinglygood agreement with the calculations of Mozumder and Magee.2 Furthermore, data

are fit through time domains of intra-spur reaction and expansion, spur overlapat different times in both high and low spur density regions and, finally,during a period of homogeneous reaction. Additionally, it is gratifying to

obtain a calculated ferric ion G value of 16.3 for the Fricke dosimeter since

this is well within the experimental error of the value expected (15.7 0.6)

for 14 MeV electrons.

In preliminary studies we have applied our model, using the same parameters

listed in Table 1, to published data obtained from cobalt 60 gamma radiolysisexperiments. Since our model is based upon data from 14 MeV electron pulseradiolysis hydrated electron decay kinetics, it is of interest to see if radia-

tion yields from cobalt 60 can be predicted with this two spur density model.Gamma ray data modeled are primarily studies of the sensitivity of various

product yields to varying concentrations of dissolved scavengers of reactive

spur intermediates. Our preliminary calculations demonstrate similar trends in

the data to those found experimentally. However, the quantitative differences

observed between calculated and experimental radiation chemical yields implythat for gamma radiation our model may be underestimating the fraction of energy

being expended in high spur density regions. According to the calculations of

Mozumder and Magee,3 there should be an increase (from 0.2 to %.38) in thefraction of the total energy assigned to the formation of blobs and short tracks

when changing from 14 MeV electrons to secondary electrons expected from cobalt

60 gamma radiation.

Our model is based upon the roughly spherical symmetry for the ArgonneLinac experiments, whereas the cobalt 60 data may depend more on a cylindrical

track geometry, even in the lower spur density regions. Most cobalt 60 sourcesare surrounded by a dense shielding material. Therefore, contributions from

backscattered radiation are bound to be more important with gamma ray experi-

ments than with pulse radiolysis. We believe a reappraisal of the experimentaldata from gamma studies may be in order, especially in view of the higher cross

sections for higher LET backscattered radiation, again resulting in a higherproportion of the energy going into short tracks and blobs.

One of the supposed failures of the classical spur model is its inabilityto fit the scavenging curves of the molecular products H2 and H202. Calcula-tions,1 2 including our own, generally err on the side of overly efficient scaven-ging of the molecular product precursors, implying that these precursors aremore closely spaced than anticipated in the model. Yet hydrated electrons and OHradicals cannot be too closely spaced on the average or the initial hydratedelectron decay in the picosecond pulse radiolysis would be faster at early times.A possible solution to the molecular product problem may lie in more closelyspaced spurs in the lower spur density regions, which are, at least in part, inregions of cylindrical geometry. Schwarz has included in his calculationsregions of cylindrical geometry, using the prescribed diffusion approximation.2bHis success in modeling molecular product yields, however, was dependent uponassuming an initial yield of H2. This yield is almost the same as that foundin the track calculations from the Oak Ridge/Berkeley groups (a G value of 0.3for H2 and 0 atoms formed from excitation processes).

We are programming a cylindrical track model and will attempt to mix con-tributions from cylindrical high spur density regions with lower spur density

regions which are either spherically or cylindrically symmetrical. While very

86

early (%l0-12-10-9s) radiolytic reactions in pure water are probably takingplace in a local geometry with a roughly spherical symmetry, later reactionsundoubtedly assume a more cylindrical geometry for lower energy electrons inlow doses delivered in gamma ray experiments.

Figure 3 illustrates the various time domains in a pulse radiolysis

I 11111 I 1111 IIv 111NI I 1111 I I I III"

Isolated Spur OverlapDose Dependent

Intraspur HomogeneReaction

High Spur DensityRegion Overlap

Dose Independent

I I 1I1 1111 1 1I 1I 1 1 111 I I 1I111111 I I 1 I1 11111

ous Rxn.

5 4 RDS-

I 5802360

3460

RDSRDS

RDS

5700 RDS7894 RDS

II I I 11i110.01 1I x 10~-0 I x 10- 9 I x Ic0 8 1x 10- 7 1 x10-6 I x I0- 5

Time, sec

F4ig9we 3. Suggested Time Domacuvs in PuPwe Radioe.lysas o{ Pwe Watei.Una ate caLCcueated vatu& emp coing onty one put dens ity egiOn.

SoL d

experiment and their relation to the spur processes we have postulated. The

region around 10-8 seconds is where our model appears to give the least satis-

factory agreement (see Figure 2c). This is also part of the time region in

which we propose the overlap of spurs in the higher LET regions takes place.

Figure 4 applies the qualitative features of our model to the type of

typical experimental results obtained in gamma radiolysis. We believe the

shapes of these type curves contain the subtle details necessary to test any

theoretical spur or track model. Because of the possible gamma ray backscatter

problem raised above, we believe more experiments designed with this effect in

mind should be performed to see whether different mixes of gamma ray source

primary and backscattered radiation give qualitatively different scavenger curves

similar to Figure 4. It should be noted in Figure 4 that following the "plateau,"the initial rise generally attributed to "spur scavenging" instead is attri-

buted by us to a scavenging of the back reactions caused by overlapping spursin the high spur density region. The importance of scavenger concentrationvariation can be seen in Figure 5 where our computer calculations for 14 MeV-pulsed electrons are applied to variable concentrations of an OH radical

87

5.0

4.0

3.0

G(e~q)

2.0

1.0

-

1 1 h ill 1 1 0 1 ll 1 K 1 1 L i ,

1 1 11111 ili I I 1 111111i I I I i mi I T T 1 11 n

5.0

4.0

G(- Solute)or

G ( Product)

3.0

2.0

1.0

0.0 L

| x 1

- -11 1 - -1 1 1 111 1 r m 1i 1 1 1 1 1 I 1 1 111 1 1 1 1 1 1

Scavenging of Radicals----- in High Spur Density Regions

Bock Reactions Competing( e~ + - OH-+OH-) - -

Penetrationof Spurs

(in highand low

densityregions)

Complete Scavenging of Radicals Escaping Spurs -

S a i 1 1 1-6

S I I I 1111

Ix i-O5

L I LI aiaiil

Ix10-4

Conc., M1x 10 3

Figure 4. Scavenging Region as a Function o Solute Concentitation.'esult 9wm gamma adioly5is expeluments.

4-

G SOH]

2

n

10-7

S I I 1 1 101

X10-2

Type.cat

10-6[s],M

Figune 5. Ca.cuaton o Vietds o OH Radicals Scavenged by an E Aiseent -OHScavenger (S) at VauLous S Cncentations. Two spun density region modee employed:dotted bines indicate *OH yieed at vay-ing [SI in the twio 'eonz; obid Pfineindicate s the .esut -i 80% o6 the energy t depoPsted in ow pu density egic'nsand the emaining 20% in high spun denity egons.

88

2x 10 0 M 1 S-Bulk rxn. vs. spur rxns OH + S SOH

d oced Spurs

S20 /. C oset ------ pur

cd spurs g

I 1 1 L1 1ll _,L - # 1" R 1 1 1 1 1 W

__ _ _ _ _ _ 1 &

5 1 0 a I m 0 m 0 0 0 0 0 w 5 5 5 5

r

I

scavenger. In this figure it can be seen that above about 10-6 M [S] radicalsescaping the widely spaced spurs are nearly completely scavenged whereas the

radicals in the closely spaced spurs are only beginning to react with the radicalscavenger above 10-5 M [S].

It is clear that some modifications will have to be made in applying ourmodel to data from gamma radiolysis studies. The nature of th: modifications

which result in agreement between calculations and experiments should helpreveal differences in the nature of the primary physical events occurring inradiations which have been generally thought to be fairly similar in their

effective LET.

It would appear that our present model has the most difficulty in predicting

the proper spacing of the spurs in the high spur density region. This may be ageometry problem or a problem of fine tuning of the adjustable parameters of the

spur model, itself. The concept of displacement of the hydrated electron from

the center of the spur appears to explain successfully the delay in the hydratedelectron decay in the picosecond region. However, there are also other aspects

of the model which may be refined. We may also need to energy average in the

same manner that Schwarz did in his spur calculations,2 b but this will be only

possible in our model at high solute concentrations where spur overlap in the

high spur density regions is not important. Otherwise, the permutations and

combinations of allowing overlap of spurs of varying energies becomes excessively

complex.

However, despite possible future refinements, our current model is con-

veniently and quickly able to explain a large body of data from a number of

different systems. We believe that because of the relatively complex nature

of the Oak Ridge/Berkeley track calculations, our simpler model serves to com-

plement these track calculations rather than to compete with them. The calcul-

ations of higher energy electron tracks are necessary before any direct compar-

isons can be made between the two sets of calculations.

References

1. A. Kuppermann in "Physical Mechanisms in Radiation Biology," R.D. Cooperand R.W. Wood, Eds., Proceed. Conf. at Airlie, VA 1972, Tech. Info. Center,USAEC, CONF-721001, 1974, 155-76.

2. (a) A. Kuppermann in "Radiation Research, 1966," G. Silini, Ed.; North-Holland Publishing Co. - Amsterdam, 1967; pp. 212-34.

(b) H.A. Schwar.:, J. Phys. Chem. 73 1928 (1969).

3. A. Mozumder and i.L. Magee, Radiat. Res. 28, 203 (1966).

4. C.D. Jonah, M.S. Matheson, J.R. Miller and E.J. Hart, J. Phys. Chem. 80,1276 (1976).

5. C.D. Jonah and J.R. Miller, J. Phys. Chem. 81, 1974 (1977).

6. J.E. Fanning, Ph.D. Thesis, 1975, Univ. of Delaware, Newark, DE 19711

89

References count ' d)

7. J.E. Fanning, C.N. Trumbore, P. Glenn Barkley and J.H. Olson, J. Phys. Chem.81, 1264 (1977).

8. J.E. Fanning, C.N. Trumbore, P.G. Barkley, D.R. Short, and J.H. Olson,J. Phys. Chem. 81, 1026 (1977).

9. C.N. Trumbore, D.R. Short, J.E. Fanning and J.H. Olson, J. Phys. Chem. 82,2762 (1978).

10. D.R. Short, C.N. Trumbore and J.H. Olson, J. Phys. Chem. 85, 2328 (1981).

11. '. Mozumder and J.L. Magee, Chapter 13 in "Physical Chemistry, An AdvancedTreatise," Volume VII, Academic Press, New York, 1975, pp. 712-16.

12. Ref. 1 p. 166.

90

EFFECTS OF PHASE ON ELECTRON TRANSPORT IN WATER*

J. E. Turner, H. G. Paretzke, R. N. Hamm

H. A. Wright and R. H. Ritchie

Health and Safety Research DivisionOak Ridge National LaboratoryOak Ridge, Tennessee 37830

Abstract. Dual sets of Monte Carlo calculations were

performed of electron slowing down and transport inwater in the liquid and vapor phases. Collision spec-tra, stopping powers, yields, depth-dose curves, and

other quantities are compared for the two phases.

1. Introduction

Dual sets of Monte Carlo calculations were carried out for electron

energy loss and transport in water. The code developed at ORNL for

liquid water and that developed at GSF for water vapor were used. In

general, two basic differences characterize energy loss in the liquid

compared with the vapor. At energies > 100 eV, ionization accounts for

85-95% of the inelastic cross section for the liquid, as contrasted with50-75% for the vapor. In addition, the spectrum of energy losses forthe liquid is shifted upward due to collective effects, which do not

exist in the vapor.

The following sections compare a number of quantities for the two

phases, some that depend on electron transport and some that do not.

The final section summarizes the major differences found and theirphysical bases. Details of this work are given in Refs. 1 and 2.

2. Ionization and Excitation Probabilities

Figure 1 shows some basic input data for the liquid and the vaporcodes for electron transport in water. The mean free paths (g/cm2 )are displayed for ionizations and excitations in the two phases asfunctions of electron energy. The ionization mean free paths are com-parable above several hundred electron volts, but the excitation meanfree path is considerably larger in the liquid. These data give for therelative ionization probabilities the curves shown in Fig. 2 for theliquid and vapor. The ordinate represents the fraction of the totalinelastic cross section due to ionization (as opposed to excitation).As already mentioned, the partitioning of the energy loss into ioniza-tion is considerably greater in the liquid than in the vapor at energiesabove about 50 eV.

Research sponsored by the Office of Health and EnvironmentalResearch, U. S. Department of Energy, under contract W-7405-eng-26with Union Carbide Corporation.

tGesellschaft fur Strahlen- und Umweltforschung, D-8042 Neuherberg,

West Germany.

91

3 S ORNL-W S2-6413

10 1 ----Vapor- Liquid - 10OALDW6 91-11376

- 0.g _LIQUID

w- I.- a

g 06 6 R. +VAPOR

0.

,67 lous.

-0.2

f10

-s I I I I I i iit 111111 / 1101 10 210 l00 0 0 0 510 '

ENERGY (eV) ENERGY (eV)

Fig. 1. Mean free paths for Fig. 2. Relative probabilitiesexcitation and ionization in the of ionization as a function ofvapor and liquid phases of water electron energy.as functions of electron energy.

3. Single-Collision Spectra

Normalized single-collision spectra in liquid water for electronsof energy 30, 50, 150, and 10,000 eV are presented in Fig. 3. Excita-tion dominates at the lowest energy, where the curve shows resonancestructure. The collision spectra for electrons with energies aboveabout 100 eV are remarkedly similar. The curves for 150 eV and 10,000 eValmost coincide except for the low-lying tail at the higher energy. Thespectra of secondary electrons at energies 4 80 eV are thus very similar.In addition, however, a 10,000 eV electron occasionally gives rise to ahigh-energy secondary.

Figure 4 shows the average and median energy transfer as a functionof electron energy in liquid water. The general structure of thesecurves can be expected on the basis of Fig. 3. The average energytransferred in a collision increases steadily with electron energy dueto the increasing length of the tail on the single-collision spectrum.The median energy transferred, however, changes little for electronswith energies above 100 eV.

92

70.10

wa.

U)

J

0

J

00 25 50

ENERGY (cV)75

ONNL-owo S-1594

100

Fig. 3. Normalized single-collision spectra ofenergy losses for electrons of energy 30, 50, 150,and 10,000 eV in liquid water.

60

"

L

4

I-

wZWJ

40

20

t'

ORNL-DWG 61-15947

AVERAGE

EDIAN

to?ENERGY (.V)

Fig. 4. Average and median energy transfer asa function of electron energy in liquid water.

The normalized single-collision spectra for 1-keV electrons in theliquid and in the vapor are compared in Fig. 5. The harder spectrum inthe liquid is due to the upward shift in the oscillator-strength distri-bution for this phase relative to the vapor.

93

30 IV

50 IV

- -

- / , 150eV10,000 eV

1 2i i if --- -- -

.et I

tos_

104

0.06CML-DS6 01-11377

I _ I 1 I C T~ I

0.05 - -UV LLLTONU..

T

0.04

I-

r0.03

VAPOR

0

0 20 40 60 SO 100ENERGY IsV)

Fig. 5. Single-collision spectra of1-key electrons in the liquid and vapor.

4. Stopping Power

Mass stopping powers in the liquid and vapor are compared in Fig.6. The larger values in the liquid at energies A 100 eV are due to the

J2

harder collision spectrum. Our peak value of 310 MeV cm2/q is largerthan that of 260 MeV cm2 /g found by J. C. Ashley3 in a more recentcalculation for the liquid. The difference might arise from differenthandling of electron exchange. This point is still being investigated.

One effect of the existence of the long tails on the single-collisionspectra on the stopping power is illustrated in Fig. 7. It shows therelative number of the hardest collisions that contribute 10% to thestopping power as a function of electron energy for liquid water. Forexample, at 1 keV, about 1% of the collisions contribute 10% of -dE/pdx.In these collisions, 336 eV or more energy is transferred. At lO5 eV,a small fraction of 1% of the collisions transfer 6650 eV or more tomake up 10% of the stopping power.

5. Fano Factor

The Fano factors for the two phases are compared in Fig. 8 forelectrons of a given initial energy. The smaller value in the liquidreflects the greater number of ionizations (lower W-value) for the con-densed phase.

94

300 F

ORNL-DWG 61-11378

LIQUID

VAPOR

S // \ 0 ICRU 16

//

0/

E- \

i10 102ENERGY (eV)

Fig. 6. Mass stopping powers in the liquidand vapor as a function of electron energy.Open circles are from ICRU Report 16.

Omes.L-Dws SI-B340

0.061.. iii liii I III51.2 *v

0.05

0

C 0.04

0.03

0.02

336 W

0.01

2640 W

02 to 104 Io

ENERGY t#)

Fig. 7. Relative number of collisionsthat contribute 10% to the stopping powerof liquid water as a function of electronenergy. Numbers above arrows indicateminimum energy transferred in such colli-sions at the electron energies designated.

1.0

0.6

Ig

0

I-V

Osi

0.6

0.4

0.2

O NL-OwS 61-11370

\~ " (IN -A)2/KA

-lo-

VA POR

- LIQUID

010'

a illI iI I II i L I

ENERGY (iV)

Fig. 8. Fano factor forelectrons in liquid water andwater vapor.

95

Eu 200

I Inn

0

I

ivv Ii -

104

6. Slowing-Down Spectra

The slowing-down spectra for 103 eV and 104 eV electrons in water

in the two phases are shown in Fig. 9. The curves for 104 eV virtually

coincide with the ones for 103 eV electrons below 100 eV, and so the

curves for the higher energy are not shown. The step in the functions

around 500 eV is due to Auger electrons that are produced following the

creation of a vacancy in the K shell of the oxygen atom.

The curves for the liquid lie below those for the vapor at thehighest energies, because the harder collision spectra for the liquid

more efficiently degrade the electron energies. Because of the lowerW-value, the number of low-energy electrons is larger in the liquid.

7. Yields

Ionization and excitation yields are plotted in Fig. 10 as functions

of electron energy. The ionization G-values at 104 eV are 4.07 and 3.33per 100 eV for the liquid and vapor, respectively. The correspondingcalculated W-values for the liquid and vapor are 24.6 and 30.0 eV per

ion pair. The value for water vapor agrees with experiment. While Wfor liquid water has never been measured, the value found here is con-sistent with measured G-values of the order of 4.4 to 4.8 for the hydratedelectron at - 10-10 s.

OANL-DWG 61-11390

10.6 to-,

H 1-LIQUID

- -- VAPORE

2

a 1O-1 \

z

g 103 v-

o ,IO5.V s o*

10E1E101 101 1O3 104ENERGY IsV)

9. Slowing-down spectra forand 104 eV electrons in waterliquid and vapor phases.

10

8

00

0z

w

4 4

2

1o

ORNL-DWG 61-1139i i i I lii I II I

- LIQUID

-- VAPOR

EXCITATIONS

ONIZATIONS

104101ENERGY (V)

Fig. 10. Excitation and ionizationG-values for electrons in the liquidand vapor as functions of energy.

96

Fig.103 eVin the

j t 1 1 1 1.

11

The open circles in Fig. 10 show G-values for ionization obtainedby modifying the vapor code crudely to try to approximate the liquid.Specifically, the Lyman-a, -S, -y, Ha, HS, and diffuse-band excitationsin the vapor code were all changed to ionizations. One sees that theresults are not very satisfactory.

The ionization yield has been formulated in a special way byInokuti,5 who discusses its physical significance. A plot of specificyield -- the number of electrons N(E) as a function of l/E, where E isthe primary electron energy -- is presented in Fig. 11. The high-energylimit W, on the W-value can be found by extrapolation to 1/E = 0.

Yields for ionizations fromslowing down of 10-keV electronscompared in Table 1.

~0.04

W

..!

L.

0.

different shells produced by completeand all of their secondaries are

ORNL-DWG 82-15815

iF F{ 1 I -1--i

0 002 0041/E (sV 1)

0.06 008

Fig. 11. Specific ionization yields as a functionof initial electron energy in water in the liquidand vapor phases.

Table 1. Ionization yields for complete slowing downof l0-keV electrons in water in the liquid and vapor phases

Yields (per 100 eV)Shell Vapor Liquid

1B1 1.418 1.77

3A1 0.964 1.20

1B2 0.717 0.929

2A 0.186 0.116

K 0.00596 0.00683

97

---- Vapor

'N Liquid

- -N

l l.._

8. Depth-Dose Calculations

The calculated quantities presented thus far do not involve electron

transport explicitly. We now compare the spatial distributions of dose,which do depend on transport. Figure 12 shows a comparison of depth-dosecurves for 1-keV electrons in the liquid and the vapor. A broad beam of

electrons originates at zero depth traveling toward the right. Theordinate gives energy deposition in eV/A at depths in units of 10-8g/cm2 , equivalent to 1 A in unit density water. The depth-dose curve inthe liquid peaks at a lesser depth and is somewhat higher, reflectingthe harder collision spectrum. In addition, more electron energy is

deposited in the liquid by backscattering. This may be due, in part, tothe harder collision spectrum, but it is likely that elastic scatteringdifferences are more significant. This point was not investigatedfurther.

ORNL-DWG 81-11362

1 I I

-keV ELECTRONS

2/W/

W

W

WI \<VAP0R

LIQUID

0-100 0 200 400 600

DEPTH (10g/cm2)

Fig. 12. Depth-dose curves for a broad beamof 1-keV electrons in water in the liquid andvapor phases. The electrons originate at depth0 traveling initially toward the right.

The radial dose distributions around a pencil beam of 1-keV electronsat a depth of 285x10-8 g/cm2 are compared in Fig. 13. The distributionin the vapor falls ff rapidly at small distances. The function in theliquid falls off less rapidly near the origin because of the collectivesharing of energy close to the original direction of the electron beam.

98

ORNL-DWB 61-11313

1001-keV ELECTRONS

DEPTH 285

49 1---

-o.. ...--- VA POR

10-2 -LI QUID

10-3

0 100 200 300 400 500RADIAL DISTANCE (10p /cm2 )

Fig. 13. Comparison of radial-dose distributions

around a pencil beam of 1-keV electrons in liquid

water and water vapor. These radial profiles are

calculated at a depth corresponding to 285x10-8

g/cm2 in Fig. 12.

9. Summary

These studies were undertaken to quantitatively assess differences

in electron energy loss, yields, and dose deposition in water in the

vapor and liquid phases. The following statements summarize the principal

phase effect found and their apparent physical bases.

a. Ionization yield is greater in liquid: due to close neighbors

in liquid and to upward shift of oscillator strengths, favoring

ionization.

b. Single-collision spectrum is harder in the liquid: due to

upward shift of oscillator strengths.

c. Stopping power is greater in liquid than in vapor at energies

> 50 eV: a result of b.

d. Fano factor is smaller in liquid, except at lowest energies:

due to greater ionization yield in liquid.

e. Slowing-down spectra at higher energies are lower in liquid

than in vapor: liquid more efficient in degrading higher-

energy electrons.

f. Slowing-down spectra at lower energies are higher in liquid:

liquid produces more secondary electrons.

99

g. Average energy needed to produce the ion pair, Wliquid24.6 eV/ip and WYapor = 30.0 eV/ip: ionization yield isgreater in liquid; calculated value is reasonable forliquid water.

h. Depth-dose curves rise higher and peak earlier in liquid comparedwith vapor: due to harder collision spectrum in liquid.

i. Somewhat more backscattering is present in liquid depth-dose

curve: possibly due to harder energy-loss spectrum for the

liquid, but is undoubtedly affected also by elastic scattering

(not investigated here).

j. Falloff of radial dose distribution is much more gradual in

liquid over first 20x10-8 g/cm2: due to delocalization ofenergy transferred to the liquid because of collective sharing

by many molecules in the condensed phase.

References

1. J. E. Turner et al., "Comparative Study of Electron Energy Deposition

and Yields in Water in the Liquid and Vapor Phases," Radiat. Res. 92,

47 (1982).

2. J. E. Turner et al., "Comparison of Electron Transport Calculations

for Water in the Liquid and Vapor Phases," Proceedings of Eighth

Symposium on Microdosimetry, Jilich, Germany, Sept. 27-Oct. 1, 1982

(in press).

3. J. C. Ashley, Radiat. Res. 89, 25 (1982).

4. C. D. Jonah et al., J. Phys. Chem. 80, 1267 (1976).

5. M. Inokuti, Radiat. Res. 64, 6 (1975).

100

TRACK MODELING BY MONTE CARLO TECHNIQUES*

W. E. Wilson

Pacific Northwest LaboratoryRichland, Washington 99352

These brief comments will survey the several effortsin modeling charged particle tracks by Monte Carlo tech-niques, point out some of their similarities and also someof the limitations of the technique.

All three active efforts (ORNL, Columbia/LASL, PNL/GSF)derived out of a need for microscopic dosimetry to supportthe interpretation of radiobiological effects. Because ofthis origin these efforts are all specific to the radio-biologically important water molecule.

The significant increase in our ability to modelcharged particle tracks via Monte Carlo arises in largepart cat of the invention of the channeltron, a detectorof charged particles whose efficiency is stable upon re-peated exposure to air. Its availability opened the wayto a variety of collision experiments not previously possi-ble, or possible only with large uncertainties. Since theprimary interaction of fast charged particles with matteris the creation of ionization in the medium by ejectingvalence electrons, one important class of measurements isthe cross section for electron emission by charged particlesdifferential in electron energy and angle of emission. Opaland collaborators at JILA pioneered this area for incidentfast electrons (1); Professor M. E. Rudd (University ofNebraska) has done the same with fast ions (2). N. Stolterfoht(Bcrlin) and especially L. H. Toburen (PNL) have added con-siderable radiologically important data (3).

The doubly differential ionization measurements per-formed at PNL with the apparatus shown in Fig. 1 areclassical single collision experiments which measure theprobability that a secondary electron will be ejected from(I isolated molecule at an angle 0 and with energy e.These distributions are precisely the functions neededfor the primary source term oF energetic secondary elec-trons (delta-rays) in simulatng fast ion tracks.

*Work supported by United States Department of Energy

Contract DE-AC06-76RLO-1830.

101

FARADAY CUP

TARGET CELL

SUPPRESSOR

COLLIMATOR

BEAM

INTEGRATOR

VOLTAGERAMP

GENERATOR CYLINDRICAL PROTONMIR40R BEAMANALYSER

DIGITAL

COMPUTER

PULSE --s CHANNEL ELECTRONMULTIPLIER

AMPLIFIER

Figure 1. Experimental design for measurements of thedoubly differential cross section for ioniza-tion by high energy protons.

A typical result is shown in Fig. 2 for 1 MeV protonscolliding with water molecules. This plot illustrates thethree main features common to this type of data, 1) thevery large, essentially isotropic yield of low energy elec-trons, 2) the peak in yield of energetic electrons, describedby an almost binary encounter (collision) between the inci-dent ion and the valence electron, and finally 3) an en-hanced yield at forward angles of emission for a small rangeof electron energies in which the velocity of the ejectedelectron is near the velocity of the passing positive ion.This latter process has been interpreted as a "chargetransfer" to continuum states. The peak occurring atall angles at ejected electron energies near 540 eV re-sults from Auger electron emission following inner shellionization of the oxygen atom of the water molecule.

Electron emission from a large variety of moleculeshave been studied (3), and the spectra all exhibit thesethree basic features. Furthermore, they all exhibitessentially the same relative distributions in angle andenergy for electrons emitted above t 30 eV. This relative

102

1 KI/ (.

Figure 2. Doubly differential cross sections fcrionization of water molecules by 1 MeVprotons.

insensitivity to the molecular environment encouragesthe development of mathematical models of the experimentaldata for application to biologically interesting targetsand provides a degree of confidence to their applicabilityin condensed phase material.

A second, equally important class of experiments thathas provided important data for track structure modelingis the photo reflectance measurements on liquids done atORNL and the University of Tennessee by Painter andco-workers (4). Ritchie and his collaborators at ORNLhave used these data to deduce inverse mean free paths(cross sections) for fast charged particles in liquidwater (5). These cross sections are the basis for theelectron transport code presently being developed by Hamm,et al. (6) at ORNL.

A collaboration between Columbia University and theLos Alamos National Laboratory has resulted in a transportcode based on evaluation of considerable experimentalliterature on electron elastic and inelastic scatteringin the gas phase (7). Our own electron transport code (8)uses a Kim analysis (9) of the data of Opal, et al. (1)for ionization of H20 by electron impact and our ion

103

transport code employs a semi-theoretical algorithm fordelta-ray generation by positive ions with energy up to50 MeV/amu.

Monte Carlo calculations, in general, have majorshort comings. These efforts directed at track structuresimulation are not exceptional in this regard. The tech-nique is a very inefficient computational method and hencethe practitioner is often tempted to produce huge quanti-ties of "data"; none of which are more reliable than thecross sections upon which they depend (unfortunately, theperceived "worth" of such data is often proportional to thedifficulty of producing them).

The cross sections for most of the processes involvedin radiation action are simply not known; our presentefforts are therefore primative and tentative. Two de-velopments indicate hope for the future, however; first,there is a slowly but steadily growing data base uponwhich to draw, second, there is a rapidly increasingcomputer hardware capability. Very large volume discstorage, replacing slow and bulky tapes, will make newdetailed simulations feasible. Track structure simulationhas a bright future.

REFERENCES

1. C. B. Opal, E. C. Beaty, and W. K. Peterson, At.Data 4, 209 (1972).

2. M. E. Rudd and J. H. Macek, Case Studies in AtomicPhysics 3, 47 (1972).

3. L. H. Toburen and W. E. Wilson, Radiation Research;edited by S. Okada, M. Ima-Mura, T. Terashima, andY. Yamaguchi (Japanese Association for RadiationResearch, Tokyo, 1979), pp. 80-88; and referencestherein.

4. J. M. Heller, Jr., R. N. Hamm, R. D. Birkhoff, andL. R. Painter, J. Chem. Phys. 60, 3483 (1974).

5. R. H. Ritchie, R. N. Hamm, J. E. Turner, and H. A.Wright, Sixth Symposium on Microdosimetry, Brussels,Belgium, May 1978, EUR 6064 DE-EN-FR, pp. 345-354.

6. R. N. Hamm, H. A. Wright, R. H. Ritchie, J. E. Turner,and T. P. Turner, Fifth Symposium on Microdosimetry,Verbania Pallanza, Italy, September 1975, EUR-5452d-e-f, pp. 1037-1053.

104

REFERENCES (cont'd)

7. D. J. Brenner, Physics in Medicine and Biology,in press.

8. W. E. Wilson and H. G. Paretzke, Radiat. Res. 81,326, (1980) ; Radiat. Res. 87, 521 (1981) .

9. Y.-K. Kim, Radiat. Res. 61, 21 (1975); 64, 204 (1975).

105

EARLY PHYSICAL AND CHEMICAL EVENTS IN ELECTRON TRACKS IN LIQUID WATER*

H. A. Wright, J. E. Turner, R. N. Hamm, and R. H. Ritchie

Health and Safety Research DivisionOak Ridge National LaboratoryOak Ridge, Tennessee 37830

and

J. L. Magee and A. Chatterjee

Lawrence Berkeley LaboratoryUniversity of California

Berkeley, California 4720

During the last few years we have developed a program to transportan electron and all of its secondaries through liquid water.1' 2 Themethod used to infer the mean free paths of the electrons from opticaldata is discussed by R. N. Hamm in another paper in this workshop. Wehave used these mean free paths in a Monte Carlo computer program thattraces the history of each electron and identifies the position andtype of each energy transfer to the medium. The physical electronictransition events that occur during the passage of an electron through alocal region of matter are complete in a time <10-15 s. The next bigquestion that remains is to link these initial physical events to laterchemical events that occur during the diffusion stage of the developmentof the track.

It is the purpose of this paper to describe a program which we haveinitiated to calculate the details of an electron track from the initialphysical stage at <10-15 s through the later chemical stage to "'1 iswhen chemical diffusion is essentially complete.

The first stage in this program is to describe the events thatoccur between 10-5 s and 10-1 s, the latter being the time at whichdiffusion begins. The results of this phase of our program were presentedin Oxford, U.K., at the Seventh Symposium on Microdosimetry.3 We assumethat three species are present at 10-15 s--H20+ ions, H0* excitedmolecules, and subexcitation electrons. The Monte Carlo computer codegives the positions of all such quantities. We assume that the H20+ ionreacts (in 'l0-14 s) with a neighboring H20 molecule by capturing an Hatom, forming a hydronium ion, and leaving an OH radical:

H20+ + H20 - H30+ + OH . (1)

We assume that the decay of an excited neutral molecule, H20*, depends onthe particular mode of excitation. Electronic transitions associatedwith Rydberg, diffuse-band, or dissociative excitation in water vaporare assumed to result, in the liquid, in an electron being lost from themolecule leaving an H20+ which is treated as described above. Electronic

"Research sponsored by the Office of Health and Environmental Research,

U.S. Department of Energy, under contract W-7405-eng-26 with the UnionCarbide Corporation.

106

transitions associated with A1B1 excitations are assumed to result indissociation of the molecule into H and OH radicals, whereas transitionsassociated with B1A1 excitations cause dissociation into H2 and 0 radicals.A subexcitation electron is assumed to migrate about its original position ina random-walk fashion until it becomes hydrated. Details of this phaseof our program have been described elsewhere. 3'4 The results of thisphysico-chemical stage of the development of the track are presented inTable I and Figs. 1-3. Figure 1 shows the positions of all products inthe track of a 5-keV electron which initially started at the origin andwas directed along the axis to the right. Each point shows the positionof an H20+ ion or H20* excited molecule at 10-15 s. Figure 2 shows a20-fold blow-up of the initial portion of this track. Figure 3 showsthe same portion of the track at 10- 1 1 s and identifies the positions ofindividual radicals or ions as well as the hydrated electrons at thattime.

Table I. Species Present Around Track in Liquid Water at10-15 s and 10-11 s After Passage of Primary Electron of

Energy 5 keV and Calculated Yields at 10-11 s

10-15 s 10~11 s

Species Species G-Value

OH

aq

H 30+

H

H2

0

8.4

6.3

6.3

2.1

0.3

0.3

OUl 0M400- m3

'A.

-w

,-' I+,

Fig. 1. Location ofinelastic events producedby a 5-keV electron andall of its secondaries inliquid water. Original5-keV electron started atthe origin, travelingtoward the right alongthe horizontal axis.

1000 A'

107

H 2 0+

H2 0*

e

.__

1 a a

'0

oiUIow)31 sI Fig. 2. Blow-up view

of initial portion oftrack in Fig. 1 showinglocation of H20 (circles)and H20+ (triangles) at10-15 s.

S.

50 A'

Fig. 3. Same portion oftrack from Fig. 2 at 10-11 s.Legend: o, H; A, OH; X, e ;0 , H 30+. There were no aqH2 or 0 in this portion ofthe track.

R

a. "

50 A'

The next stage of our rogram is the diffusion and chemical reactiondevelopment of the track.4 ,' We assume that the products listed inTable I at 10-11 s can undergo thermal motion and react according toTable II when they diffuse close enough to one another.

We assume that H2 does not react further and that 0 combines withH20 to form H202 , which is not considered further. The diffusion constantsand reaction radii for the other four reactant species are shown inTable III.

We simulate the actual diffusive motion by assuming that thereactant species undergo discrete jumps. Each reactant is jumped onceand then those that are separated by less than the sum of their reactionradii are assumed to react according to Table II. Those that react areremoved and tabulated and the remainder are jumped again. A more complete

108

description of the jumping scheme is given elsewhere.4'5 Results ofthis stage of the track evolution are described in the remaining figuresand tables.

Table II. Chemical Reactions at Times >10-11 s

OH + OH

OH + eaq

OH + H

+ H2 02

-+ OH

+ H20

H30 + e~

e + e +22H20aq aq

eaaq

+ H + H20

H + H

+ H + H20

+. H2 + 20H

+ H2 + OH

+ H2

Table III. Diffusion Constants, D, and Reaction Radii,R, for Chemical Reactants

Species D(10- 5 cm2 s'1) R (A)

OH 2 2.41

e 5 2.14aq

H 30+ 8 0.30

H 8 0.42

Figure 4 shows three examples of the tracks of 5-keV electrons.The points represent positions of the reactants ac 10-11 s. Figure 5shows the subsequent diffusion and development of the top track inFigure 4. The number of reactants remaining at various times are indi-cated on the figure and the corresponding positions are shown. It isseen in the lower right panel that at 0.28 Vs only 410 of the original1174 reactants remain and their initial spatial correlations no longerexist. Figure 6 shows similar development of the track of a 20-keVelectron.

109

om.-ows 0-1E

ORNL-OWG 61-18322

.0.1pm

Fig. 4. Three examples ofthe spatial distribution ofchemically active speciespresent at 10-11 s aroundthe tracks of 5-keV elec-trons in liquid water.

-4 O.1, m

N-11741.0x104''1

N-985

3.5 x10" s

N" 68729 x10"

Fig. 5. Example ofof a 5-keV electron2.8 x 10~7 s.

011 .m

N-5192.8x1Q''s

N-4392.8 x1075 s

N-41028 10's

the chemical evolutiontrack from 10-11 s to

.. ..M "1

N-45931.0 x 1071 -

Fig. 6. Example of the chemical evolutionof a 20-keV electron track from 10-11 s to2.8 x 10-7 s.

N-1936

N-1813-2.8x10 s ".-

110

It is seen that 1813 of the original 4593 reactants remain at 0.28Ps and there remains some indication of the clustering that was presentat earlier times. Table IV shows a breakdown of the numbers of eachreactant species for this 20-keV electron track at 10~11 s and 0.28 ps.The numbers of hydrated electrons and OH radicals are dramaticallydecreased whereas the numbers of H30+ and H only decrease slightly. G-values (number per 100 eV) for a number of species at 0.28 ps are shownin Table V for electrons of various energies from 100 eV to 20 keV. Itcan be observed that more chemical reactions occur for electrons of approx-imately 1-keV energy than for electrons of other energies.

Table IV. Number of Chemical Species Present in the Trackof a 20-keV Electron at Various Times

Species 10-11 s 2.8 x 10-7 s

e 1247 205aq

H30+ 1242 1002

H 431 395

OH 1673 211

H2 72 191

H202 72 383

Table V.at

G-Values (Number Per 100 eV) for Various Species0.28 ps for Selected Electron Energies

Electron Energy (eV)

Species 100 200 500 750 1,000 5,000 10,000 20,000

e 1.87 1.44 0.82 0.71 0.62 0.89 1.18 1.13aq

H30+ 4.97 5.01 4.88 4.97 4.86 5.03 5.19 5.13

H 2.52 2.12 1.96 1.91 1.96 1.93 1.90 1.99

OH 1.17 0.72 0.46 0.39 0.39 0.74 1.05 1.10

H2 0.74 0.86 0.99 0.95 0.93 0.84 0.81 0.80

H202 1.84 2.04 2.04 2.00 1.97 1.86 1.81 1.80

OH 3.97 4.07 4.26 4.39 4.34 4.17 4.04 4.03

Fe+3 17.9 15.5 12.7 12.3 12.6 12.9 13.9 14.1

111

No experimental data exist to make direct comparison with experiment

possible. However, experimental data for the Fricke dosimeter areavailable so we calculate a G-value by the formula

G++3 = 2G + G + 3(G +G_ ) . (2)ne 2u2 OH 'H e

aq

This value is shown in the bottom row of Table V for electrons of eachenergy. The measured value for tritium beta rays is 12.9. If we averagethe values in Table V over the tritium a-ray spectrum, we obtain thevalue 13.3, which is considered very good agreement with experiment.

In conclusion, we have made an attempt to extend our detailedevent-by-event calculations of electron tracks in liquid water forwardin time from the initial deposition of energy through the completion ofthe track reactions. We realize that little information is availablefor detailed justification of the steps we have had to make in thisprogram, but we are certainly encouraged by the results that we haveobtained at later times where chemical G-values can be measured. We nowwish to :attempt to make other comparisons with experiment, and we welcomesuggestions from chemists as to specific steps that we should take inour program. This is just the beginning of our program, and we expectthat some of the assumptions in the present studies will be modified asnew information becomes available.

REFERENCES

1. R. N. Hamm, H. A. Wright, R. H. Ritchie, J. E. Turner, andT. P. Turner, in Proceedings of the Fifth Symposium on Microdosimetry,Verbania Pollanza, Italy, September 22-26, 1975, Vol. II, edited byJ. Booz, H. G. Ebert, and B.G.R. Smith (Commission of the EuropeanCommunities, Brussels, 1976), pp. 1037-1053.

2. R. H. Ritchie, R. N. Hamm, J. E. Turner, and H. A. Wright, inProceedings of the Sixth Symposium on Microdosimetry, Brussels,Belgium, May 22-26, 1978, Vol. I, edited by J. Booz and H. G.Ebert (Commission of the European Communities, Brussels, 1978),pp. 345-354.

3. J. E. Turner, J. L. Magee, R. N. Hamm, A. Chatterjee, H. A. Wright,and R. H. Ritchie, in Proceedings of the Seventh Sympcsium on Micro-dosimetry, Oxford, U.K., September 8-12., 1980 (Commission of theEuropean Communities, Brussels, 1980), pp. 507-517.

4. J. E. Turner, J. L. Magee, H. A. Wright, A. Chatterjee, R. N. Hamm,and R. H. Ritchie, "Physical and Chemical Evolution of ElectronTracks in Liquid Water," submitted to Radiation Research.

5. H. A. Wright, J. E. Turner, R. N. Hamm, R. H. Ritchie, J. L. Magee,and A. Chatterjee, in Proceedings of the Eighth Symposium on Micro-dosimetry, Jilich, West Germany, September 26-October 1, 1982 (in press).

112

COMPUTATIONAL DETAILS OF THE MONTE CARLO SIMULATIONOF PROTON AND ELECTRON TRACKS

M. Zaider* and D. J. Brennert

I. Introduction

In recent years, as the need for detailed information about energydeposition in subcellular sites has become apparent (e.g., Kellerer et al.1980, Cox et al. 1977), considerable effort has been devoted by several groups(e.g., Wilson and Paretzke 1980, Terrissol et al. 1978, Hamm et al. 1978,Berger et al. 1970, and Brenner 1982) with the aim of producing realisticMonte-Carlo "event by event" transport codes for heavy charged particles andelectrons in water.

The code PROTON, developed in our laboratories, simulates the elastic andnon elastic interactions of protons and electrons in water vapor. An effort

was made to incorporate in this code the best available experimental andtheoretical cross sectional data over a wide energy range; in particularelectron interactions are simulated down to sub-electronvolt energies makingthe results of the calculation highy relevant as an input to radiation

chemistry studies. The immediate result of a typical calculation with PROTONis a set of simulated particle tracks containing the spatial coordinates ofall the non-elastic processes together with the energies deposited locally.Calculated tracks are then analyzed in terms of various distribution functionssuch as microdosimetric spectra, radial dose distributions, proximityfunctions of energy deposition, etc. A detailed description of the codePROTON can be found in an article recently submitted for publication (Zaideret al. 1982).

The application of track structure results to radiation biophysics restsessentially on two (not necessarily independent) aspects of the energydeposition in the medium: The primary injury event is determined by theamount of energy deposited locally (i.e., ionization and excitationthresholds). The endpoint of interest however, is most probably a function ofthe spatial configuration of the primary events. While agreement exists amongcalculations concerning the physical treatment of the former aspect,comparatively little attention has been paid to the most important factor indetermining the spatial distribution of energy deposition, namely the electrontotal and angular elastic scattering particularly at low energies. Theimportance of this aspect is further enhanced by the fact that, in the absenceof detailed information concerning the angular distribution of non-elasticscattering, a reasonable approach (Nicoll and Mohr 1933) is to assume that theangular distributions of these processes are similar to those for elastic

* Columbia University, Radiological Research Laboratories, 630 W. 168th

St., New York, NY 10032.

t Los Alamos National Laboratory, MP-3, MS-809, Los Alamos, NM.

113

scattering.

In the first part of this report the treatment of elastic angularscattering of electrons as utilized in PROTON is described and compared withalternate formalisms. The sensitivity of the calculation to different

treatments of this process is further examined in terms of proximity functions

of energy deposition.

II. The Treatment of Electron Elastic Angular Scattering

The elastic angular scattering of electrons is usually described witheither the "screened Rutherford" approach of Bethe (1953) or with the "phase-shift" approach of Mott (1929).

In the Bethe approach the Rutherford cross section is modified by ascreening parameter:

2 4a(T,6) = 2 4 Ze (1)

m v (1 + 2n - cos6)

where T and v are the kinetic energy and velocity of the electron (mass m,charge e) and the screening parameter n is determined either from the theoryof Moliere (1947) or semiempirically:

n = c ~( /m 2 (2)T(T/mc + 2)

S= a + allnT (3)

In Eqs. (2-3) the parameters k, al, a are obtained by fitting the data.

This formalism, Eq. (1), describes satisfactorily the data for electronenergies T > 0.2 keV and is used as such in the code PROTON. Unfortunately atlower energies the agreement with data is very poor as can be seen forinstance in Fig. 1 where the strong forward and backward peaks are notreproduced adequately.

In the phase-shift approach, the phase shifts for scattering off thewater molecule are frequently calculated in a static central potential (e.g.,Terrissol 1978). Such an approach is also inadequate at low energies, evenfor the simpler case of scattering off atoms. Fig. 2 shows the results ofsuch a calculation by Terrissol (1978) foratomic oxygen - one of the twoatomic constituents of water - compared with the experimental data of Dehmelet al. (1976).

In view of these problems low energy (T < 0.2 keV) electron elasticscattering was treated in PROTON using a semiempirical approach suitable forMonte Carlo simulation. Among several such formalisms available in theliterature, that of Porter and Jump (1978) was found to have the greatestflexibility in reproducing the data. Thus the angular distribution isrepresented as:

a(T,6) 1~ 1_2+2(4)

(1 + 2Y - cosh) (1 + 26 + cose) 2

114

where a, y, and 6 are parameters dependent on the energy, T, of the

electron. The values of these parameters at selected energies were obtainedby fitting Eq. (4) to the data of Seng (1975) (0.35 - 10 eV, 200 - 1080),Trajmar et al. (1973) (15 - 53 eV, 100 - 900), Nishimura (1979, and privatecommunication) (30 - 200 eV, 100 - 1400), Hilgner et al. (1969) (60 - 300 eV,350 - 1500), and Bromberg (1975) (300 - 500 eV, 20 - 1600). The resultingvalues of a, y, and 6 were further fitted as a function of electron energy topolynomials or exponential of polynomials as follows:

4a(T) = exp[i 0 %Ti] (5)

46(T) = exp[ 1 % 6iTi] (6)

5

Y(T) = exp YiT] 0.35 < T < 10 eV (7)

4

= exp[1 E0 YiTij 10 < T < 100 eV

2

=O YiT 100 < T < 200 eV

Typical fits (Fig. 3) are in very good agreement with the experimental data.

III. Sensitivity Study

The three formalisms described above vary greatly in both their agreementwith the data and computational complexity. It is by no means obvious however

if the average quantities normally calculated from simulated particle tracksare actually sensitive to a very precise description of the elasticscattering, if at all. In order to investigate this aspect proximityfunctions of energy deposition have been calculated for 1-keV electrons inwater vapor using modified versions of PROTON with various treatments of theelastic scattering. The proximity function, t(x)dx, is defined (Yellerer andChmelevski 1975) as the average energy deposited in a spherical shell ofradius x and thickness dx centered at a randomly chosen interaction point.The term "random" in this definition refers to selection probabilitiesproportional to the energy deposited at the interaction point. Equivalently,the proximity function can be thought of as an energy-weighted distancedistribution between random pairs of energy deposition events in the track.It is, a fortiori, the quantity most related to the spatial distribution ofprimary injuries mentioned at the beginning.

A selection of proximity functions is shown in Fig. 4. The calculationswere performed with: (D) the code PROTON, (E) screened Rutherford cross

section, (F) phase-shift approach, (A) ionization cross sections decreased by25% and excitation cross sections increased by the same amount, (C) excitationangular scattering identical to elastic scattering, and (B) ionization crosssections increased by 25% and excitation cross sections decreased by the sameamount.

The significance of the differences between various proximity functioncalculations can be appreciated with respect to Fig. 5 where the proximity

functions for the three soft x-ray beams are displayed (C 0.27 keV; Al 1.5keV; Ti 4.5 keV): while the variations in Figs. 4 and 5 are of the same order

115

of magnitude, radiobiological experiments (Cox et al. 1977) indicate

pronounced differences in the effectiveness of the three soft x-ray beams. Itappears therefore that, at least for biological models which employ proximityfunctions, an accurate treatment of the elastic scattering processes isessential..

Acknowledgements

This investigation was supported in part by Grant CA 15307 to theRadiological Research Laboratories/Department of Radiology, and by Grant CA

13696 to the Cancer Center/Institute of Cancer Research, awarded by NCI, DHHS.

References

- Berger M J, Seltzer S M and Maeda K 1970 J. Atmos. Terres. Phys. 32 1015- Bethe H 1953 Phys. Rev. 89 1256- Brenner D J 1982 Rad. Res. 89 194- Bromberg J P 1975 In "The Physics of Electronic and Atomic Collisions" IXth

International Conference on the Physics of Electronic and AtomicCollisions, Seattle (Risley J S and Geballe R Eds.) p. 98 Univ. of Wash-ington Press, Seattle

- Cox R, Thacker J and Goodhead D T 1977 Int. J. Radiat. Biol. 31 561- Dehmel R C, Fineman M A and Miller D R 1976 Phys. Rev. A _3 115- Hamm R N, Wright H A, Turner J E and Ritchie R E 1978 In Proceedings, Sixth

Symposium on Microdosimetry, Brussels, Belgium. (Booz J and Ebert H G,Eds.) p. 179. Commission of the European Communities, Harwood, London1978 (EUR-6064-d-e-f)

- Hilgner W, Kessler J and Steeb E 1969 Z. Physik 221 324- Kellerer A M and Chmelevski D 1975, Radiat. Environ. Biophys. 12 321- Kellerer A M, Lam Y-M P and Rossi H H 1980 Rad. Res. 83 511- Moliere G 1947 Z. Naturf. 2a 133- Mott N F 1929 Proc. R. Soc. A124 425- Nicoll F H and Mohr C B 0 1933 Proc. R. Soc. A142 647- Nishimura H 1979 in "Electronic and Atomic Collisions" XIth International

Conference on the Physics of Electronic and Atomic Collisions, Kyoto,Japan (Takayanagi K and Oda N, Eds.) Vol. II, p. 314, Society for AtomicCollisions Research, Japan

- Porter H S and Jump F W 1978 Computer Science Corp. Report CSC/TM-78/6017- Seng G 1975 Thesis, Universitt Kaiserslautern- Terrissol M, Patau J P and Eudaldo T 1978 in Proceedings, Sixth Symposium

on Microdosimetry, Brussels, Belgium (Booz J and Ebert H G, Eds.) p. 169Commission of the European Communities, Harwood, London 1978(EUR-6064-d-e-f)

- Trajmar S, Williams W and Kupperman A 1973 J. Chem. Phys. 58 2521- Wilson W E and Paretzke H G 1980 Rad. Res. 81 326- Zaider M, Brenner D J and Wilson W E 1982 Radiat. Res. submitted for

publication

116

4-

C

4-

0

b

4

3

2

0'0 30 60 90 120

SCATTERING ANGLE (deg)150 180

Fig. 1 Comparison of experimental elastic differential cross sections for 30-

eV electrons (Nishimura, 1979) with the "screened Rutherford"

prediction of Eq. (1), for water vapor. The data have been normalizedto the theoretical cross section at 150.

0

0,

0 30 60 90 120SCATTERING ANGLE (deg)

150 180

Fig. 2 Comparison of experimental elastic differential cross sections for 5-

eV ( 0 ) and 15-eV ( 0 ) electrons (Dehmel et al. 1976) on atomicoxygen with the static potential "phase-shift" calculations ofTerrissol (1978) at 10 eV. All the data have been arbitrarilynormalized at 45*.

117

- "* .

0

00

Ia

"

0

5 --00

.SS

"

00

" o

0

1 I 1 1

11

w,

1

F 10z

~10\

10 --- -

ra10

0 20 40 60 80 tOO 120 140 160 180

SCATTERING ANGLE

Fig. 3 Comparison of angular distributions for electron elastic [cattering onwater as calculatd with our semiempirical formalism with experimentaldata at various electron energies: 0.6 eV ( O, Seng 1975), 15 eV (o,Trajmar et al. 1973), 40 eV (A, Nishimura 1979) and 100 eV (A,Nishimura 1979, +, Hilgner et al. 1969)

ELECTRON ENERGY= 1.00 keV. PROXIMITY FUNCTION35 -

2o-

10-

0

10 10 '1C 1x (nm)

Fig. 4. Proximity functions of energy deposition calculated with differenttheoretical cross sections: A (long dash) ionization cross sectiondecreased by 25% and excitation cross section increased by the sameamount, B (dot-dash) ionization cross section increased by 25% andexcitation cross section decreased by the same amount, C (short dash-long dash) excitation angular distribution identical to elasticscattering, D (short dash) "screened Rutherford" scattering, and F(dots) "phase-shift" scattering.

118

50

X 40- 'c

C. Al Ti

Fig. 5 Proximity functions for three soft x-ray beams: C (0.27 keV), Al (1.5

keV), and Ti (4.5 keV).

119

10

U 1

10- idi I --I I 1 1 11T1t

d (x (n m)

1 T 1 l I

t

an

COMMENTS ON TRACKS AND DELTA RAYS

Robert Katz, University of Nebraska, Lincoln NE 68588

TRACK: The locus of "observable events" clustered about the path of an

energetic charged particle, and caused by its passage.

The character of a track depends both qualitatively and quantitatively onthe "end-point" used to define the "observable event".

The term "end-point" encompasses a variety of historical and proceduraldetail. For example, the array of developed grains in a nuclear emulsion

after passage of a heavy ion depends on manufacturing and doping conditions,on fading of the latent image, on the details of development, and even onobservation conditions (for the observation of a developed grain may depend onits size in relation to the resolving power of the observing instrument). Allof these, as well as the charge and speed of the particle, serve to modify thecharacter of the track. Similar considerations, such as the pre- and post-irradiation culture conditions play a role in biological track structure.Indeed this is the case for all except the most primitive of track structures,the array of initial excitation and ionization events.

DELTA RAYS: All secondary electrons arising from the primary ionizationsgenerated by the passage of an energetic charged particle.

120

TRACKS, SPURS, BLOBS AND DELTA-RAYS

J. L. Magee and A. ChatterjeeBiomedical Division, Lawrence Berkeley Lab-atory

University of California, Berkeley, Californ1i 94720

The track of a high energy particle is the collection of all transient

species created by the particle in the total degradation of its energy. Suchtransient species change their character with time and so tracks evolve intime. At first excited states and ion pairs predominate; at later timesradicals and radiation product molecules are prominent; at all times thespatial inhomogeneties of the species created in the track are being smoothedby diffusion and ultimately all radiation products are homogeneouslydistributed. A description of charged particle tracks from the point of view

of radiation chemistry has been presented by Mozumder.'

A heavy particle has a track which is generally in the form of a straightline with deviations produced by scattering and with branch tracks created byknocked-out electrons. Such electron tracks, if they are visible, are calleddelta-rays. Radiation chemists have found that a microscopic description ofthe track with all its knocked-out electrons is useful for radiation chemicalmodels, and such a d scription leads to spurs, blobs and short tracks.Mozumder and Magee2 - have described these track entities and shown how they

can be applied in radiation chemical models.

The average energy loss -dE/dx by a arged particle is given by theBethe formula which depends on a spectrum of energy losses which in turndepends on the oscillator strength distribution of the stopping medium. Thetrack entities are best understood in terms of a particle with a small linearenergy transfer (LET); consider an electron or proton with-dE/dx ~ 0.02 eV/A penetrating in liquid water. In low-Z media almost alloscillator strength except that pertaining to K-electrons can be assumed to becontained within 100 eV. Therefore, an arbitrary but useful demarcationbetween glancing and knock-on collisions may be made at 1.00 eV. For thisdemarcation about half the energy loss is due to glancing collisions with anaverage energy loss of about 40 eV and the other half is due to knock-oncollisions with an average energy loss of perhaps 1000 eV. the averageseparation of the glancing losses is - 40/0.01 101000 A and theaverage separation of the knock-on losses is 10 /0.01 a 10 5A. We see that

the track is a string of beads with widely spaced track entities. Most of theoscillator strength is contained in the region 0 - 100 eV in water and this iswhere the glancing or "resonant" losses occur; we have defined the trackentities arising from these losses as "spurs."

Let us consider some of the chemical significance of a spur in water. Inthe early, prethermal processes (t < 10~ sec) the energy loss (~ 40 eV) isused in the creation of (on the average) 5 radicals located in a sphericalregion with radius 20-30 A. A period of diffusive expansion occurs in whichthese radicals react with or escape their siblings. The spur expansion isusually terminated by a scavenger reaction in, typically, 10-6 sec, at whichtime the radius of the spur is ~ /EDt ~ 900 A. We see that spurs initiallyseparated by 4000 A are very much isolated for the entire time.

121

The knocked-out electrons form track entities which in the case of low-

LET radiations normally develop in isolation. Clearly we can make generalstatements about the radiation chemistry of Suh systems and this situationhas been considered by Magee and Chatterjee. 0 '' It is also clear that theknocked-out electrons which have a range of energy from 100 eV to a maximumvalue of perhaps 1 MeV form tracks which have widely varied natures. If the

energy is not much over 100 eV, single track entities are formed and althoughthey behave very much like spurs they are different 0rom spurs and we have

called them "blobs." According to the definition, ' a "blob" is generated bya knocked-out electron which has insufficient energy to escape the attractionof its sibling hole despite some screening offered by intermediate ionizationprocesses. It is estimated from the Onsager relation that in water at roomtemperature the distance for an a 1 probability of escape is 180 A. Theenergy of2 a2 electron with this range in water is ~ 625 eV; however, Mozumderand Magee2' round off the maximum energy in a blob at 500 eV.

Knocked-out electrons with energies above 500 eV form tracks, and we callthem "short tracks." We do not use "delta rays" in this microscopicdescription o the track. We have considered the upper energy limit for ashort track2 , and on the basis that at 5 keV such a short track is perhaps

beginning to have isolated spurs near its origin, we took this value (5 keV)as the upper limit. Of course knocked-out electrons with energy greater than5 keV form branch tracks which, in turn, are composed of spurs, blobs andshort tracks.

In summary, the following energy deposition criteria for the 3 trackentities can be given: spur, 6 - 100 eV; blob, ~ 100 - 500 eV; short track,

500 eV - 5 keV. Of course, it is clear that demarcations are not sharp andthat there is in fact a continuous distribution in energy of ejected

electrons. The most important entity is the spur; about half of the energy isused up in creating spurs. The short track is perhaps the entity next inimportance. All low-LET radiations are recognized to contain high-LET regionsand the short tracks are responsible for them. The blob is a transition

entity defined as we have indicated because there are energy losses betweenthose responsible for spur and for short track. Little use has actually beenmade of blobs in track models.

References and Notes

1. A. Mozumder, in Advances in Radiation Chemistry (M. Burton and J. L.

Magee, Eds.), Vol. 1, pp. 1-102. Wiley-Interscience, New York, 1969.

2. A. Mozumder and J. L. Magee, Rad. Res. 28, 203-214 (1966).

3. A. Mozumder and J. L. Magee, Rad. Res. 28, 215-231 (1966).

4. A. Mozumder and J. L. Magee, VII. J. Chem. Phys. 45, 3332-3341 (1966).

5. Such a proton would have an energy of 1 GeV; the electron would have an

energy of ~-1 MeV.

6. J. L. Magee and A. Chatterjee, J. Phys. Chem. 82, 2219-2226 (1978).

7. J. L. Magee and A. Chatterjee, Radiat. Phys. and Chem. 15, 125-132 (1980).

122

What Is a Spur?

C. N. Trumbore

In the first session of this Workshop I described our approach to fittingexperimental radiation chemical data to a "spur" model. My own definition of aspur is an operational one, namely that arising from the unique shape of a radia-tion chemical yield vs. log scavenger concentration curve. In a typical curve,illustrated schematically in Fig. 1,

1.0

0.8

-* 0.6N

~0.4

0.2

0.010 10-3 10-2 10"'

[S]xf

Figue 1. T ypZcal Piot o Moecu at Pkoduc t YieCd (H2 ) az aFunction o6 H2 PLecwiuoL Scavenger Concent 'ton.

expvehimenta2 data; - - - anticipated nebuLt 6 pile-cwrso's were easen aLZy homog eneoulyq dZitibw ted.Otdina.te - tad a-tcion yield o6 H2 'LeLalive to the H2 yce2dat zero concevtLaution o6 H2 pnecwuttoL 6cavengen. Abc c sa -Zog o6 e6a6ecive caveng4ng powve o6 H2 p'eccvux (pkod-UCt 06 'Late constant 6o 6caveng tng time4 no'[ma&.zaton6acto4, ,)).

the solid line represents typical experimental results and clearly demonstratesthat the precursors are distributed in a nonhomogeneous fashion. These andother curves, illustrating the sensitivity of various radiation yields to theconcentration of solutes which react with track or spur intermediates, are theraw data which must be fit by any track or spur modelling effort. Such concen-tration dependence curves and the hydrated electron decay curves we showed in

our paper are examples of data which contain information regarding "fine grain"

123

N

Ifwo

-5 10- 4

-I

- \

-N

1.0 10

1 m 1

details of track structure. Low reactive solute concentration (e.g. ~10-3 Mor less) or late time (~10-8 sec. and beyond) pulse radiolysis studies lackthe resolution necessary to model or even predict relatively early physical orchemical processes in the track or spur.

I was interested to note that the three-dimensional track structurecalculations shown by the Oak Ridge and Berkeley groups in this workshop wereon a relatively large scale. In their previously published work (Proceed. ofVII Symp. on Microdosimetry, Sept. 8-12, 1980, Oxford, U. K.; Ed., J. Booz,H. G. Ebert and H. Hartfield, Harwood Academic Publishers, N. Y. p. 507) thereis a Figure 2 reproduced below which is on a much smaller scale than those shownin this Workshop. The following observations regarding this Figure have somerelevance to the discussions of this Workshop: (1) The spurs in this figurecan be seen as localized clusters of intermediates. In the center of this figurethere is one large cluster representing approximately six to seven ionizationsand a number of smaller clusters, representing one or two ionizations. (2) Inthe large cluster in the center of Figure 2 it appears as though the hydrated

R "

It O

50 A'

Figwte 2. Stow-up o6 Initiat PoMt.on o6 5 kev Etect'on Tuckat 10-114. ( Fig. 3 6nom te6erence cited in text. Repno -duced by peAnmiaion. ) e H; X e- ; A OH; * H3 0+.

aq

124

electron density is on the periphery of the center of the cluster and isoutwardly displaced with respect to the density of hydroxyl and hydrogenions in agreement with our model. Many more such regions from electrontracks of this energy (5 keV) and higher energy must be examined before anyconclusions may be drawn regarding average behavior. However, the resultsshown in Figure 2 when added to less highly magnified details of the calcula-tions shown in this Workshop by Wright, Turner and their colleagues lead meto believe that the basic ideas of Mozumder and Magee are at least in goodqualitative agreement with these track calculations. This is illustratedespecially clearly in Figure 3 of the paper in this Workshop (Wright et al.).At 10-11 seconds the short tracks and branch tracks are clearly visible. At2.8 x 10 seconds expanding blobs are visible and there are clearly discernableregions of high and low spur density. More detail at higher resolucion and instereoprojection is needed to clarify the nature of the spatial distribution ofthe radiation chemical intermediates.

125

THE PHYSICO-CHEMICAL STAGE: 10-1 6 - 10-12 SECOND

J. L. Magee and A. ChatterjeeBiomedical Division, Lawrence Berkeley Laboratory

University of California, Berkeley, California 94720

At the present time the only information on the physico-chemical stagecomes from theoretical considerations and speculations and from interpretationof chemical experiments which are not time-resolved. It would appear to beimpossible to penetrate the pico-second barriers using pulse radiolysis orlaser techniques. This situation has been discussed by Mozumder and Magee.'

The radiation physicist can help the radiation chemist by trying his handat giving the initial conditions for the chemical species at 10 sec. Thenature of the problem can be seen from examination of the papers by Turner etal.2'3 and Wright et al.4 It is clear that space, time, energy and speciesare involved in very complicated ways, and there are many hierarchies ofproblems. The attempt has been made by Turner, Wright et al. to bull theirway through the problem to look at it as a whole. Physicists are invited toreexamine all the assumptions and to make improvements wherever they can. Itappears that we may have a roughly valid description of the physico-chemicalstage, but this may be an illusion.

One thing we learn from the Monte Carlo treatment is that tracks (of a 5-keV electron, for example) may have widely varied shapes. Most track modelcalculations use simple forms for tracks (see Ref. 5). One important problemis to understand the statistical properties of tracks and how chemical yieldsdepend on them.

Physicists have studied electron impact processes in the gas phase andhave tried to predict the changes to be expected for the same processes in

condensed phases. We are interested in things which are more difficult toobtain. We want to know the locations of all spec:t es created by an energetic

particle (electron, say) which is stopped in a condensed phase. There arethree parts of the problem: excited states and their behavior; ionizedelectrons; and ions.

All states created by a fast particle in the condensed phase are wave-packet states. An excited molecular state M , for example, is notlocalized. If it dissociates, M + A + B, the products A and B arelocalized. The problem is to say what kinds of dissociations occur and whatthe distribution in space of the products is.

An ionized electron becomes a subexcitation electron in 10-15 sec or lesstime. How does it get thermalized nd hydrated? Of course some of them arerecaptured by positive ions. Magee has concluded that in water the hydration

time must be the same as the longitudinal relaxation time, 4 x 10 sec. Healso says that the most important parameter in determining the spatialdistribution of hydrated electrons is the transport mean free path of thesubexcitation electron.

Positive ion states are important and very little has been done in thisfield. Such states, of course, are not localized. On general theoretical

126

grounds we expect that many excited positive ions should be formed.Dissociation processes and ion molecule reactions should usually occur. Inwater, for example, we say that the reaction of H20+ + RIO -- H3 0+ + OH occursin the vibration time of a water molecule. Some theoretical considerationshave been made by Kalarickal 7 and Lorquet8 and they support the assumptions weusually make, but we cannot claim any real progress here. After rigorouscalculations of potential functions of gaseous ions are available, effects ofthe condensed state must be incorporated into the considerations.

Turner et al.2 have made a coherent picture of the physico-chemical stageand presented a set of recipes to use with a Monte arlo calculation andobtain a distribution of radiation products at 10~ sec. Radiation

physicists are invited to improve this picture at any point.

A systematic method for studying the prethermal period (time < 10~11 sec)is the use of experimental radiation chemical results obtained at long timesand an interpretation in terms of theoretical concepts of the phlsico-chemicaltime period. Hamill and associates 9 -11 and Hunt and associates have madevery interesting studies using this technique. For example, smallconcentrations of molecules which will accept a positive charge from H2 0+ orcapture a prethermal electron, change the course of the early reactions andthus cause changes which can be measured without time resolved techniques.(Actually Hunt used pulse radiolysis, but his observations were only in thet > 10~1 sec time scale and time resolution was not the important point).These experiments are interpreted in the framework of track formation by meansof a series of processes in the physico-chemical stage which have prethermalspecies undergoing reactions which can be altered by additives.

A kind of theoretical framework for the physico-chemical stage which has

been more or less static for ten years or more exists. Physicists can dig inanywhere and give the chemists a hand.

127

References

1. A. Mozumder and J. L. Magee, Int. J. Rad. Phys. Chem. 7, 83-93 (1975).

2. T. E. Turner, J. L. Magee, R. N. Hamm, A. Chatterjee, H. A. Wright, andR. H. Ritchie, in Proceedings of the Seventh Symposium on Microdosimetry,Oxford, U.K., September 8-12, 1980, pp. 507-517, Commission of theEuropean Communities, Brussels, 1980.

3. J. E. Turner, J. L. Magee, H. A. Wright, A. Chatterjee, R. N. Hamm and R.H. Ritchie, Rad. Res., forthcoming.

4. H. A. Wright, J. E. Turner, R. N. Hamm, R. H. Ritchie, J. L. Magee and A.Chatterjee, in Proceedir gs of the Eighth Symposium on Microdosimetry,Julich, W. Germany, September 27-October 1, 1982. Forthcoming.

5. J. L. Magee an A. Chatterjee, J. Phys. Chem. 82, 2219-2226 (1978).

6. J. L. Magee, Can. J. Chem. 55, 1847-1859 (1977).

7. S. Kalarickal, thesis, Department of Chemistry, University of Notre Dame,1959.

8. A. J. Lorquet an J. C. Lorquet, Chem. Phys. 4, 353-367 (1974). Theseauthors and their collaborators have a large number of papers on ions,their properties and their behavior.

9. W. H. Hamill, J. Phys. Chem. 73, 1341-1347 (1969).

10. T. Sawai and W. H. Hamill, J. Phys. Chem. 74, 3914-3924 (1970).

11. H. Ogura and W. H. Hamill, J. Phys. Chem. 77, 2952-2954 (1973).

12. J. W. Hunt, in Advances in Radiation Chemistry (M. Burton and J. L.Magee, Eds.), Vol. 5, pp. 185-315. Wiley-Interscience, New York, 1976.

128

COMMENT ON THE POSSIBILITY OF SECURING EXPERIMENTAL DATA FOR

VERY SHORT TIMES AND THE DETERMiNATION OF INITIAL YIELDS*

William Prinmak, C. J. Delbecq, and D. Y. Smith

Argonne National Laboratory

The shortest time resolution of effects of ionization based on chemicaltechniques reported here was from about 10-12 sec. The mobility of thechemical systems studied limited the shortest observable times to those whichcould be seen in pulsed radiation experiments. In solids there is thepossibility ttiat a state resulting from the action of radiation may be fixedin the system and then studied at some time thereafter; or, alternatively,that the subsequent changes may be slow enough that, through an investigationof their kinetics, an extrapolation can be made to determine primary yields.The possibility of doing this for the passage of a heavy particle is limitedbecause of the intense disorder along its path and the confusion of effectscaused by energetic secondary displacements. However, for the lightestparticles, protons, deuterons, and helium ions, for electrons, and forelectromagnetic radial. won, it should be possible to establish primary yieldsin suitable systems. Although it is usually believed that initial electronevents are concluded by about 10-16 sec-id events involving the slowing downof atomic particles in a fraction of 10 sec, the shortest tim s which areusually considered for solids are of the order of magnitude 10-1 sec. Thus,if initial products are truly frozen in, it should be possible to obtaininformation for times two orders of magnitude shorter than those reported forchemical systems.

For the number of displaced atoms, among materials which might be used toestablish yields, the first which comes to mind are the simple covalentcrystals like graphite and diamond. 1 ' 2 For ionizing events, perhaps more isknown about centers formed in alkali halides than for any other material.However, most of the work in this field has been directed toward determiningconfigurations rather than yields, a failing in most of the studies ofradiation effects in solids. It is known that even at very low temperatures,a problem which would arise in any attempt to determine yields would be therecombination of close pairs. Then, as the temperature is raised, subsequentevents occur along different paths resulting in the formation of a multi-plicity of centers through complex mechanisms.3 However, when certainimpurities are present in relatively high concentration (particularly Pb+ orAg , ~0.2 mole %), these will capture the emitted electron, and at tempera-tures below 80 K the complementary positive hole will be trapped in the orderof lattice vibration times as a Vk center (e.g., C12 in KCI:AgCl).4 Theresultant impurity centers, namely Ag0 , or the hole centers, can be countedwithout concern for the complications which in pure alkali halides would arisefrom the formation of other centers. The number of centers can be determinedby paramagnetic resonance measurements. There is an experimental complicationin that the magnetic measurements can be made only on small samples for which

the concentration of centers required may be so large that the yield will have

*Work supported by the U. S. Department of EnerLy.

129

begun to decrease because of recombination. However, it should be possible tocalibrate optical absorption measurements with the magnetic resonancemeasurements; and then, by using other, much larger samples, for opticalmeasurements, obtain the greater sensitivity which would be required to extendthe measurements to lower concentrations for the determination of initialyields.

At temperatures and in systems for which radiation-induced defects arenot frozen in frr long times, the temporary trapping of radiation products canbe studied optically using pulsed techniques. Time-resolved luminescence andabsorption measurements have been employed for some time to follow radiation-

induced processes in alkali-halide phosphors5,6 and defect formation in ionicsolids. 7 Recently, lattice configuration relaxation about defects has beeninvestigated8 on the picosecond time scale using laser techniqu s, and opticalpulses in the femtosecond regime (30-90 fs) have been achieved.

In the pure alkali halides, it appears that (see Ref. 5, 6, 10, 11)electron-hole pairs are produced either directly by processes such as Comptonscattering or indirectly by the decay of plasma excitations. The hole istrapped in the order of lattice vibration times by the formation of Vk centerswhile the electron moves in conduction band states losing kinetic energy by

scattering. At low temperatures, the Vk center is immobile and in purematerials electron-hole recombination occurs by the capture of the mobileelectron from near the bottom of the conduction band by Vk centers. Thisyields bound excitons which subsequently decay radiatively. At least in thealkali iodides this recombination process appears to take place with nearlyunit quantum efficiency. 1 2

In samples doped with heavy-metal impurities, the electrons, or holes (attemperat rg r which Vk centers are mobile) are trapped at theimpurity 4 ' and the radiative recombination occurs at the metalion.13, 4 however, the quantum efficiency of this process is stronglydependent on the ion in question.

In the case of the alkali halides where specific centers have beenidentified, and their quantities can be measured, it is possible to performkinetic studies for the particular species, just as in the case of chemicalsystems. In the case of other solids in which the radiation damage ismeasured by a change in a physical property, it is still possible to study thekinetics, but here contributions to the change are made by many different

configurations, and thus there is no discrete activation energy,15 and in manycases no discrete frequency factor. 1 6 17 However, the kinetics can yet beinvestigated, and hence an extrapolation can be made to initial conditions.Thus, even when configurations are not frozen in, it may be possible toestimate initial yields.

Chemical changes in solids irradiated at low temperatures could be usedto establish jgitial yields. Both inorganic and organic glasses have beeninvestigated. Other possibilities are nitrates, chromates, carbonates, andother crystalline materials. At one time it was thought that initial speciescould be "frozen in" in glasses at temperatures as high as liquid nitrogentemperatures, but it is now understood that even at very low temperatures,changes occur by tunnelling, and (as in alkali halides) the stabilization ofinitial products requires the presence of strong trapping sites.19'

2 0

130

REFERENCES

1. W. Primak, Phys. Rev., 103, 1681 (1956)2. W. Primak, L. H. Fuchs, and P. P. Day, Physa Rev. 103, 1184 (1956)3. W. A. Sibley and D. Pooley, "Treatise on Materials Science," H. Herman,

Ed., Academic Press (New York, 1974) Vol. 5, p. 454. C. J. Delbecq, W. Hayes, M. C. M. O'Brien, and P. H. Yuster, Proc. Roy.

Soc. A271, 243 (1963)5. W. Van Sciver, IRE Trans. Nuc. Sci., NS-3 [4] 39 (1956)6. W. J. Van Sciver and L. Bogart, IRE Trans. Nuc. Sci., NS-5 [3], 90

(1958)7. For a recent review, see: N. Itoh, in Defects in Insulating Crystals,

edited by V. M. Tuchkevich and K. K. Shvarts (Zinatne, Riga/Springer,Berlin, 1981) p. 343

8. J. M. Wiesenfeld, L. F. Mollenauer, and E. P. Ippen, Phys. Rev. Lett.47, 1668 (1981)

9. R. L. Fork, B. I. Greene, and C. V. Shank, Appl. Phys. Lett. 38, 671(1981); C. V. Shank, R. L. Fork, R. Yen, and R. H. Stolen, ibid., 40,761 (1982); and R. L. Fork, C. V. Shank, and R. T. Yen, ibid, 41, 223(1982)

10. R. B. Murray, IEEE Trans. Nuc. Sci. NS-22, 54 (1975)11. H. B. Dietrich, A. E. Purdy, R. B. Murray, and R. T. Williams, Phy.

Rev. B 8, 5894 (1975)12. The energy conversion efficiency of Nal is ~26% at liquid nitrogen

temperature (Ref. 6) and it is estimated that energies of from 3 to 4times the bandgap are required to produce an electron-hole pair (Ref.10), so that nearly all the electron-hole pairs must recombine toproduce exciton luminescence.

13. C. J. Delbecq, Y. Toyozawa, and P. H. Yuster, Phys. Rev. B 9, 4497(1974)

14. C. J. Delbecq, D. L. Dexter, and P. H. Yuster, Phys. Rev. B 17, 4765(1978)

15. W. Primak, Phys. Rev., 100, 1677 (1955)16. W. Primak, J. Appl. Phys., 3_1 1524 (1960)17. W. Primak, J. Appl. Phys., 50, 1286 (1979)18. "Radical Ions," E. T. Kaiser and L. Kevan, Eds., Wiley-Interscience

(New York, 1968)19. J. V. Beitz and J. R. Miller, J. Chem. Phys., 71, 4579 (1979)20. J. R. Miller and J. V. Beitz, J. Chem. Phys., 74, 6746 (1981)

ACKNOWLEDGEMENTS

We are indebted to Y.-K. Kim, M. Inokuti, L. F. Mollenauer, R. B. Murray,and J. R. Miller for advice in preparing this comment.

131

Comments on Subexcitation Electrons

Robert J. HanrahanChemistry Department

University of FloridaGainesville, FL 32611

The topic, or concept, of subexcitation electrons was mentioned severaltimes during the conference. This concept also came in for discussion at theGordon Conference on Radiation Chemistry, held in the summer of 1982. Certainlyone can have no objection if the term "subexcitation electrons" merely serves toidentify a portion of the secondary electron population distribution,specifically the population of electrons with energies less than ca. 4-6 eV intypical systems. It is suggested, however, that the term is usually used in thesense or from the viewpoint introduced somn. years ago by Dr. Robert Platzman -that is, there is an implicit assumption that such electrons are of specialimportance because of a presumed long lifetime in the medium. This viewpointhas been challenged vigorously by L.G. Christophorou, particularly in his book"Atomic and Mol cular Radiation Physics" published some twelve years ago (Wiley- Interscience, London, 1971). Relying on theoretical arguments as well asexperimental data from the Radiation Physics group at Oak Ridge Laboratory(taken by Compton and others), Christophorou argues (cf. for example pp 189-190)that the assumed inefficiency of energy loss for subexcitation electrons in mosttypical systems (including, for example, water or hydrocarbons) is nonexistent.The reason is that there is an efficient energy loss channel involving transientnegative ion states, which operates for large classes of molecules ofexperimental interest, with a few exceptions, notably the rare gases. IfChristophorou is right, then the selective funneling of substantial amounts ofenergy (and subsequent radiation effect) into a minor constituent in a mixturewill generally occur only if the major constituent is something of specialproperties, such as a rare gas.

The above comments do not argue against the possibility of a low-yieldprocess involving low energy electrons, particularly if the process involves thesubstrate itself. In view of the special importance of water in much of thework described at this Conference, it is of interest that there may indeed besuch a process which is of significance in water radiolysis. In particular, ithas been known for many years that the dissociative electron attachment processoccurs in water vapor with reasonable efficiency, and with an energy thresholdof only 5.6 eV.

e + H2O H + OH (1)

(A good discussion is given by R.I. Reed in "Ion Production by Electron Impact",Academic Press, 1962. The existence of this reaction is noted in Fig. 1 of thepaper by A.E.S. Green and D.E. Rio in these Proceedings.) It is of interest thatthe products of Reaction (1) are not hydrogen atom plus hydroxide ion; Reedmakes a considerable point of the fact that the latter process is not seen undergas phase electron impact conditions.

If hydride ion is formed via Reaction (1) in either the liquid or gasphase, it would presumably be precursor to molecular hydrogen via the very fastproton transfer process

H + H2O- H + OH (2)2 2

132

The maximum contribution of this process would presumably be limited by thevalue of the "molecular" H2 yield in liquid water, which has been assigned avalue of about 0.4 (Spinks and Woods, 1964). Its actual yield would appear tobe even lower, since there are other known routes to H formation.Nevertheless, a tantalizing hint that processes (1) and (2 may indeedcontribute to the radiolysis of liquid (and presumably also gaseous) water isfound in the paper on water radiolysis modeling calculations given by Trumboreand Youngblade at this conference. They note that

"One of the supposed failures of the classical spur model is its inabilityto fit the scavenging curves of the molecular products H and H202'Calculations .... generally err on the side of overly efficien scavengingof the molecular product precursors..." "...success (by Schwartz) inmodeling molecular product yields ... was dependent on assuming an initialyield of H2 .

It is suggested that the mechanism of the "initial yield of H2" assumed bySchwattz is, in fact, Reactions (1) and (2).

133

A SELECTION OF PROBLEMS IN RADIATION PHYSICS AND CHEMISTRY

Daryl A. Douthat, Departments of Physics and Chemistry, The University ofAlaska, Anchorage, 3221 Providence Drive, Anchorage, Alaska 99508

In the spirit of the discussions of the ANL 1982 Workshop on theInterface Between Radiation Chemistry and Physics, I wish to comment brieflyon some problems in radiation physics and chemistry that I feel meritattention in the near future. These problems are familiar to many Workshopparticipants and I am indebted to several attendees for sharing their ownperspectives over the past several years.

While the eventual aim of radiation physics and chemistry is toelucidate the response of complex systems--including those in the condensedphase--to ionizing radiation, I think there is still much to be gained bystudying gases. For the gas phase a large body of cross-section data nowexists. Furthermore, there are apparently no ambiguities for gases such asthe definition of ionization in condensed matter. Hence, gas phase studiesare especially appropriate for the development of new theoretical methods aswell as for sensitivity analysis and serve to emphasize areas where theoryand experiment require improvement. Gas-phase calculations have alreadyprovided some guidelines. It is now known, for example, that preciseknowledge of the total ionization cross section Qi(T) is more important thanprecise knowledge of the shape of the secondary electron ejectioncross-section in the calculation of primary yields 1. Since measured valuesof Qi(T) differ by about 20%, remeasurement of Qi(T) would be very desirable.At the same time, it is important to confirm the existing cross-section datafor secondary electron ejection and to extend the data over a wider range ofincident and ejected energies with simultaneous determination of the state ofthe remaining ion.

Only limited contact now exists between transport theory andexperiment. Calculations usually provide some init al yields, including themean energy per ion pair W. Gas-phase calculations have shown thatcalculated values of W are rather sensitive to cross-section input. However,most calculations employ data that are refined only until calculated andobserved W values agree. Consequently comparison of theory and experimentcan be misleading even for the gas phase if, e.g., collateral ionization issignificant. As Inokuti has emphasized2, comparison of calculated andexperimental ion yields for condensed materials requires knowledge of thedecay process of collective excitations. The measurements of degradationspectra in solids performed by Birkhoff and co-workers3 are important, butextension to other phases has not been achieved, and the difference betweentheory and experiment at spectral energies of a few hundred eV remains to beresolved.

One means of testing the primary yields from transport calculationsis that of resonant ionization spectroscopy (RIS). Although RIS wasdeveloped initially4 ,5 to measure primary yields in irradiated atomic gases,initial yield data apparently exists only for helium gas bombarded byprotons. Theoretical yields can now be calculated for excited states ofother irradiated noble gases, and comparison with experiment would be veryuseful.

134

While calculations of primary yields are a first step, knowledge oftheir spatial distribution may also be required for many problems , and trackstructure theory has attempted to provide an appropriate vocabulary. In viewof the considerable debate over the utility of the usual terminology--blobs,spurs, etc.,--it may be worthwhile to emphasize (following Fano7) thateventually one would like as the starting point for further calculation thecorrelation function for the formation of reactive species. In view of thedetailed results emerging from Monte-Carlo codes8-10, this seems to be a moreaccessible goal today than it was when proposed a decade ago.

Another unsolved problem is that of mixtures. Detailed calculationsexist for airll as well as for instellar molecular clouds12. We are nowcapable of performing calculations of primary yields in irradiated mixturesof simple gases and investigating the consequences of varying mole fractions.Okazaki and co-workers13 have employed binary collision cross-sections in apilot study of noble gas mixtures. A calculation should be done with morereliable cross-sections for a benchmark mixture such as He and H2.

Several calculations now exist for water vapor and liquid water8-10 .It seems to be generally agreed that, expecially for the liquid, furthersensitivity testing is required to establish the predictive ability of thecalculations. Gas-phase studies indicate that sensitivity testing shouldinclude: (1) variation of the shape of the cross-section for secondaryelectron ejection at incident energies below a few hundred eV, (2) variationof the ratio of the total ionization cross section to the total inelasticcross-section, (3) the effect of extrapolating the Born approximation to lowenergies, (4) the effect of uncertainty in the lowest ionization potential,(5) exploration of the consequences of various plasmon decay modes. It wouldalso be very helpful if additional constraints were available for condensedphase scattering data. In this respect, the studies of Sanche14 andco-workers on the transmission of low energy electrons through thin films areuseful. Another approach is that of charged-particle scattering by clustersof molecules. This second approach has not yet produced decisive data.

Further exploitation of optical data is also possible for liquids.For example, the subexcitation electron stopping power is important indetermining the spatial distribution of ions and hydrated electrons in liquidwater. Frlich and Platzman15 obtained an estimate of the contribution ofdipolar relaxation to the subexcitation stopping power but the contributionof the vibrational modes apparently has not been determined for liquid water.The infrared data of Bayly et a1 16 can be used in the context of theFri5lich-Platzman method to estimate this contribution.

I wish also to comment on the question of time scales. It oftenseems implicit in discussion that the various temporal stages in Platzman'sclassification are sharply separated. In fact, as Platzman emphasized, thereis likely to be considerable overlap of at least the physical andphysico-chemical stage. This implies that the time dependence of initialyields is likely to be important. As an example, calculation of the timedependence of the yields of vibrational and rotational excitations in H2 gaswould be useful. This calculation is now possible and such information mayprove more useful than related quantities such as the time required forelectron thermalization.

135

References:

1. D.A. Douthat, J. Phys. B 12, 663 (1979).2. M. Inokuti, in Applications of Atomic Collision Physics Vol. IV.

Condensed Matter, ed. H.S.W. Massey, B. Bederson, and E. W. McDaniel(Academic Press, New York), in press.

3. R.D. Birkhoff, in Penetration of Charged Particles in Mater: ASymposium, National Academy of Sciences, Washington, D.C., 1970, p.1.

4. G.S. Hurst, M.G. Payne, M.H. Nayfeh, J.P. Judish, and E.B. Wagner, Phys.Rev. Lett. 35, 82 (1975).

5. M.G. Payne, G.S. Hurst, M.H. Nayfeh, J.P. Judish, C.H. Chen, E.B. Wagner,and J.P. Young, Phys. Rev. Lett. 35, 1154 (1975).

6. D.T. Goodhead, J.Thacker, and R. Cox, in Proceedings of the SixthSymposium on Microdosimetry, Harwood Academic Publishers, Ltd. (London),1978, p.8.

7. U. Fano, in Charged Particle Tracks in solids and Liquids. Proceedingsof the Second L.H. Gray Conference, U.K., April 1969, The Institute ofPhysics, London.

8. H.G. Paretzke and M.J. Berger, in Proceedings of the Sixth Symposium onMicrodosimetry, Harwood Academic Publishers, Ltd.~(London), 1978, p.749.

9. M. Terrisol, J.P. Patau, and T. Edualdo, in Proceedings of the SixthSymposium on Microdosimetry, Harwood Academic Publishers, Ltd. Thondon),1978, p. 169.

10. R.N. Hamm, H.A. Wright, R.H. Ritchie, J.E. Turner, and T. P. Turner, inProceedings of the Fifth Symposium on Microdosimetry, Verbania-Pallanza,Commission of the European Committee, Luxembourg, 1976, p. 1037

11. B. Grooswendt and E. Waibel, Nucl. Inst. and Methods, 155, 145 (1978).12. A.E. Glassgold and W.D. Langer, Ap. J. 193, 73 (1974).13. K. Okazaki, E. Oku, and S. Sato, Bull. Chem. Soc. Jpn. 49, 1230 (1976).14. L. Sanche, G. Bader, and L. Caron, J. Chem. Phys. 76, 4016 (1982).15. H. Frlich and R.L. Platzman, Phys. Rev. 92, 1152 (1953).16. J.G. Bayly, V.B. Kartha, and W.H. Stevens, Infrared Phys. 3, 211 (1963).

136

Tuesday, October 26, 1982, AM

G. R. Freeman (communicated):

Dr. Inokuti and Prof. Fano have commented that the schematic energydiagrams in Figures 8 and 9 seem to ignore the de Broglie parameter X/27,which would be 0.6 nm for a 0.1 eV electron and too large to correlate withan interstitial cavity in a liquid. A low energy electron would sensefluctuations over such short distances only by wave mechanical averaging.That is the basis of the pseudopotential treatment (Cohen & Lekner, Rice &co.) of thermal electrons in liquids. However, the general nature of theenergy diagrams in Figures 8 and 9 would not be altered. Electron mobilityand thermalization range data (Figs. 5-7) indicate that the magnitudes ofthe potential fluctuations increase with decreasing degree of sphericityof nonpolar molecules, and the fluctuations increase further for stronglypolar molecules. Figure 9 provides a useful visualization of the approachof an electron to the localized state. Figure 18 is a less schematicrepresentation of the charge distribution in a localized state.

It would be helpful if theoreticians would attack the problems depictedin Figures 8 and 9 by calculating electron potential fluctuations as afunction of position in liquids. The fluctuations would be functions ofelectron energy and molecular shape (one could begin with the anisotropy ofpolarizability). A next step would be to estimate electron-medium energyexchange parameters that would permit the estimation of electron thermalizationranges, say from 1.0 eV to the localization event, and thermal electronmobilities in different liquids.

137

HOW RADIATION CHEMISTRY CAN HELP UNDERSTAND PRIMARYPROCESSES IN THE ENERGY DEPOSITION PROCESS

Charles D. JonahArgonne National Laboratory, Argonne, Illinois 60439

By definition, radiation chemistry is only concerned with and onlymeasures events on a chemical time scale; however, the state of the systemat times greater than a picosecond depends on what has occurred at earliertimes. It is because of this fact one can extract information about ear-lier processes from radiation-chemical experiments.

One of the major uncertainties in the pre-chemical period is thetravel of the electron prior to thermalization. The motion requires anunderstanding of the sub-eV scattering processes in a liquid; a non-trivialundertaking. The "initial" distribution of ions (at the beginning ofchemical times) will depend on the motion of the electron in the thermali-zation processes. While the distribution cannot be determined directly,chemical kinetics can provide tests. For instance, Schwarz' derived adiffusion-kinetic process and assumed spatial distribution functions ofapproximately 6.2 A and 18 A for the OH and electron respectively, inwater. Measurements by Hunt2 and ourselves3 showed that the decay of thehydrated electron was an order of magnitude slower than that predicted bythe model. In polar media, there is little effect of the coulombic attrac-tion, and the dominant process is diffusion. Diffusion is not sensitive tothe exact form of the distribution function. In non-polar media, recombi-nation kinetics depend much more on the distribution function as can beseen in figure 1 from Van den Ende et. al. 4"

Fran: Vn den Ende. Nylkos, rMson , 9iwel20 Rodlot. Phvs. Chen. 15, 273 (1980)

0.33

uss Figure 1. Theoretical depen-dence of the time dependenceof a gemirate ion pair(W(T)/W(o)) as a function of

W()dimensionlesstime T. T =

10-' Dt/ rc 2 where D is the diffu-.--0 sion constant, t is time and

1- .--"rc is Onsager capture radius.-" Gauss is for a gaussian dis-

tribution of ions, exp for an0.50 exponential distribution of

ions, and .33 and .50 are for5- .delta function distributions

of .33 and .50 of rc.

L _ _ ..00 5 10 15

138

Figure 2 shows an experimental determination of recombination times(Jonah). It is clear, then, that radiation chemistry, while unable todetermine the distribution of ions, can act as a sensitive test for distri-butions. Similarly, the experimental data also act as a test for anytheory which will attempt to predict the spatial evolution of the electron.

Chemical evolution in the "pre-chemical" times may also be inferred.The reactions of the precursor of the solvated electron in polar media havebeen observed 5 7. The form of the kinetics, and the temperature and solventdependence may be interpreted to give information about the state of theelectron which is reacting. This, therefore, would mean that such a statedoes exist in the energy degradation chain. Unfortunately, while much datahave been collected, little have been analyzed with this goal.

In the next several years I see radiation chemistry rediscovering andreanalyzing much of the data on electron precursor reactions. From theseexperiments, information about the states of the electron can be inferred.The major studies in hydrocarbons will be concerned with ion recombinationlifetimes and from those lifetimes, inferring information about thermaliza-tion distances. The role of excited states in the energy deposition pro-cess will be explored with aromatic hydrocarbons. One important new tech-nique will be photoionization using far UV lasers. This will allow well-defined electron energies and thus more specific thermalization distancesmay be obtainable. In addition, shorter pulses will be possible with theselasers.

I//T

100 I 2 3 4 5 6 7 8 9

8- 0 Figure 2: Experiment-al data for thedecay of the positive

6- o0 ion in n-hexane00 measured at 600 nm.

090 The X's and 0's are4 x for two different

experiments, one 1' nsec full scale, the

2 x other 4 nsec fullscale. The data on

X the two runs were

not normalized toeach other.

.02 .04 .06 .08 .10 .12 .14(it 1012) 1/2

139

REFERENCES

1. H. A. Schwarz, J. Phys. Chem. 73, 1928 (1969).2. J. W. Hunt, R. K. Wolff, M. J. Bronskill, C. D. Jonah, E. J. Hunt, and

M. S. Matheson J. Phys. Chem. 77, 425 (1973).3. C. D. Jonah, M. S. Matheson, J. R. Miller and E. J. Hart J. Phys. Chem.

80, 1267 (1976).4. C. A. M. van den Ende, L. Nyikos, J. M. Warman and A. Hummel Radiat.

Phys. Chem. 15, 273 (1980).5. K. Y. Lam and~J. W. Hunt, Int. J. Radiat, Phys. Chem. 7, 317 (1975).6. H. Ogura and W. H. Hamill, J. Phys. Chem. 78, 504 (1974).7. C. D. Jonah, J. R. Miller and M. S. Matheson 81, 1618 (1977).

140

Is the Fricke Dosimeter a 1-Hit Detector

Robert Katz, University of Nebraska, Lincoln NE 68588

To a non-chemist the explanations of radiation chemistry aresomewhat baffling. There is evidently a set of agreements and con-ventions well accepted by chemists but not known to others. Thereis an array of reactions, reaction rates, diffusion coefficients,blobs, spurs, short tracks, cores, and clouds. One does not knowwhat has been neglected and with what justification. I recall someskeptical remarks by Platzman (1) so that the difficulties are notonly for non-chemists. Nevertheless the approach is a detailedelectron by electron, step by step, analysis of the problem Thisis a different approach than that of track physics, in which a detec-tor is parameterized in a deliberate attempt to avoid detail.

In dealing with the response of the Fricke dosimeter to heavyions we should consider the approach of track theory, attempting tomake some order out of an otherwise confusing picture with a mini-mal number of concepts and parameters, all clearly expressed in oper-ational terms though usually not well connected to the microscopicdetail of electron interaction with the molecules of the detector.It would be useful to the non-chemist if chemical models of radiationchemistry enumerated clearly the number of fitted parameters. Onegets the impression that there are many more than two, but it hasbeen difficult to get a clearly enumerated statement. The tracktheory model of the 1-hit detector requires 2 fitted parameters, Eothe dose at which the response is reduced by l/e, and a0 , the radiusof the sensitive target. We require that the response of the detectorto dose be exponential. The Fricke dosimeter satisfies this condition.We require that the response declines with an increase in z2/S2 ofthe bombarding ions. The Fricke dosimeter satisfies this condition.We expect that response plots more smoothly as a function of z2/S2

than as a function of LET. The Fricke dosimeter meets this expect-ation. We shall see that at least some of the available data arereasonably well fitted by the model. For the present we make noattempt to fit the decline in yield with a decline in initial energyof bombarding electrons and photons, below 100 keV, taking this tobe a small effect in comparison with the decline in yield with LET.

According to track theory we may take the probability for affect-ing a sensitive element (leading to the observed end-point) asP = (1-exp D/Eo) where D is the dose of gamma rays (or delta rays)and Eo is the characteristic dose at which there is an average of1 hit per sensitive element. We take the radius of the element tobe a0 , accepting that size may reflect diffusion distance. To findthe action cross-section we make use of the radial distribution oflocal dose from delta rays to find the radial distribution in activa-tion probability, and then integrate radially about the ions path tofind the action cross-section. For gamma-rays the radiosensitivityis l/Eo. For heavy ions the radiosensitivity is LET/a. The yieldis taken to be proportional to the radiosensitivity. Then a singleset of parameters, and a single constant of proportionality, mustyield agreement with all experimental data, including Febetron pulses,heavy ions, and neutrons (?). When irradiated with electron pulses

141

for times short compared to the "characteristic time" oelement the yield must decline exponentially with dosethe same value of E. as has been fitted to the high LETin Fig. 1 is a plot of the ratio of G values for normalradiations (3,4) plotted against the dose per pulse, asthe prediction of the 1-hit model. The decline in yielwith dose, as characterized by the numerical values ofted and deaerated Fricke dosimeters found for high LETwe show the yield of the aerated Fricke dosimeter, withcurves from track theory superimposed on the experimentShuler and Allen, plotted as a function of the initialof D, He, and C ions used in the bombardment. For thethe cross-sections have been integrated along the ion's

f the sensitiveper pulse withdata. Shownand pulsed ir-compared to

d is exponentiaE. for the aeradata. In Fiq.2the fitted

al data ofkinetic energycalculationpath.

These fits were made some years ago. We have not taken theopportunity to examine the newer data. But based on these fits toa reasonably well established model of detector response, it seemsthat an attempt should be made to connect the track structure modelwith that of radiation chemistry. Can radiation chemistry providean explanation for the fact that the 1-hit detector concept providesa good fit to the experimental data ? Can it explain the numericalvalues of its parameters? Can radiation chemistry tell us what tracktheory means, in the Fricke dosimeter, by the sensitive element of60A radius? Or by a characteristic time?

References:

(1) Platzman, R(1974), R.D

(2) Katz, R., S13 (1972).

(3) Sehestad, KJour. Chem.

(4) Hart, E. J.

2.0

02

200 .00ILONAAM / PUJLSE

Fig. 1. Linesthe parameters

remarks in Physical Mechanisms inCooper and R.W. Wood, eds., USAEC.C. Sharma and M. Homayoonfar, Nucl.

Radiation Biology,

Instr. Meth. 100

., E. Bjergbakke, 0. L. Rasmussen, and H. Fricke,Phys. 51, 3159 (1969).in Proc. Int. Conf. NLABS, (1963).

600

are drawnfitted to

AERATED FRICXr DOSIMETER

S

.o -

7ff

fromFig. 2

EXTENDED TARGET o, .601 D S 1 e

0

.. "

-J

.4

d ., rIA 3 ALLEN 0'5'

" w S..I&ER end ALLEN

.a - ... E- 96'

- , 10 .0 'SC E b0 ET 0 ICINA . .N444 EERG. r%

Fig. 2. Lines are calculfrom track theory for a 1detector, with parametersto these data.

ated-hitfitted

for the aerated case

142

1

FRICKE DOSIMETER

a DF(d0orat.d). l00Okioroo W~(o~rot.O). 500 Mocas

1

The Special Nature of Water

C. N. Trumbore

A number of comments have been made during the Workshop regarding thedesperate attention paid to liquid water. Appropriately, the defense has beenmade that water is an obviously important biological fluid. However, I wouldlike to add that water is also a liquid with a unique structure in that eachwater molecule is capable of forming two relatively strong hydrogen bonds totwo other water molecules. Presumably because of its three-dimensional struc-ture water has a number of unique physical properties besides the well-knownmaximum density at 4*C.1

Therefore I believe that radiation physicists and chemists need to takeinto account the possibly unique quantum mechanical nature of liquid waterwhich has just been exposed to the passage of a high energy electron. It isnot a single water molecule which is ionized at 10-1 6 s but is probably a groupof "n"antum mechanically coupled water solutions which during this time periodmay have a relatively ordered structure, at least in certain regions. Thephysical problem is: what is the fate of the newly created electron and holepair? Could the "dry" electron move in conduction bands formed through thequantum mechanical coupling of many water molecules? What is the effect of adopar.t (solute) at low and high concentrations on the fate of the electron andhole pair. It has been postulated that there are structure-making and structure-breaking solutes.1 Little is known about the effects of these solutes on thelong range order of water during the critical time period from 10-16 to 10-11second. The known scavenging of the precursors of the hydrated electron at highsolute concentrations might be attributable to alteration of the local waterstructure. It is possible that at concentrations of solutes where the activitycoefficient of water is different from unity the nature of the primary radiationphysical process may be different from dilute aqueous solutions because ofalterations in the nature of the quantum mechanical binding of water molecules.For example, in biopolymers the nature of the water hydration layer on the sur-face of the biopolymers is apparently different from that of bulk water.

Since the structure of pure liquid water itself is far from settled'there would appear to be many unsolved problems in the theoretical treatment ofthe interaction of radiation with this interesting liquid. For example, is itappropriate to apply to the liquid phase the very large cross section in thegas phase for proton transfer from H20+ to H20 to give the hydrated proton andthe OH radical? Does the positive hole in liquid water perhaps have a longerlifetime in the liquid than in tha gas phase? The application of new data from

1iguid water reported by Painter is this Workshop is certainly a welcome addi-tion for the above stated reasons.

1. F. Franks, Water: A Comprehensive Treatise, Plenum Press, New York, 1972.

143

144

List of Participants in the Workshop on theInterface Between Radiation Chemistry and Radiation Physics

Argonne National Laboratory, 9-10 September 1982

Dr. Pierre AusloosNational Bureau of StandardsWashington, D.C. 20234

Dr. Dave BartelsChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Martin J. Berger

National Bureau of StandardsWashington, D.C. 20234

Dr. David J. BrennerLos Alamos Scientific LaboratoryMail Stop 809Los Alamos, NM 87545

Dr. Aloke ChatterjeeLawrence Berkeley LaboratoryUniversity of CaliforniaBerkeley, CA 94720

Dr. Joseph L. DehmerRadiological and Environmental

Research DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Patricia M. DehmerRadiological and Environmental

Research DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Michael A. DillonRadiological and EnvironmentalResearch Division

Argonne National LaboratoryArgonne, IL 60439

Dr. Daryl DouthatDepartments of Chemistry and Physics

Univerity of Alaska at Anchorage3221 Providence DriveAnchorage, Alaska 99054

Dr. Gilles DuPlatreChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Ugo FanoDepartment of PhysicsThe University of ChicagoChicago, IL 60637

Dr. Richard FirestoneDepartment of ChemistryOhio State UniversityColumbus, OH 43210

Dr. Gordon FreemanChemistry DepartmentUniversity of AlbertaEdmonton, Canada T6G 2G2

Dr. Alexander E. GreenDepartment of PhysicsUniversity of FloridaGainesville, FL 32611

Dr. Robert N. HammHealth and Safety Research DivisionOak Ridge National LaboratoryOak Ridge, TN 37830

Dr. Robert HanrahanChemistry DepartmentUniversity of FloridaGainesville, FL 32611

145

Dr. Edwin J. Hart2115 Hart Rd.Port Angeles, WA 98362

Dr. Richard HolroydDepartment of ChemistryBrookhaven National LaboratoryUpton, NY 11973

Dr. Keh-Ning HuangRadiological and Environmental

Research DivisionArgonne National Laboratory

Argonne, IL 60439

Dr. Frank P. HudsonOffice of Health and

Environmental ResearchOffice of Energy ResearchDepartment of EnergyWashington, D.C. 20545

Dr. Mitio InokutiRadiological and Environmental

Research DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Charles JonahChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Robert Katz

University of Nebraska364 Behlen LaboratoryLincoln, NE 68588

Dr. Yong-Ki KimRadiological and EnvironmentalResearch Division

Argonne National LaboratoryArgonne, IL 60439

Dr. Cornelius E. KlotsHealth and Safety Research

DivisionOak Ridge National LaboratoryOak Ridge, TN 37830

Dr. Steven LefkowitzChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Sanford LipskyDepartment of ChemistryUniversity of MinnesotaMinneapolis, MN 55455

Dr. Daniel MeiselChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Gerhard MeiselsDepartment of ChemistryUniversity of NebraskaLincoln, NB 68588

Dr. John H. Miller

Pacific Northwest LaboratoryRichland, WA 99352

Dr. William MulacChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Conrad Naleway

Division of ChemistryAmerican Dental Assoc.211 E. Chicago Ave.Chicago, IL 60611

Dr. Anthony PagnamentaRadiological and Environmental

Research DivisionArgonne National LaboratoryArgonne, IL 60439

146

Dr. Linda R. Painter

Department of PhysicsUniversity of TennesseeKnoxville, TN 37916

Dr. William PrimakSolid State Science DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Leon SancheFaculty of MedicineUniversity of SherbrookeSherbrooke, QuebecCanada J1H 5N4

Dr. Myran SauerChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Klaus SchmidtChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. David SpenceRadiological and Environmental

Research DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Larry H. ToburenPacific Northwest LaboratoryRichland, WA 99352

Dr. Alexander TrifunacChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Conrad TrumboreChemistry DepartmentUniversity of DelawareNewark, DE 19711

Dr. James E. TurnerHealth and Safety Research DivisionOak Ridge National LaboratoryOak Ridge, TN 37830

Dr. John UnikChemistry DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Ren-Guang WangRadiological and Environmental

Research DivisionArgonne National LaboratoryArgonne, IL 60439

Dr. Walter E. WilsonPacific Northwest LaboratoryRichland, WA 99352

Dr. Harvel A. WrightHealth and Safety Research DivisionOak Ridge National LaboratoryOak Ridge, TN 37830

Dr. Marco A. ZaiderRadiological Research LaboratoriesDepartment of RadiologyColumbia UniversityNew York, NY 10032

147

148

Workshop on the Interface BetweenRadiation Chemistry and Radiation Physics

All scientific sessions will be held in Bldg. 221, Rm. A216

Thursday, 9 September 1982

0830 Bus to Argonne leaves Holiday Inn, Willowbrook

0900 - 0915

0915 - 1230

1230 - 1400

1400 - 1730

1730 - 1830

1830 - 2100

2100

Welcoming Remarks, Walter Massey (Argonne National Laboratory)

Radiation ChemistryChairman: Gerhard Meisels (University of Nebraska)Introductory Speaker: Gordon Freeman (University of Alberta)

Lunch

Radiation Physics and ModelingChairman: Martin Berger (National Bureau of Standards)Introductory Speaker: John Miller (Battelle Northwest)

Cocktail Hour (Cafeteria, cash bar)

Dinner (Cafeteria, included in the Registration Fee of $25)

Bus to Holiday Inn leaves Argonne

Friday, 10 September 1982

&is to Argonne leaves Holiday Inn

0900 - 1200

1200 - 1300

1300 - 1530

1545

Gas-Liquid Phase EffectsChairman: Aloke Chatterjee (Lawrence Berkeley Laboratory)Introductory Speaker: James Turner (Oak Ridge National Laboratory)

Lunch

SummaryChairman: Sanford Lipsky (University of Minnesota)Introductory Speaker: Mitio Inokuti (Argonne National Laboratory)

Bus to O'Hare Airport leaves Argonne.The bus will stop briefly at Holiday Inn, Willowbrook, to pick upluggage, and arrive at the airport around 1700 hours

149

0830

150

Author Index

R. D. Birkoff, 44

D. J. Brenner, 58, 113

A. Chatterjee, 106, 121, 126

C. J. Delbecq, 129

M. A. Dillon, V

D. A. Douthat, 134

G. R. Freeman, 9, 31, 137

T. Fujii, 40

A. E. S. Green, 65

R. N. Hamm, 32, 91, 106

R. J. Hanrahan, V, 132

E. J. Hart, 1, 37

R. Holroyd, v

M. Inokuti, 4

C. D. Jonah, 138

R. Katz, 120, 141

Y.-K. Kim, v

J. L. Magee, 106, 121, 126

G. G. Meisels, 40

J. H. Miller, 73

L. R. Painter, 44

H. G. Paretzke, 91

W. Primak, 129

D. E. Rio, 65

R. H. Ritchie, 32, 91, 106

L. Sanche, 56

M. C. Sauer, Jr., v

D. Y. Smith, 129

L. H. Toburen, v

C. N. Trumbore, 82, 123, 143

J. E. Turner, 32, 91, 106

W. E. Wilson, 73, 101

H. A. Wright, 32, 91, 106

W. Youngblade, 82

M. Zaider, 58, 113

151

Distribution for ANL- 82-88

Internal:

W. E. MasseyK. L. KliewerJ. RundoP. FaillaS. GordonP. F. GustafsonR. H. HuebnerY.-K. Kim (18)

J. MillerA. F. StehneyE. P. SteinbergParticipants (20)ANL Patent Dept.ANL Contract FileANL Libraries (2)TIS Files (6)

External:

DOE-TIC, for distribution per UC-34A and UC-4 (258)Manager, Chicago Operations Office, DOERadiological and Environmental Research Division Review Committee:

A. K. Blackadar, Pennsylvania State U.A. W. Castleman, Jr., Pennsylvania State U.R. E. Gordon, U. Notre DameR. A. Hites, Indiana U.D. Kleppner, Massachusetts Inst. TechnologyG. M. Matanoski, Johns Hopkins U.R. A. Reck, General Motors Research Lab.L. A. Sagan, Electric Power Research Inst.R. E. Wildung, Battelle Pacific Northwest Labs.

Chemistry Division Review Committee:D. Berg, Carnegie-Mellon U.F. A. Cotton, Texas A&M U.G. Feher, U. California, San DiegoJ. R. Huizenga, U. RochesterL. Kevan, U. HoustonJ. M. Shreeve, U. IdahoE. Wasserman, E. I. duPont de Nemours and Co., Wilmington

Participants (28)D. Armstrong, U. Calgary, CanadaL. G. Christophorou, Oak Ridge National Lab.R. N. Compton, Oak Ridge National Lab.K. Funabashi, U. Notre DameM. E. Gress, Office of Basic Energy Sciences, USDOER. J. Kandel, Office of Basic Energy Sciences, USDOEJ. Magee, Lawrence Berkeley National Lab.A. Mozumder, U. Notre DameNotre Dame, U. of, Radiation Lab.R. H. Ritchie, Oak Ridge National Lab.R. Schuler, U. Notre DameH. Schwarz, Brookhaven National Lab.J. K. Thomas, U. Notre DameR. W. Wood, Office of Energy Research, USDOE

152

Distribution for ANL-82-88