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LA-UR-Approved for public release;distribution is unlimited.

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Submitted to:

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Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by the University of California for the U.S.Department of Energy under contract W-7405-ENG-36. By acceptance of this article, the publisher recognizes that the U.S. Governmentretains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S.Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under theauspices of the U.S. Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher’s right topublish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness.

CASCADE�EXCITON MODEL DETAILED ANALYSIS

OF PROTON SPALLATION AT ENERGIES

FROM �� MeV TO � GeV

S� G� Mashnik� and A� J� SierkT�� Theoretical Division� Los Alamos National Laboratory� Los Alamos� NM ��

O� BersillonCEA� Centre dEtude de Bruyeres�le�Ch�atel� � �� Bruyeres�le�Ch�atel� France

and

T� GabrielOak Ridge National Laboratory� Oak Ridge� Tennessee ��

Abstract

An extended version of the Cascade�Exciton Model �CEM� of nuclear reactions isapplied to analyze more than �� excitation functions for interactions of protons withenergies from �� MeV to GeV with nuclei ��C ��N ��O ��Al ��P ��Ca ��Fe ��Fe��Fe �Fe natFe �Co �Zr �Zr �Zr �Zr �Zr natZr and ��Au� The relative rolesof di�erent reaction mechanisms and the e�ects of nuclear structure in the productionof speci�c �nal nuclides are discussed� A comparison with results of two dozenother popular models and with predictions of several phenomenological systematicsis given� Possible reasons for observed discrepancies between some theoretical resultsand experimental data and possible further improvements to the CEM and to othermodels are discussed�

�On leave of absence from Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear Research Dubna Russia

Contents

�� Introduction � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Extended Version of the CEM Realized in the CodeCEM��

�� Sensitivity of Results to Details of Calculations andInput Parameters � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Results and Discussion � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Targets ��C� ��N� and ��O � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Target ��Al � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Targets ��P and ��Ca � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Targets �Fe� ��Fe� ��Fe� ��Fe� and natFe � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Target �Co � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Targets �Zr� �Zr� �Zr� �Zr� �Zr� and natZr � � � � � � � � � � � � � � � � � � � � � � � � � � �� Target ��Au � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Summary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

Acknowledgments � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

References � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Introduction

Precise nuclear data on excitation functions for reactions induced by nucleonsphotons pions and other projectiles in the energy range up to several GeV are ofgreat importance both for fundamental nuclear physics and for many applications�First such data are necessary to understand the mechanisms of nuclear reactionsto study the change of properties of nuclei with increasing excitation energy and to�nd out the e�ects of nuclear matter on properties of hadrons and their interactions�� Excitation functions are more sensitive to mechanisms of nuclear reactionsthan are double di�erential cross sections of emitted particles or their integrals overenergy and�or angles� Therefore excitation functions are a convenient tool to testmodels of nuclear reactions�

Second and perhaps more important today expanded nuclear data bases in thisintermediate energy range are required for several important applications ��Recently one of the most challenging problems requiring reliable nuclear data �lesis Accelerator�Driven Transmutation Technology �ADTT� for elimination of nuclearwaste �� To understand how this problem is important for any country witha strong commitment to commercial nuclear power and especially for the USA andRussia with large stocks of weapons plutonium it is su�cient to note that di�er�ent aspects of transmutation of radioactive wastes were discussed at all recent in�ternational �� and national �see e�g� Japanese Meetings �� conferenceson nuclear data� a dozen international meetings devoted solely to these problemswere organized recently and are planned for the future in many countries �see e�g�� work on several ADTT projects is already going on in the nuclear cen�ters of the USA Europe Russia Japan China and Korea �see e�g� the recentreviews �� and invited talks given at the last conference on ADTT held inKalmar � �� The problems of Accelerator Transmutation of Waste �ATW� areclosely connected with Accelerator�Based Conversion �ABC� �� aimed to completethe destruction of weapons plutonium and with Accelerator�Driven Energy Pro�duction �ADEP� �� which proposes to derive �ssion energy from thoriumwith concurrent destruction of the long�lived waste and without the production ofweapons�usable material though substantial di�erences among these systems do ex�ist �� Precise nuclear data are needed for solving problems of radiation damageto microelectronic devices �� and not only of radiation protection of cosmonautsand aviators or workers at nuclear installations but also to estimate the radiologicalimpact of radionuclides such as �Ar arising from the operation of fusion reactors orhigh�energy accelerators and the population dose from such radionuclides retainedin the atmosphere so as to avoid possible problems of radiation health e�ects for thewhole population �see e�g� Ref� �� Another important new application whichrequires large nuclear data libraries at energies up to several hundreds of MeV isthe radiation transport simulation of cancer radiotherapy used for selecting the op�timal dose in clinical treatment planning systems �� Many excitation functionsare needed for the optimization of commercial production of radioisotopes widely

�

used in di�erent branches of nuclear medicine �� mining and industry ��Also residual product nuclide yields in thin targets irradiated by medium� and high�energy projectiles are extensively used in cosmochemistry and cosmophysics e�g� tointerpret the production of cosmogenic nuclides in meteorites by primary galacticparticles �� etc�

Nuclear data needed for these purposes may be measured or evaluated usingdi�erent theoretical models and phenomenological approximations� As of now thereis no sophisticated model or phenomenological systematics available to predict withgood accuracy all the data required even for a single given projectile target andincident energy suggesting that the best way to obtain these data may be to measurethem�

As far as we know the most precise and voluminous measurements of proton�induced spallation cross sections for a large range of target nuclei and proton energiesup to �� GeV have been performed recently by R� Michel et al� �see Refs� �� and references therein�� A short but comprehensive review of experimental resultsobtained by �� may be found in Ref� �� To the best of our knowledge the mostcomplete compilation of experimental excitation functions is published in Ref� ��and is available presently in an electronic version as an IBM PC code named NU�CLEX �� Many data on experimental excitation functions are already includedin the EXFOR compilations at the international nuclear data banks� Unfortunatelyexperiments to measure all necessary data are costly and there are a limited numberof facilities available to make such measurements �� In addition most mea�surements have been performed on targets with the natural composition of isotopesfor a given element and what is more often only cumulative yields of residual prod�uct nuclei are measured� In contrast to study the physics of nuclear reactions andfor many applications independent yields obtained for isotopically separated targetsare needed� Furthermore only some �� cross section values of residual prod�uct nuclei are normally determined in the experiments with heavy nuclei whereasaccording to calculations over �� residual product nuclei are actually produced�Therefore it turns out that reliable theoretical calculations are required to providethe necessary cross sections ��

In some cases it is more convenient to have fast�computing semiempirical system�atics for various characteristics of nuclear reactions instead of using time�consumingmore sophisticated nuclear models� After many years of e�ort by many investigatorsmany empirical formulae are now available for spallation cross sections and excitationfunctions� Many current systematics on excitation functions have been reviewed re�cently by Koning �� most of the old systematics available in �� were analyzed inthe monograph �� the majority of systematics for mass yields charge dispersionsenergy and angular distributions of fragments produced in pA and AA collisions atrelativistic energies available in �� are presented in the review by H�ufner �� use�ful systematics for di�erent hadron�nucleus interaction cross sections may be foundin the recent review �� Below we perform a comparison of some of our results withpredictions of only those systematics in Refs� �� and direct readers interested

in references on other phenomenological systematics to reviews �� and to therecent work by Michel with co�authors �� The authors of Ref� �� have performeda special analysis of predictabilities of di�erent semiempirical systematics and haveconcluded that �Semiempirical formulas will be quite successful if binding energiesare the crucial parameters dominating the production of the residual nuclides i�e�for nuclides far from stability� In the valley of stability the individual properties ofthe residual nuclei such as level densities and individual excited states determinethe �nal phase of the reactions� Thus the averaging approach of all semiempiricalformulas will be inadequate�� In this case one has to perform calculations in theframework of reliable models of nuclear reactions� As was mentioned by SilberbergTsao and Shapiro �� there are also additional cases when Monte Carlo calculationsshould be used� �� when it is essential to know the distributions in angle and energyfor the ejected nucleons � � when the nuclear reaction is induced by neutrons and�� when the particles have relatively low energies �E � �� MeV��

Di�erent models of the statistical preequilibrium and intranuclear cascade typeor their combinations realized in many computer codes are presently available tocalculate excitation functions in di�erent regions of incident energy targets andprojectiles� To test several available codes for calculation of isotope yields fromnucleon�induced reactions at intermediate energies and to �nd the product nuclideyield domains where each of the codes is most e�ective a benchmark calculationhas been performed recently by the Theoretical Calculation Code Working Group ofthe Japanese Nuclear Data Committee �� and an attempt for intercomparisonof some codes for the calculation of excitation functions in this region was done atNEA�OECD during the �rst step of the International Code Comparison for Interme�diate Energy Nuclear Data for proton�induced reaction on thin �Zr and ��Pb targets�� A more detailed analysis of predictions of �� Groups from � Laboratories forspallation product yield A� and Z�distributions was performed during the second part�The Thick Target Benchmark� of this Intercomparison �� As a third step anInternational Codes and Models Intercomparison for Intermediate Energy ActivationYield which involves a larger number of popular codes was initiated recently �� atthe request of the NEA Nuclear Science Committee� After our work was completedthe report on this Intercomparison was published as an NEA OECD Document ��This report gives detailed information about the di�erent models and codes usedsurveys extensively the target element and product nuclide coverage of the di�er�ent contributions and gives information about the predictive power of models andcodes when calculating cross sections for the production of residual nuclides fromthreshold up to GeV� From this intercomparison it was concluded that �modelingcalculations of intermediate energy activation yields on a predictive basis may at besthave uncertainties of the order of a factor of two� therefore �there is need for majorimprovements of models and codes��

During the last two decades several versions of the Cascade�Exciton Model�CEM� �� of nuclear reactions have been developed at JINR Dubna �for anoverview see e�g� �� A large variety of experimental data for reactions induced

�

by nucleons �� pions �� and photons �� has been analyzed in the frameworkof the CEM and the general validity of this approach has been con�rmed� The re�cent International Code Comparison for Intermediate Energy Nuclear Data �� hasshown that the CEM adequately describes nuclear reactions at intermediate energiesand has one of the best predictive powers for double di�erential cross sections ofsecondary nucleons as compared to other available modern models �see Tabs� and� in the Report �� and Fig� � in Ref� ��

Recently the CEM has been extended to calculate hadron�induced spallation ��and used to study several excitation functions from reactions induced by protons on��C ��Al ��Fe �Co and ��Au at incident energies up to �� MeV �� as wellas to analyze the new measurements of yields of residual nuclei from ��Cu ��Cu��Pb ��Pb ��Pb and ��Bi irradiated by �� GeV and �� MeV protons and from�Co targets irradiated by �� GeV protons �� Recently the CEM has beenapplied successfully by Konshin �� to calculate the production of several isotopesof U Pa Th and Ac from p��U reactions at �� and �� GeV as well asto calculate yields of U Pa and Th isotopes from ��U targets and yields of Pa Thand Ac isotopes from p��Th interactions at �� GeV� Nevertheless previously theCEM has not been applied to study all possible excitation functions in large rangesof incident energies and mass�numbers of targets� therefore its predictive power andapplicability to evaluate arbitrary spallation cross sections was unknown�

Here we apply the extended version of the CEM �� to perform a detailed anal�ysis of more than �� reactions induced by protons from �� MeV to GeV on nucleiof ��C ��N ��O ��Al ��P ��Ca ��Fe ��Fe ��Fe �Fe natFe �Co �Zr �Zr �Zr�Zr �Zr natZr and ��Au with several aims� a� to determine the capability of thepresent version of the CEM realized in the code CEM� to predict unknown excita�tion functions b� to compare our results with calculations of other popular modelsand phenomenological systematics and with available experimental data that mayserve as an independent benchmark and a guidance for further evaluation of data �lesand c� to study nuclear reaction mechanisms involved in the production of speci�cnuclides to understand the dependence of our results on the physics incorporated inthe code on the values of input parameters and on the speci�c mode of calculationwith the hope of identifying possible improvements to CEM� and to other codesto improve their predictive powers� This last point was the major reason for our work�

�

�� Extended Version of the CEM Realized in the CodeCEM��

A detailed description of the CEM may be found in Refs� �� therefore onlyits basic assumptions and the di�erences of the extended version used here fromthe standard one �� will be outlined below� The CEM assumes that the reactionsoccur in three stages� The �rst stage is the intranuclear cascade in which primaryand secondary particles can be rescattered several times prior to absorption by orescape from the nucleus� The excited residual nucleus remaining after the emissionof the cascade particles determines the particle�hole con�guration that is the startingpoint for the second preequilibrium stage of the reaction� The subsequent relaxationof the nuclear excitation is treated in terms of the exciton model of preequilibriumdecay which includes the description of the equilibrium evaporative third stage of thereaction�

In a general case the three components may contribute to any experimentallymeasured quantity� In particular for the inclusive cross sections to be discussedlater we have

��p�dp � �in�Ncas�p� �Nprq�p� �N eq�p��dp � ��

The inelastic cross section �in is not taken from the experimental data or independentoptical model calculations but is calculated within the cascade model itself by theMonte Carlo method and is equal to the geometrical cross section of the targer nucleus�geom times the ratio of the total number of inelastic interactions Nin to the totalnumber of elastic Nel and inelastic Nin simulated events� �in � �geomNin��Nin�Nel��geom � �R� where R is the radius of the last zone of the target nucleus �for detailssee ��

The cascade stage of the interaction is described by the standard version of theDubna intranuclear cascade model �ICM� �� All the cascade calculations arecarried out in a three�dimensional geometry� The nuclear matter density ��r� isdescribed by a Fermi distribution with two parameters taken from the analysis ofelectron�nucleus scattering namely

��r� � �p�r� � �n�r� � ��f� � exp��r� c��a�g � �

where c � ��A�� fm A is the mass number of the target and a � �� fm� Forsimplicity the target nucleus is divided by concentric spheres into seven zones inwhich the nuclear density is considered to be constant� The energy spectrum of thetarget nucleons is estimated in the perfect Fermi gas approximation with the localFermi energy TF �r� � �h��r�� mN � where mN is the nucleon mass� Thein uence of intranuclear nucleons on the incoming projectile is taken into accountby adding to its laboratory kinetic energy an e�ective real potential V as well asby considering the Pauli principle which forbids a number of intranuclear collisionsand e�ectively increases the mean free path of cascade particles inside the target�For incident nucleons V � VN �r� � TF �r� � � where TF �r� is the corresponding

Fermi energy and � is the mean binding energy of the nucleons �� MeV ��For pions in the Dubna ICM one usually uses �� a square�well nuclear potentialwith the depth V� � MeV independently of the nucleus and pion energy� Theinteraction of the incident particle with the nucleus is approximated as a series ofsuccessive quasifree collisions of the fast cascade particles �N or �� with intranuclearnucleons�

NN � NN� NN � �NN� NN � �� iNN

�N � �N� �N � �� iN �i � � � ��

To describe these elementary collisions one uses experimental cross sections for thefree NN and �N interactions simulating angular and momentum distributions ofsecondary particles using special polynomial expressions with energy�dependent co�e�cients �� and one takes into account the Pauli principle�

The Pauli exclusion principle at the cascade stage of the reaction is handled byassuming that nucleons of the target occupy all the energy levels up to the Fermienergy� Each simulated elastic or inelastic interaction of the projectile �or of a cascadeparticle� with a nucleon of the target is considered forbidden if the �secondary�nucleons have energies smaller than the Fermi energy� If they do the trajectory ofthe particle is traced farther from the forbidden point and a new interaction point anew partner and a new interaction mode are simulated for the traced particle etc�until the Pauli principle is satis�ed or the particle leaves the nucleus� Besides theelementary processes �� the Dubna ICM also takes into account pion absorption onnucleon pairs

�NN � NN� ��

The momenta of two nucleons participating in the absorption are chosen randomlyfrom the Fermi distribution and the pion energy is distributed equally between thesenucleons in the center�of�mass system of the pion and nucleons participating in theabsorption� The direction of motion of the resultant nucleons in this system is takenas isotropically distributed in space� The e�ective cross section for absorption isrelated �but not equal� to the experimental cross sections for pion absorption bydeuterons�

In the standard version of the Dubna ICM used in the code CEM� the kineticenergy of cascade particles is increased or decreased as they move from one potentialregion �zone� to another but their directions remain unchanged� That is in ourcalculations refraction or re ection of cascade nucleons at potential boundaries isneglected�

The standard version of the Dubna ICM does not take into account the so�called�trawling� e�ect �� That is in the beginning of the simulation of each event thenuclear density distributions for the protons and neutrons of the target are calculatedaccording to Eq� � � and a further decrease of the nuclear density with the emissionof cascade particles is not taken into account� Our detailed analysis �see e�g� �� and references therein� of di�erent characteristics of nucleon� and pion�induced

�

reactions for targets from C to Am has shown that this e�ect may be neglected atincident energies below about GeV� At higher incident energies the progressivedecrease of nuclear density with the development of the intranuclear cascade hasa strong in uence on the calculated characteristics and this e�ect has to be takeninto account �� Therefore to use the CEM approach at incident energies higherthan about GeV the standard version of Dubna ICM has to be replaced by aversion which includes the non�linear trawling e�ect of the local reduction of thenuclear density during the development of the cascade �� The standard versionof the Dubna ICM is described in detail in the monograph �� and more brie y inthe review �� and in the recent book by Iljinov Kazarnovsky and Paryev �� Adetailed comparison of the Dubna ICM with the well known Bertini ICM developedat Oak Ridge National Laboratory �� and with the popular version developed atBrookhaven National Laboratory and Columbia University by Chen et al� �� ismade in Ref� ��

An important point of the CEM is the condition for transition from the in�tranuclear cascade stage to preequilibrium processes� In a conventional cascade�evaporation model cascade nucleons are traced down to some minimal energy thecut�o� energy Tcut being about �� MeV below which particles are considered tobe absorbed by the nucleus� Calculations �� show that a reasonable variation of thevalue Tcut does not signi�cantly change the average number of particles in a nuclearcollision� As a zero�order approximation to the CEM this �sharp cut�o�� methodfor passing to preequilibrium nuclear decay was also considered in Refs� �� andwe show an example of this case below in Figs� � and � In a real case the cut�o�is expected to be somewhat smoothed �� Moreover when we move towards lowerenergies the relative contributions of particles captured by peripheral and interiorregions of a nucleus are changed� But this fact is completely outside the scope ofthe sharp cut�o� approximation� Therefore in the CEM �� it was proposed torelate the condition for a cascade particle to be captured by the nucleus to the simi�larity of the imaginary part of the optical potential calculated in the cascade modelWopt�mod��r� to its experimental value Wopt�exp��r� obtained from analysis of data onparticle�nucleus elastic scattering� This was inspired by a comparison of the classi�cal kinetic equation describing the intranuclear cascade with its quantum�mechanicalform in which the particle transport through nuclear matter is governed by the opticalpotential �for more details see Ref� ��

In the �weak�coupling� approximation the imaginary part of the optical potentialcan be expressed in terms of the cross section � for scattering of a particle on targetnucleons

Wopt�r� � ��h

� ��vrel�vrel �T �r� � ��

Here the averaging is carried out over the spectrum of target nucleons and includesthe Pauli exclusion principle� Practically in the version of the CEM realized in thecode CEM� for ��vrel� we take the average of � proton�proton and � proton�neutron scattering cross sections calculated by the Monte Carlo simulation method

�

and introduce a factor e�ectively taking into account the Pauli principle exactly asis done in the Fermi�gas model �see e�g� ��

��vrel� ��

��pp�vrel� � �pn�vrel��TF�T � where ��

�x� �

��

�x� if x � ��

�� x� �

�x� � �

x�� if x ��

��

Here vrel is the relative velocity of the cascade nucleon and the target nucleon inunits of the speed of light and T is the kinetic energy of the cascade nucleon� Thefree�particle interaction cross sections �pp�vrel� and �pn�vrel� in Eq� �� are estimatedusing the relations suggested by Metropolis et al� ��

�pp�vrel� ��

v�rel� ��

vrel� � ��

�pn�vrel� ��

v�rel� � �

vrel� � � ��

where the cross sections are given in mb� Formula �� is valid only at su�ciently highenergies and for the nuclear interior� As is seen from Eq� �� the radial behavior ofthe density �T �r� follows that of the optical potential� In a general case the �T �r�function lags behind Wopt�r� due to the �nite radius of particle interactions and thenon�linear relation ofWopt to �T � Since at present these e�ects cannot be considered ina consistent manner the imaginary part of the optical potential for cascade particlesis de�ned in the CEM by relation �� To allow for the e�ect of the non�linearrelation between Wopt and �T in the CEM �� it was suggested to use for �T �r� atwo parameter Fermi distribution like Eq� � � but with parameters correspondingto the volume part of the imaginary optical potential taken from the analysis ofexperimental data� In CEM� this idea is implemented as� following Ref� �� weuse Eq� � � to calculate �T �r� with c � RI � �� A�� fm and a � aI � �� fmfor cascade neutrons and c � RI � �� A�� fm and a � aI � �� N � Z��Afm for cascade protons� For the experimental values of the imaginary part of theoptical potential Wopt�exp��r� in CEM� one employs the results of Becchetti andGreenlees �� for protons and neutrons with T � MeV and at higher energiesthe potential by Menet et al� �� for protons and by Marshak et al� �� for neutrons�Such a realization serves only as one possible approach from other possibilities� Itshould be added that the conditions for validity of the cascade and optical modelsdo not coincide �� the cascade model considers the scattering from bound nucleonsrather than from a potential well as the optical model does� Thus the agreementbetween Wopt�mod� and Wopt�exp� is assumed to occur when the proximity parameter

P �j �Wopt�mod� �Wopt�exp��Wopt�exp� j ��

�Unfortunately� formulae �� and �� were published in Ref� �� with some misprints� in theprevious publication � �� they are printed correctly�

�

becomes small enough� In CEM� we use a �xed value P � �� extracted from theanalysis �� of experimental proton� and pion�nucleus data at low and interme�diate energies�

From a physical point of view such a smooth transition from the cascade stage ofthe reaction seems to be more attractive than the �sharp cut�o�� method� In addi�tion as was shown in Ref� �� this improves the agreement between the calculatedand experimental spectra of secondary nucleons especially for low incident energiesand backward angles of the detected nucleons �see e�g� Fig� �� of Ref� ��

Let us note here that in the CEM the initial con�guration for the preequilibriumdecay �number of excited particles and holes i�e� excitons n� � p� � h� excitationenergy E�

� linear momentum P � and angular momentum L� of the nucleus� di�erssigni�cantly from that usually postulated in exciton models� Our calculations �� have shown that the distributions of residual nuclei remaining after the cascadestage of the reaction i�e� before the preequilibrium emission with respect to n� p�h� E�

� P � and L� are rather broad��

As an example Fig� � shows distributions of residual nuclei remaining after thecascade stage of the reaction p�� GeV��Mo that serve as input for the secondpreequilibrium stage of the CEM with respect to mass A and charge Z numbersexcitation energy E� momentum jP �j and angular momentum jL�j numbers ofexcitons n� exciton�particles p� and exciton�holes h� calculated as proposed in theCEM �solid histograms� and using the �sharp cut�o�� method as in a conventionalICM �dashed histograms�� One can see that all distributions calculated in both theCEM and ICM approaches are very broad� Let us note here that as a rule thesmooth method of the CEM leads to an earlier completion of the cascade stage ascompared to that of the ICM� As a result of this the distributions with respectto A Z n� and especially with respect to p� and h� calculated by the CEM arenarrower than those of the ICM� The distributions with respect to jP �j and jL�jcalculated by both methods are very similar while the distribution with respect toE�

� of the CEM is broader than that of the ICM� Our calculations show that thedi�erence in the distributions of residual nuclei calculated by the CEM and ICMincreases with decreasing incident energy of the projectile and vice versa� Fig� shows angle�integrated energy spectra of all secondary particles emitted from thisreaction calculated in the CEM using both methods of �nishing the cascade stageof the reaction� One can see that for this incident energy of � GeV the spectra of

�Unfortunately� this fact was misunderstood by the authors of the code HETC��STEP � �� Inspite of the fact that it has been stressed explicitly� and �gures with distributions of excited nucleiafter the cascade stage of a reaction with respect to the number of excitons and other characteristicswere shown in a number of publications �see� e�g� Fig� � in Ref� �� Fig� � in Ref� � �� p� �� inRef� �� p� �� in Ref� �� the authors of Ref� � �� misstated this fact as �Gudima et al� assumed

the state of two particles and one hole at the beginning � � � Hence� their assumption is not valid for

the wide range of incident energy�� claiming this as a weakness of the CEM and a priority of thecode HETC��STEP� where smooth distributions of excited nuclei after the cascade stage of reactionswith respect to n� are used� This had already been suggested and used in the CEM ��

�

nucleons calculated by both methods are almost the same� Let us note again that atincident energies below � �� MeV the di�erence between nucleon spectra calculatedby these methods is larger� As one can see from Figs� � and �� of Ref� �� the CEMapproach gives a better agreement with the experimental data� The spectra of pionsare just the same as both methods of �nishing the cascade do not deal at all withpions� But the spectra of composite particles calculated with the CEM method aresigni�cantly higher and broader than those of the ICM� This is caused mainly by thedi�erence in the distributions of residual nuclei with respect to p� and h� �see Fig� ��

The subsequent interaction stages �preequilibrium and equilibrium� of nuclearreactions are considered in the CEM in the framework of an extension of the modi�edexciton model �� At the preequilibrium stage of a reaction we take into accountall possible nuclear transitions changing the number of excitons n with !n � � �� and � as well as all possible multiple subsequent emissions of n p d t �He and �He�The corresponding system of master equations describing the behavior of a nucleusat the preequilibrium stage is solved by the Monte Carlo technique ��

��

Fig� �� Distributions of excited residual nuclei remaining after the cascade stage of the

reaction p�� GeV��Mo with respect to the mass A and charge Z numbers� excitation

energy E�� momentum jP �j and angular momentum jL�j �labeled in the plot as P and M��

number of excitons n�� exciton�particles p�� and exciton�holes h�� Solid histograms corre�

spond to a completion of the cascade as proposed in the CEM �� dashed histograms

are calculated in the �sharp cut�o�� approximation in which a cascade particle is absorbed

when its energy falls below a �xed value�

��

Fig� �� Angle�integrated energy spectra of secondary particles from the reaction

p�� GeV��Mo� As in Fig� �� solid and dashed histograms are calculated with the com�

pletion of the cascade stages of the reactions according to the CEM �� and to a

conventional ICM� respectively� The pion spectra are identical for both models�

For a preequilibrium nucleus with excitation energy E and number of excitonsn � p � h the partial transition probabilities changing the exciton number by !nare

��n�p� h�E� � �

�hjM�nj��n�p� h�E� � ��

The emission rate of a nucleon of the type j into the continuum is estimated accordingto the detailed balance principle

"j�p� h�E� �

E�BjZV cj

�jc�p� h�E� T �dT

�jc�p� h�E� T � � sj � �

��h� jj�p� h�

��p � �� h�E �Bj � T �

��p� h�E�T�inv�T � ��

where sj Bj V cj and j are the spin binding energy Coulomb barrier and reduced

mass of the emitted particle respectively� The factor j�p� h� ensures the conditionfor the exciton chosen to be the particle of type j and can easily be calculated bythe Monte Carlo technique�

�

Assuming an equidistant level scheme with the single�particle density g we havethe level density of the n�exciton state as ��

��p� h�E� �g�gE�p�h��

p#h#�p� h� ��#� ��

This expression should be substituted into Eq� �� For the transition rates ��one needs the number of states taking into account the selection rules for intranu�clear exciton�exciton scattering� The appropriate formulae have been derived byWilliams �� and later corrected for the exclusion principle and indistinguishabilityof identical excitons in Refs� ��

��p� h�E� ��

g�gE �A�p � �� h� ��

n � �

�gE �A�p� �� h� ��

gE �A�p� h��n��

��p� h�E� ��

g�gE �A�p� h��

n�p�p� �� ph � h�h� ��

��p� h�E� ��

gph�n� � ��

where A�p� h� � �p� � h� � p � h�� h� � By neglecting the di�erence of matrixelements with di�erent !n M� �M� � M� �M we estimate the value of M for agiven nuclear state by associating the ��p� h�E� transition with the probability forquasi�free scattering of a nucleon above the Fermi level on a nucleon of the targetnucleus� Therefore we have

� ��vrel�vrel

Vint��

�hjM j� g�gE �A�p � �� h� ��

n� �

�gE �A�p� �� h � ��

gE �A�p� h��n��

� ��

Here Vint is the interaction volume estimated as Vint �� rc�� with the De

Broglie wave length �� corresponding to the relative velocity vrel �q Trel�mN �

A value of the order of the nucleon radius is used for rc in CEM�� rc � �� fm�The averaging in the left�hand side of Eq� �� is carried out over all excited

states taking into account the Pauli principle in the approximation

� ��vrel�vrel �� vrel� � vrel � ��

The averaged cross section � ��vrel� is calculated according to Eqs� �� The rel�ative kinetic energy of colliding particles necessary to calculate� vrel and the factor in Eqs� �� is estimated in the so�called �right�angle collision� approximation ��i�e� as a sum of the mean kinetic energy of an excited particle �exciton� measuredfrom the bottom of the potential well Tp � TF �E�n plus the mean kinetic energy ofan intranuclear nucleon partner TN � �TF� that is Trel � Tp� TN � �TF��E�n�Combining �� and �� we get �nally for the transition rates�

��p� h�E� �� vrel�vrel

Vint

��


Vint

n� �

n

�gE �A�p� h�

gE �A�p � �� h� ��

�n�� p�p � �� ph � h�h� ��

gE �A�p� h�


Vint

�gE �A�p� h�

gE �A�p� �� h� ��

�n��ph�n � ��n � �

�gE �A�p� h��

To economize on computing time in the version of CEM� used here the calcula�tions are performed with the approximation A�p� h� � �� Our experience with manyyears of calculations in the framework of the CEM shows that at incident energies ofabout �� MeV and above the use of such an approach does not signi�cantly changethe �nal results but allows us to reduce signi�cantly the computing time�

The CEM predicts forward peaked �in the laboratory system� angular distribu�tions for secondary particles� Primarily this is due to the high asymmetry of thecascade component �for ejected nucleons and pions�� Another possibility for forwardpeaked distributions of nucleons and composite particles emitted during the preequi�librium interaction stage is related to retention of some memory of the projectile$sdirection� It means that along with energy conservation we need to take into ac�count the conservation of linear momentum P � at each step when a nuclear state isgetting complicated� In a phenomenological approach this can be realized in di�er�ent ways �� The simplest way consists in sharing an incoming momentum P �

�similarly to energy E�

�� between an ever�increasing number of excitons interacting inthe course of equilibration of the nuclear system� In other words the momentumP �

should be attributed only to n excitons rather than to all A nucleons� Then particleemission will be symmetric in the rest frame of the n�exciton system but will havesome forward peaking in both the laboratory and center�of�mass reference frames�

In another approach to the asymmetry e�ect for the preequilibrium componentthe nuclear state with a given excitation energy E� should be speci�ed not only bythe exciton number n but also by the momentum direction %� Following Ref� ��the master equation �� from Ref� �� can be generalized for this case providedthat the angular dependence for the transition rates �� and �� Eq� �� isfactorized� In accordance with Eqs� �� and �� in the CEM it is assumed that

� � �� F �%�

where

F �%� �d�free�d%Rd%�d�free�d%�

�

The scattering cross section d�free�d% is assumed to be isotropic in the referenceframe of the interacting excitons thus resulting in an asymmetry in the laboratoryframe� This calculational scheme is easily realized by the Monte Carlo technique�Calculations �� have shown that both methods give rise to similar distributionsfor preequilibrium particles� In comparing with experiment the details of these dis�tributions become more obscured due to the contribution of cascade and evaporative�equilibrium� components� In CEM� we use the second method to allow for theasymmetry of a particle emitted at the preequilibrium interaction stage�

��

Complex particles can be produced in nucleon�nucleus reactions at di�erent in�teraction stages and due to many mechanisms� These may include fast processes likedirect knock�out pick�up reactions or �nal state interactions resulting in coalescenceof nucleons into a complex particle� CEM� neglects all these processes at the cas�cade interaction stage� Therefore fast complex particles can appear in our approachonly due to preequilibrium processes� We assume that in the course of a reaction pjexcited particles are able to condense with probability �j forming a complex particlewhich can be emitted during the preequilibrium state� A modi�cation of Eq� �� forthe complex particle emission rates is described in detail in Refs� �� The �con�densation� probability �j is estimated as the overlap integral of the wave function ofindependent nucleons with that of the complex particle �cluster�

�j � p�j �Vj�V �pj�� p�j �pj�A�

pj��

This is a rather crude estimate and we will see below that it does not provide agood prediction of emission of preequilibrium��particles� In the usual way the values�j are taken from �tting the theoretical preequilibrium spectra to the experimentalones which gives rise to an additional as compared to �� dependence of the factor�j on pj and excitation energy �see e�g� Refs� �� In virtue of the varietyof complex particle emission mechanisms mentioned above we do not see a physicaljusti�cation for such a �tting procedure �� Therefore the condensation prob�ability �j was de�ned in the CEM by the relation �� just as a �rst approximation�The single�particle density gj for complex particle states is found in the CEM by as�suming the complex particles move freely in the uniform potential well whose depthis equal to the binding energy of this particle in a nucleus ��

gj�T � �V � sj � �� j��

��h��T � Bj�

��

As we stated previously this is a crude approximation� Another approach is toassume preformed alpha clusters whose preformation probability is adjusted to �tobserved alpha particle spectra �� The clusters are assumed to be singleexcitons with a level density g� � g��

The angular distributions of preequilibrium complex particles are assumed �� tobe similar to those for the nucleons in each nuclear state� However the angular dis�tributions summed up over all populated nuclear states will certainly di�er becausethe branching ratios for di�erent particles depend in detail on the decaying nuclearstates�

By �preequilibrium particles� we mean particles which have been emitted afterthe cascade stage of the reaction but before achieving statistical equilibrium at atime teq which is �xed by the condition ��neq� E� � ��neq� E� from which we getneq �

p gE� At t � teq �or n � neq� the behavior of the remaining excited com�

pound nucleus is described in the framework of both the Weisskopf�Ewing statisticaltheory of particle evaporation �� and �ssion competition according to the Bohrand Wheeler theory ��

�

In the initial version of the CEM �� which was used mainly to describe spec�tra of secondary particles from interactions of nucleons with not too heavy targetsat energies of about �� MeV and below several e�ects such as pairing energy an�gular momentum of preequilibrium and evaporated particles and rotational energiesof compound and precompound nuclei as well as �ssion of compound nuclei werenot taken into account and calculations were performed with constant values for thelevel density parameters a � Const � A�� Such an approach was quite justi�ed forthose problems that have been solved in the framework of that version �� Itis well known from the literature that excitation functions are more sensitive to thephysics of any model and to the values of input parameters than are inclusive spectraof secondary particles�

To be able to analyze reactions with heavy targets and to describe accurately ex�citation functions over a wider range of incident particle energy the CEM has beenextended recently �� The extended version incorporates the competition betweenevaporation and �ssion of compound nuclei takes into account pairing energies con�siders the angular momentum of preequilibrium and evaporated particles and therotational energy of excited nuclei and can use more realistic nuclear level densities�with Z N and E� dependences of the level density parameter�� In the versionof the CEM realized in the code CEM� the following models for the level densityparameters are incorporated� Malyshev$s �� systematics for a � a�Z�N� and �parameter sets for a � a�Z�N�E�� two from Ignatyuk et al� �� two fromCherepanov and Iljinov �� and four from Iljinov et al� �� The possibility ofcalculating with a � a�A where a� is a constant input value �as in the earlier ver�sions� is also provided� In CEM� it is possible to calculate with three di�erentshell and pairing corrections namely those due to Cameron �� Truran Cameronand Hilf �� and Myers and Swiatecki �� A comprehensive comparison of leveldensity parameters �and of level densities themselves for several excited compoundnuclei� calculated in the framework of these models with the available experimentaldata may be found in the recent review ��

The following models for �ssion barriers are incorporated in CEM�� the phe�nomenological approach of Barashenkov et al� �� the semiphenomenological ap�proach of Barashenkov and Gereghi �� the liquid�drop model �LDM� with Myersand Swiatecki$s parameters �� the LDM with Pauli and Ledergerber$s parame�ters �� the single�Yukawa modi�ed LDM of Krappe and Nix �� the Yukawa�plus�exponential modi�ed LDM of Krappe Nix and Sierk �� the subroutineBARFIT of Sierk �� which provides macroscopic �ssion barriers of rotating nucleiin the Yukawa�plus�exponential modi�ed LDM �� double�humped �ssion barri�ers for transuranium nuclides as proposed in Ref� �� giving a �xed input valuefor single�humped �ssion barriers Bf and giving �xed input values BA

f and BBf for

double�humped �ssion barriers�

�Here and everywhere below� the level density parameter a is de�ned in units of ��MeV� but forthe sake of brevity we do not explicitly write this unit�

��

CEM� allows one to calculate both without taking into account the dependenceof Bf on the excitation energy E� and with the dependences Bf �E�� proposed byBarashenkov et al� �� and by Sauer Chandra and Mosel ��

With CEM� one may calculate either without taking into account the depen�dence of Bf on the angular momentum L of a �ssioning nucleus or with the de�pendences Bf �L� estimated by a phenomenological approach with the values for themoment of inertia of a nucleus at the nonrotating saddle�point from Ref� �� orfrom �� or by using the subroutine BARFIT of Sierk �� To calculate Bf threedi�erent models �� for ground�state shell and pairing corrections may beused�

A detailed comparison of these di�erent �ssion barriers and an analysis in theframework of the extended version of the CEM of nuclear �ssilities and �ssion crosssections for several nuclei including a comparison with available experimental dataare given in the recent review �� An example of the dependence of calculated ��Uproton�induced �ssion cross sections on these di�erent models for �ssion barriers andlevel density parameters may be found in Ref� ��

Every model for �ssion barriers shell and pairing corrections and level densityparameter a incorporated in the code CEM� may be selected by input switchesthat permit one to perform calculations either with �the best� set of parameters forpredictions in a wide range of incident energy and�or target nuclei or to choose aspeci�c model to analyze a speci�c characteristic in a special case�

We used in our recent extension of the CEM �� many results of Iljinovet al� �� who realized similar schemes in their cascade�evaporationmodels� In the Weisskopf�Ewing statistical theory of particle emission �� andBohr and Wheeler theory of �ssion �� the partial widths "j for the emissionof a particle j �j � n p d t �He �He� and "f for �ssion are expressed by theapproximate formulas �units� �h � c � �� see e�g� ��

"j �� sj � ��mj

��c�Uc�

Uj�BjZVj

�jinv�E��j�Uj �Bj � E�EdE ��

"f ��

��c�Uc�

Uf�BfZ�

�f �Uf �Bf �E�dE � � ��

Here �c �j and �f are the level densities of the compound nucleus the residualnucleus produced after the emission of the j�th particle and of the �ssioning nucleusat the �ssion saddle point respectively� mj sj and Bj are the mass spin and thebinding energy of the j�th particle respectively and Bf is the �ssion barrier height�The code CEM� calculates the binding energies of particles using the Cameronformulas �� and �jinv�E� is the inverse cross�section for absorption of the j�thparticle with kinetic energy E by the residual nucleus� The approximation proposed

��

by Dostrovsky et al� �� is used

�jinv�E� � �jgeom�j

��

�jE

� � ��

where

�jgeom � �R�j � Rj � &r�A

��fj � &r� � �� fm � � �

�n � �� A��fj �

�n � � �� A��fj � ��n �

For charged particles �j � �Vj where Vj is the e�ective Coulomb barrier andthe constants �j are calculated for a given nucleus by interpolating the values ofRef� �� Following Refs� �� the angular momentum dependence of thelevel density is approximated by ��E�� L� � ��U� �� where U � E��ER and ER arethe �thermal� and rotational energies of the nucleus respectively�

Uc � E� � EcR �!c � Uj � E� �Ej

R �!j � Uf � E� � EfR �!f �

Here E� is the total excitation energy of the compound nucleus� EcR E

jR and Ef

R

are the rotational energies for the compound residual and �ssioning nucleus at thesaddle point respectively and they are determined as�

EgsR �

L�L� ��h�

Jrb�

EspR �

L�L� ��h�

Jsp� � ��

Jrb � ��mNr��A

��

Here L is the angular momentum of the nucleus mN is the nucleon mass and thevalues calculated and plotted in �� or tabulated in �� are used for the momentof inertia of a nucleus at the saddle�point Jsp�

Following Ref� �� the pairing energies of the compound nucleus !c of theresidual nucleus !j and of the �ssion saddle point !f are estimated as�

!c � �c � � �qAc � !j � �j � � �

qAfj � and !f � �c � ��

qAc �in MeV��

Afj � Ac�Aj where Ac and Aj are the mass numbers of the compound nucleus andof the j�th particle and �k � � � or for odd�odd odd�even or even�even nucleirespectively�

Particle emission and �ssion widths �� are obtained within the Fermi�gasapproach to the nuclear level density

��E�� Const � expf paE�g �

��

The �ssion cross section �f is determined by the ratio of the number Nf of �ssionevents to the total number Nt � Nel �Nin of Monte Carlo simulations in CEM�

�f � �inPf � �inNf

Nin� �geom

Nf

Nt� � ��

Here Pf is the �ssility of nucleus� In the case of low��ssility nuclei �e�g� gold�Nf �� Nt and as a consequence a large number of cascades should be calculatedto obtain the value of �f with su�cient statistical accuracy so that the calculationof �f becomes extremely time�consuming� Therefore besides the direct calculationof the �ssion cross section via the expression � �� we have incorporated in CEM��following Barashenkov et al� �� a Monte Carlo calculation by means of the sta�tistical functions Wn �

QNi �wni and Wf � � �Wn� Here Wn is the probability of

the nucleus to �drop� the excitation energy E� by a chain �cascade� of N successiveevaporations of particles� Wf is the probability for the nucleus to �ssion at one ofthe chain stages� wni � � � wfi is the probability of particle emission at the i�thstage of the evaporative cascade� wfi is the corresponding �ssion probability whichis easy to determine using the formulae �� for the widths "j and "f � After thesubsequent averaging of Wf over the total number Nin of the cascades followed andafter multiplication of the result by the corresponding total inelastic cross section�in we obtain the following expression for the �ssion cross section�

�f ��inNin

NinXi �

�Wf �i � � ��

The intranuclear cascade model �� considers angular momenta of emitted par�ticles as classical vectors mcas

i � �ripi� where ri is the radius vector at the exit ofthe cascade particle i from the nucleus and pi is its momentum� Following Ref� �� angular momenta of preequilibrium and evaporation particles are also considered asclassical vectors since j X

i

mcasi j �� In CEM� angular momenta of preequilib�

rium and evaporated particles mj are estimated in the sharp cut�o� approximationas was proposed by Iljinov et al� �� In this approach the distribution of mj

satis�es the expression

P �mj�dmj � mjdmj� � � mj � mmaxj �

q j�Ej � Vj�Rj��h �

Here Rj is the radius of the interaction of the jth emitted particle with the residualnucleus Ej Vj and j are the energy in the center�of�mass system Coulomb barrierand reduced mass of the particle respectively� Following Ref� �� the spins of theemitted particles are not taken into account when estimating the angular momen�tum of the residual nuclei though they are taken into account in the correspondingstatistical factors of the emission rates �� Angular momenta of residual nucleiare calculated in CEM� without taking into account the spin of the initial targetnucleus and of intermediate nuclei during consecutive emission of particles�

��

Let us note that in CEM� nuclear structure is taken into account at the pree�quilibrium and evaporation stages of reactions through the level density parametersnuclear masses pairing energies and binding energies of secondary particles� As wasmentioned above CEM� uses nuclear masses from Ref� �� while pairing energiesare calculated according to Eq� � �� To take into account shell e�ects on level densi�ties and their decrease with increasing excitation energy we used in our calculationsthe third systematics for a�Z�N�E�� by Iljinov et al� �� for all reactions exceptinteractions with the lightest ��C ��N and ��O targets for which to avoid somecalculational di�culties we used �xed values a � �� A� Recall that the authors ofRef� �� have obtained this approximation for a�Z�N�E�� by �tting not only mea�surements on neutron resonances but also data at higher excitation energies �usingthe same Cameron$s mass formulas �� in a functional form proposed by Ignatyuket al� ��

a�Z�N�E�� &a�A�

�� Wgs�Z�N�

f�E� �!�

E� �!

��

where&a�A� � �A� �A��Bs � ��

is the asymptotic Fermi�gas value of the level density parameter at high excitationenergies� Here Bs is the ratio of the surface area of the nucleus to the surface areaof a sphere of the same volume �for the ground state of a nucleus Bs � �� and

f�E�� exp��E��

For the parameters � � and � the authors of Ref� �� have found di�erent valuesfrom those of Ignatyuk et al� �� namely

� � �� MeV��

Let us note as well that in CEM� collective e�ects are not taken into accountexplicitly� In Ref� �� the values of parameters � � and � �� were �tted �alsowithout explicit collective terms� to the experimental resonance spacing and otherdata therefore they include collective e�ects in a non�explicit phenomenological way�Our experience shows that for the version of the CEM realized in the code CEM� thesystematics � �� for a�Z�N�E�� provides a good overall agreement with di�erentexperimental data therefore we use it in our present study�

In CEM� all other CEM parameter values are �xed and are the same as de�scribed in Refs� ��

At the end of this section we show a typical example of how the code CEM�describes the inclusive spectra of secondary nucleons and �ssion cross sections� Fig� �shows a comparison of calculated and measured inclusive spectra of neutrons ��and protons �� from p�� MeV��Zr� To illustrate the relative role of the CEMnucleon production mechanisms the cascade preequilibrium and evaporative com�ponents of angle�integrated energy spectra are shown separately in the upper part

�

of Fig� �� In the lower part only the sums of all three components are shown fordouble�di�erential cross sections for �ve laboratory angles� One can see that CEM�reproduces well the absolute value and the change in the spectrum shape with in�creasing emission angle both for secondary protons and neutrons�

As an example the incident energy dependence of experimental �� andcalculated �ssion cross section for interaction of neutrons with ��U is shown in Fig� ��We performed these calculations with Krappe Nix and Sierk �ssion barriers ��Cameron shell and pairing corrections �� the third Iljinov et al� systematics for thelevel density parameters �� with a dependence Bf�L� estimated by a phenomeno�logical approach �formulas � �� from Ref� �� with the value of the momentof inertia of a nucleus at the saddle�point Jsp from Ref� �� without taking intoaccount the dependence of Bf on excitation energy E� and with the value for theratio af�an � �� For comparison two values of �ssion cross sections calculatedin Ref� �� with the well known code LAHET �� are shown for Tn � �� and�� MeV� One can see that CEM� describes correctly �and no worse than LAHET�the shape and the absolute value of the �ssion cross section at these intermediateincident energies�

�

Fig� �� Angle�integrated energy distributions �upper row� and double di�erential cross

sections �lower row� of neutrons and protons from �� MeV protons on �Zr� In the upper

row� histograms �� and � show the total spectra and contributions of cascade� pre�

equilibrium� and evaporative components� respectively� In the lower row� di�erent emission

angles are drawn with di�erent symbols� as indicated� The experimental data are from

Ref� �� for neutrons and from Ref� �� for protons�

Fig� �� Energy dependence of the neutron�induced �ssion cross section of ��U� Calcu�

lations are performed with Krappe� Nix� and Sierk �ssion barriers �� Cameron shell and

pairing corrections �� the third Iljinov et al� systematics for the level density parame�

ters �� with a dependence Bf �L� estimated by a phenomenological approach �formulas

�� from Ref� �� with the value for the moment of inertia of a nucleus at the saddle�

point Jsp from Ref� �� without taking into account the dependence of Bf on excitation

energy E�� and with the value for the ratio af�an � �� The experimental points are

from Refs� �� For comparison� two values of �f calculated at Tn � �� and ��

MeV in Ref� �� with the code LAHET �� are shown by open triangles�

�

�� Sensitivity of Results to Details of Calculations and InputParameters

Our previous analysis of excitation functions in the framework of the CEM hasshown �� that if one uses the usual �default� parameters CEM� describes satisfac�torily �and no worse than other models� the majority of isotope yields in the spallationregion� At the same time for a few cases in the same spallation region where themodel �has to work� it underestimates or overestimates some individual measuredexcitation functions sometimes by a order of magnitude� Similar results have beenobtained by many authors with other codes �see e�g� Refs� �� To understand this situation we �rst perform a detailed analysis of the dependenceof calculated excitation functions on those input parameters of the CEM which canbe changed without a�ecting the basis of the model� Moreover such a study seemsto be necessary as to our knowledge there is not a common point of view in theliterature on the question� �How do calculated excitation functions depend on theinput values of the same parameters used in di�erent models'�

Our �rst trivial but necessary test was as follows� The voluminous and time�consuming calculations of this study were performed using di�erent UNIX machinesand DOS PCs at JINR �Dubna� ORNL �Oak Ridge� and CEA �Bruy(eres�le�Ch)atel��As we used di�erent FORTRAN compilers on UNIX and DOS machines it wasimportant to check that the code would run without problems on all these di�erentmachines and that the results would be the same� As a test the reaction p��Cohas been calculated for the same incident energies on all the machines used� Withinstatistical errors we have obtained the same results serving as a convincing proof ofthe reliability of CEM��

Our second test is done to understand how the extended version of the model�� realized in the code CEM� describes excitation functions as compared to thestandard version of the CEM �� We perform calculations with both versionsof the CEM for several dozens of excitation functions for di�erent target nuclei� Asan example Fig� shows a comparison of experimental �� excitationfunctions for the production of ��Si ��Al ��Na ��Na �He �He t and d from p��Alwith predictions of both versions of the CEM� Similar results are obtain for othertargets� One can see that on the whole the extended version �� agrees better withexperimental data than the standard CEM �� does�

Our next test was to analyze the dependence of calculated excitation functionson the inverse cross sections �jinv�E� used in calculations� In CEM� inverse crosssections are used to calculate partial widths "j for particle emission at preequilibriumstages of reactions according to Eq� �� and at the evaporative stages according toEq� �� We calculate �jinv�E� using the almost �� year old approximation � � �by Dostrovsky et al� �� which in principle should be replaced by a newer onetaking into account all available experimental data� To understand how our resultsdepend on �jinv�E� we perform calculations with the Dostrovsky et al� �� valuefor &r� in Eq� � � of �� fm and with &r� � �� fm� An example of such calculations

�

for the production of ��Fe ��Mn �Cr �V ��K and ��Cl from p��Fe is shown inFig� �� Similar results are obtained for other reactions�

Fig� �� Excitation functions for the production of d� t� �He� �He� ��Si� ��Al� ��Na� and��Na from p��Al calculated with the extended version �� of the CEM �solid lines� and

with the standard version � with a � ��A �dashed lines�� Experimental data are labeled

as� BA�� KO�� NUCLEX �� and BOD��

Fig� � Dependence of calculated excitation functions for the production of ��Fe� ��Mn��Cr� �V� ��K� and ��Cl from p��Fe on the value of �r� in Eq� �� for the inverse cross

sections� solid lines are calculated with �r� � �� fm and dashed lines with �r� � �� fm�

Experimental data are labeled as� NUCLEX �� VI� �� LA� �� RU��

AL��b �� and HON� ��

One can see that our excitation functions are not very sensitive to the inversecross sections used in the calculations� Only in a few cases and at not too highincident energies do excitation functions calculated with &r� � �� fm di�er from theones calculated with &r� � �� fm by a factor of two� So we can conclude that thefew previously mentioned large discrepancies between experimental data and someexcitation functions calculated with CEM� observed in Ref� �� are not connectedwith the old inverse cross sections used in the calculations� However as one can seefrom Fig� � inverse cross sections do a�ect results in some cases up to a factor ofabout so we should use the best possible values of �jinv�E��

�

Our next test is to �nd out how excitation functions predicted by CEM� dependon the level density parameter used in the calculations� The fact that at incidentenergies below � �� MeV nuclear structure e�ects on level density parameters areimportant and have to be properly taken into account in calculations of excitationfunctions is well known and is often discussed in the literature �� Never�theless there is no common point of view in the literature on this question� So inRef� �� it was found that proton�induced excitation functions calculated with thecode ALICE�� agree better with experimental data using level density param�eters calculated in the framework of the generalized super uid model of nuclei ��as compared to the case of using of the Fermi�gas model value a � A�� the sameconclusion was made in Ref� �� and just the opposite result was obtained in thecase of ��induced reactions� At higher incident energies of about � GeV where onemay expect that the in uence of level density parameters on calculated yields is ofless importance the situation is even more confused� Recently Fukahori has con�cluded �� that isotope production cross sections calculated at these energies withthe code ALICE�P are not sensitive to the level density parameter� The di�erenceof results obtained with the Fermi�Gas Model with Ramamurthy$s method ��and with the Liquid Drop Model for the level density parameter was only about *�� On the contrary Nishida and Nakahara �� have found that the distribu�tion of some isotopes of the non��ssion component from p��Np interactions at ��MeV calculated with the code NUCLEUS �� with the values for the level densityparameter a � A�� A� � A�� A� and calculated according to an expressionderived by Le Couteur �� di�er both in shape and absolute value by about oneorder of magnitude �see Fig� from Ref� ��

The in uence of the level density parameter on excitation functions calculated byCEM� was not studied previously and as the information presented in the literaturewith other codes is contradictory we perform a detailed analysis of this point here�In Ref� �� it was found that the main CEM nuclide production mechanism inthe spallation region is the successive emission of several nucleons while emissionof complex particles is of importance �and may even be the only mechanism forproduction of a given isotope in a limited range of energy� only at low incidentenergies near the threshold while with increasing energy its relative role quicklydecreases� Taking this into account one may try to obtain an overview of the questionof how the level density parameter a�ects excitation functions predicted by CEM�in the spallation region from a study of the in uence of the level density parameteron the mean multiplicities �or yields� of emitted particles� As an example Table Isummarizes the ratios of mean multiplicities of n p d t �He and �He emitted fromp��Co interactions at � �� and �� MeV calculated with a � ��A ��A and��A to the ones calculated using the third Iljinov et al� �� systematics � �� fora�Z�N�E�� Fig� � shows the yields of n p d t �He and �He calculated with thesefour level density parameters for proton incident energies from �� MeV to GeV�One can see that the yields of neutrons and protons predicted by CEM� depend veryweakly on the value of the level density parameter a� The biggest di�erence of the

�

ratios for nucleons shown in Table I may be seen for neutrons at an incident energyof � MeV when one passes from a � ��A to a � ��A and it is only about ��*�which is consistent with the conclusion of Fukahori �� and does not agree with theresults of Nishida and Nakahara �� The yields of complex particles predicted byCEM� depend more strongly on the level density parameter� the biggest di�erencefor the ratios shown in Table I is for emission of t at � MeV where it is about � *�

TABLE IRatios of mean multiplicities of secondary particles emitted from p��Co

interactions at � �� and �� MeV calculated with the code CEM� witha � ��A ��A and ��A to the ones calculated using the third Iljinov et

al� �� systematics � �� for a�Z�N�E�� gures in parenthesis in the last rowshow the corresponding mean multiplicities themselves�

Tp �MeV� Part� a � ��A a � ��A a � ��A a � a�Z�N�E��

� n �� p �� d �� t ��

�He �� He ��

�� n �� p �� d �� t ��

�He �� He ��

�� n �� p �� d �� t ��

�He �� He ��

�

Fig� �� Excitation functions for the production of �He� �He� t� d� p� and n from p��Co

calculated with the third Iljinov et al� systematics for a�Z�N�E�� solid lines� and with

�xed values a � ��A� a � ��A� and a � ��A �dashed lines�� as indicated�

This is much lower than the corresponding di�erences of about two orders of mag�nitude shown in Table I of the work by Nishida and Nakahara �� Therefore wemay expect as was concluded by Fukahori �� that isotope yield production inthe spallation region for these incident energies is not sensitive to the level densityparameter� This inference can also be drawn from Fig� � where mass�yield distribu�tions from p��Co at � �� and � �� MeV calculated with CEM� using thefour values cited above for the level density parameter are shown together with theavailable experimental data �� Note that the experimental points inFig� � show the yields of only the several measured nuclides indicated in the �gurewhile the calculated histograms represent sums over all produced isobars thereforean exact comparison between them is not possible and we show the experimentaldata only as a guide��

�

Fig� �� Mass�yield distributions from p��Co at �� and �� MeV calculated

with the third Iljinov et al� systematics for a�Z�N�E�� solid lines� and with �xed values

a � ��A� a � ��A� and a � ��A �dashed lines�� as indicated� Experimental data for

incident energies and nuclides shown in the �gure are labeled as� MI�� MI��

MI�� and SHV��

One can see that for all these incident energies mass�yield distributions calculatedwith di�erent values of a are very close to each other especially in the spallationregion� Only for �nal isobars far away from the target nucleus do the di�erences ofcalculated yields increase slightly but still remain within a factor of two� Similarresults are obtained for charge�yield distributions� Such results suggest to us that onthe whole excitation functions calculated with the CEM� in the spallation regionare not very sensitive to the level density parameter�

A more detailed analysis of all possible excitation functions shows that such aconclusion is not exactly correct� We perform calculations of all possible excitation

��

functions for interactions of protons with energies from �� MeV up to GeV with�Co using the four values of a cited above� Figs� �� show our results for theproduction of all nuclides for which we are able to �nd experimental data as well asfor �Ni the simplest reaction channel�

��

Fig� �� Excitation functions for the production of �Ni� ��Ni� ��Ni� �Co� ��Co� ��Co�

and ��Co from p��Co calculated with the third Iljinov et al� systematics for a�Z�N�E��

�solid lines� and with �xed values a � ��A� a � ��A� and a � ��A �dashed lines�� as

indicated� The thick short dashed lines marked with a � are calculated as the solid ones

but with six times smaller pairing energies� �c � �c ��pAc and �j � �j ��

pAfj �see Eq�

�� Experimental data are labeled as� MI�� MI�� MI�� AL��

MI�� and SHV�� Here and in all following �gures� an �i� or �c� indicates whether

the experimental cross sections are given as independent or cumulative� respectively�

�

Fig� �� The same as Fig� � but for the production of �Fe� ��Fe� ��Mn� ��Mn� ��Mn��Cr� and �Cr� Experimental data are labeled as� AL�� ZA�� MI��

MI�� SHV�� MI�� and MI��

��

Fig� �� The same as Fig� � but for the production of �V� �Sc� ��Sc� ��Sc� ��Sc� and��Sc� Experimental data are labeled as� MI�� SHV�� MI�� AL��

and MI��

One can see that the majority of excitation functions calculated with these di�er�ent values for a are very similar� This is true both for the production of most nuclidesnear the target nucleus and for nuclides far away from it especially for nuclides withlarge yields� However for some nuclides with low production cross sections thein uence of a on calculated excitation functions is signi�cant� Sometimes resultsobtained with di�erent values of a di�er up to a factor of �� Unfortunately ourresults for such nuclides are less precise due to poorer statistics in the Monte Carlosimulation for these rare events� but the observed di�erences are greater than wouldbe explained by the statistical errors of the calculations� We obtain such results forthe production of several nuclides near the target nucleus� ��Ni and ��Co �Fig� ��Fe and ��Fe �Fig� �� for nuclides in the spallation region� �Cr �Fig� �� Sc�Fig� �� K and ��K �Fig� � �� and for nuclides in the fragmentation region faraway of the target� �Mg and �Be �Fig� � ��

��

Fig� �� The same as in Fig� � but for the production of ��K� ��K� �Mg� ��Na� ��Na� and�Be� Experimental data are labeled as� MI�� SHV�� AL�� and MI��

Let us note that the CEM does not contain a special mechanism for nuclearfragmentation and does not pretend to describe the production of light fragmentslike �Be from intermediate and heavy targets� But at high incident energies of about� GeV and above a deep spallation with emission of a large number of nucleons fromthe target nucleus takes place and as a result for not too heavy targets we haveevents when residual nuclei at the end of all stages of reactions are just fragments�This is only a small part of the total fragment production measured in experimentsbut as one can see from Fig� � its cross section depends also strongly on the valueof level density parameter a� Summarizing all results shown in Figs� �� wecan conclude that the mean multiplicity of nucleons predicted by the CEM doesnot depend signi�cantly on the level density parameter used in calculation and asa result of this the mass�yield and charge�yield distributions of residual nuclei as

�

well as excitation functions for the production of nuclides with large productioncross sections are not very sensitive to the level density parameter� But excitationfunctions of some nuclides with small yields are more sensitive to the value of a�Therefore to be able to predict correctly the production of arbitrary nuclides it isnecessary to perform calculations with reliable values for the level density parameter�

Although the level density parameter in uences the calculated nuclide yields wedo not think that those large discrepancies between some theoretical and experimen�tal excitation functions observed in Ref� �� were caused by use of an inappropriatevalue of a� we used in those calculations �� the third Iljinov et al� �� systematics� �� for a�Z�N�E�� which was tested to be �the best� set for CEM�� We thinkthat such large discrepancies between some calculated and experimental excitationfunctions are connected mainly with the energetics of reactions i�e� with the calcula�tion of nuclear masses binding energies and consequent Q�values and with the shelland pairing corrections used� The fact that excitation functions are very sensitiveto the nuclear masses and shell corrections used in calculations is well known in theliterature and this problem was analyzed in a number of recent works �� To our knowledge the in uence of pairing energies on excitation functions calculatedat energies of about � GeV and above has not been previously discussed� To under�stand how pairing corrections in uence excitation functions calculated with CEM�we perform calculations for the reaction p��Co with six times smaller pairing ener�

gies !c � �c � �pAc and !j � �j � �

qAfj as compared to �the standard� values

de�ned by Eq� � �� The corresponding results are shown in Figs� �� by thickshort�dashed lines which should be compared with the solid lines in the same �g�ures� One can see that excitation functions for the production of some nuclides arerather sensitive to the values of pairing energies used in calculations� This result isunexpected� our experience shows that such characteristics of nuclear reactions asinclusive spectra of secondary particles their integrals over energy and�or anglesmass�yield or charge�yield distributions of residual nuclei essentially do not dependon the values of the pairing energy used in the CEM calculations at these incidentenergies� As one can see from Figs� �� some excitation functions calculated withdi�erent values of pairing energies di�er by fairly large factors and these di�erenceseven increase with increasing incident energy� To be able to predict arbitrary excita�tion functions it is necessary to use values for the pairing energies which are reliableand well tested for the whole range of incident energies�

Several special calculations show that our conclusions from analysis of p��Cointeractions are also valid for other reactions� As an example Figs� �� showa comparison of experimental data with theoretical total inelastic cross section andexcitation functions for the production of ��O ��N ��C ��B ��Be ��Li and�H from p��O calculated in the framework of the standard version of the CEM ��with the value for &r� in Eq� � � of �� fm with �xed values for the level densityparameter a � �� A �thick solid curves labeled as �� and a � ��A �thick dashedcurves labeled as � as well as to those calculated with the extended

��

Fig� �� Total inelastic cross section and excitation functions for the production of ��O��O� ��N� ��C� ��C� ��B� and ��B from p��O calculated in the standard version of the CEM

� with a � ��A �curves �� and a � ��A �curves �� and in the extended version ��

for a � ��A with �r� � �� fm �curves �� and �r� � �� fm �curves �� Experimental data

are labeled as� BARASHENKOV�� NUCLEX �� and YI� ��

��

Fig� �� Excitation functions for the production of ��Be� Be� �Be� Li� �Li� and �H

from p��O� Experimental data are labeled as� BOD�� AM�� NUCLEX ��

YI� �� and HON� �� The rest of the notation is the same as in Fig� ��

version �� with a � ��A for &r� � �� fm �thin solid curves labeled as �� and&r� � �� fm �thin dashed curves labeled as ��

Although these calculations are performed for a smaller number of incident ener�gies �therefore the curves connecting the calculated points are not smooth� one cansee that these excitation functions are not very sensitive either to a reasonable varia�tion of the level density parameter a �compare curves � and � or to the inverse crosssections �compare curves � and �� But one can see large di�erences �compare curves� and �� between results obtained with the original version of the CEM �� and thosefrom the extended version �� Just as in the case of �Co we see that excitationfunctions generally are very sensitive to the energetics �shell and pairing energies andQ�values� of the reactions and much less so to the level density parameters and theinverse cross sections used in calculations�

��

Let us dwell now on two important details of the calculation and comparison withmeasured data� Many experimental data are obtained for targets of natural isotopiccomposition� Our experience shows that such characteristics of nuclear reactions astotal inelastic cross sections spectra and multiplicities of secondary particles etc�are not very sensitive to the values of mass�number A of the target used in CEMcalculations� For example for interactions of protons of �� MeV with iron spec�tra of secondary particles calculated with CEM� separately for the stable isotopes��Fe ��Fe ��Fe and �Fe and then summed up with the corresponding weights ofeach isotope in the target are practically the same as results obtained from a singlecalculation of the p��Fe reaction� In the case of excitation functions the situationis di�erent� As an example Fig� � shows available experimental data together withexcitation functions predicted by CEM� for the production of �Co ��Co ��Co��Co and ��Mn from interactions of protons with energies from �� MeV up to GeVwith ��Fe ��Fe ��Fe �Fe and natFe� One can see that both experimental and calcu�lated excitation functions depend critically on the mass number of the target isotope�Excitation functions for the production of the same nuclides from di�erent target iso�topes di�er both in the shape and magnitude up to an order of magnitude and morein the whole region of incident energies� Therefore to predict unknown excitationfunctions from a target with a natural composition of isotopes it is necessary toperform calculations for all isotopes of the target taking into account the percentageof each� Similar problems arise when we would like to compare calculated and ex�perimental excitation functions� for an accurate comparison it is necessary to knowthe exact isotopic composition of experimental samples and to perform calculationsfor the same composition otherwise we may obtain large discrepancies only becausewe compare di�erent things�

The next problem for an accurate comparison between experimental and theoreti�cal excitation functions is connected with the so called �individual� and �cumulative�yields� All theoretical models give �individual� cross sections for the production ofspeci�c nuclides at �zero time� after a nuclear reaction� On the contrary the gamma�spectrometry method used in the majority of current measurements provides only�cumulative� yields i�e� the �measured� cross sections contain contributions fromall radioactive precursors which through their decay chains lead to the production ofthe detected nuclides� Only if there are no radioactive precursors contributing to agiven nuclide will the measured cross section be �independent�� For many nuclidesespecially those produced from heavy targets the cumulative yields may be an orderof magnitude or more larger than the independent ones� Therefore one should bevery careful when comparing measured and calculated excitation functions as onemay obtain false di�erences of orders of magnitude simply due to comparison of dif�ferent things� This point is especially important for models and codes which canallow only a limited number of nucleons to be emitted from targets�

��

Fig� �� Excitation functions for the production of �Co� ��Co� ��Co� ��Co� and ��Mn

from interaction of protons with di�erent isotopes of iron� as indicated� Experimental data

are labeled as� SU�� MI�� MI�� AL��b �� and NUCLEX ��

��

Let us denote the �independent� yield of a nuclide �A�Z� by �i�A�Z� and the �cu�mulative� yield by �cum�A�Z�� From the de�nition of cumulative yields we have ��

�cum�A�Z� � �i�A�Z� �X

�A��Z��

b�A�� Z � � A�Z��i�A�� Z ��

where b�A�� Z � � A�Z� is the fraction of decays of �A�� Z �� that go to �A�Z�� For adecay chain

�A�� Z�� A�� Z�� An� Zn�

de�ned by decay constants �j half�lives Tj�� ln ��j and branching ratios rj the

cumulative yield of a nth nuclide in the �j �n case can be calculated �� as�

�cumn �An� Zn� � �in�An� Zn� ��n��

��n�� n�

Xj

�ij�Aj� Zj�rj � ��

For the majority of cumulative yields calculated in the present work the factors�n��n�� n� in Eq� �� and b�A�� Z � � A�Z� in Eq� �� are very close toone� For all targets and incident energies regarded here we perform at the beginningcalculations of individual yields for all possible nuclides then from these numerical�les calculate the corresponding cumulative yields� To simplify this work we takeinto account in our calculations only precursors �k� with branching rations rk nearlyequal to one and estimate cumulative yields approximately as�

�cum�A�Z� � �i�A�Z� �Xk

�i�Ak� Zk� � ��

All precursors included in the calculations of each cumulative yield are shown ex�plicitly in the �gures and tables with our results in the following section� Weuse the radioactive decay chains and corresponding branching rations published inRefs� ��

��

�� Results and Discussion

In this section we present results of calculation and analysis of �� excitation func�tions for reactions induced by protons from �� MeV to GeV on ��C ��N ��O ��Al��P ��Ca ��Fe ��Fe ��Fe �Fe natFe �Co �Zr �Zr �Zr �Zr �Zr natZr and��Au� To some extent this study was inspired by the present International Codesand Model Intercomparison for Intermediate Energy Activation Yields �� Thereforewe have included in our analysis target elements of ��O ��Al natFe �Co natZr and��Au recommended by the Intercomparison as di�erent types of materials which areimportant for technological applications �� Oxygen is a main constituent of ambi�ent air and shielding concrete� aluminum is a structural material and one of the bestinvestigated target nuclei being the most often used for monitoring purposes� ironand zirconium are structural materials also well investigated experimentally� cobaltwas selected in order to test the model when calculating nuclide production nearclosed shells� and gold was chosen to represent the heavy target elements� For thesetargets we include in our work not only the excitation functions required by the In�tercomparison �� but also all other excitation functions for which we found reliableexperimental data� Furthermore apart from the recommended targets of natFe andnatZr of natural isotopic composition we have included in our study also reactionson all isotopes of iron and zirconium in order to analyze how excitation functionsfor the production of the same nuclides from di�erent target isotopes depend on theisotopic spin of the target and how well CEM� reproduces this e�ect� In addition tothe targets recommended by the Intercomparison �� we have included in our studyalso reactions with nuclei of human tissue ��C ��N ��P and ��Ca for which reliabledata �les are needed for dosage calculation in radiation oncology� For all targetsconsidered in this work we calculate excitation functions for the production of allpossible nuclides in the framework of the extended version of the CEM �� usingthe third systematics for a�Z�N�E�� by Iljinov et al� �� except for interactionswith the lightest ��C ��N and ��O targets for which to avoid some computationaltroubles we use the �xed value a � �� A and perform calculations with the stan�dard version of the CEM �� Below we show results for the production of thosenuclides for which we found reliable experimental data and as a prediction severalexcitation functions that are not measured yet but are interesting for understandingmechanisms of nuclear reactions and for some applications�

Let us show our results starting with the lightest target ��C and moving succes�sively to heavier ones up to ��Au�

�� Targets ��C� ��N� and ��O

These lightest targets are just �the most di�cult� for us as the CEM similarly toother Monte Carlo statistical models is not well justi�ed for light nuclei� None of thethree stages of nuclear reactions considered by the CEM is well justi�ed physically

�

for such light targets� The separation energies of nucleons from light nuclei di�ersigni�cantly from the mean value of binding energy of � MeV used at the cascadestage of a reaction the �trawling� e�ect mentioned in Section is more importantfor light targets but is not taken into account in CEM� it is di�cult to justifya division of a nucleus having only � nucleons into � potential zones etc� It isalso di�cult to justify a process of statistical equilibration with possible emissionof particles at the preequilibrium stage of reactions when after emission of severalcascade nucleons we may have a system with less than �� nucleons� It is even less welljusti�ed to evaporate particles at the last stage of reaction from a residual nucleuswith only a few nucleons when the assumptions of the evaporation model lose theirvalidity� It probably makes more sense to use for the description of de�excitation ofsuch light excited nuclei the Fermi breakup model at least for relatively high values ofexcitation energy �see a detailed discussion of these questions e�g� in Refs� �� but this model is not incorporated into the CEM�

Taking all these points into account it is questionable to expect a good descriptionby the CEM of nuclide yields from such light targets� Nevertheless our previouscalculations �� have shown that the CEM satisfactorily predicts spectra of secondaryparticles even for ��C� It is interesting to check its applicability for a description ofexcitation functions from such targets� Due to a lack of better grounded and suitablemodels for incident energies of � � GeV and above similar statistical Monte Carloapproaches as implemented e�g� in the codes HETC�KFA �� DISCA ��CASCADE �� are often used �� to calculate excitation functionsfrom such light targets�

The total inelastic cross section �in and excitation functions for the production of��N ��C ��Be �Li ��He t d p n �� and �� from p��C calculated in ourpresent work are shown in Figs� �� and �� together with available experimental data�� To understand the mechanisms of productionof �nal isotopes predicted by the CEM for ��C and ��C �Fig� �� the contributionsfrom the channels �pd� �pnp� and �pnd� to the total yields are shown separately�For �He �He t d p and n the contributions to the total production cross sectionsfrom preequilibrium emission evaporation and the cascade stage of the reaction�for nucleons� as well as the contribution of residual nuclei remaining after all threestages of the reactions are shown also in Fig� �� For comparison predictions ofthe phenomenological systematics by Korovin et al� �� for the production of �He�He and t are shown in Fig� �� as well� CEM� cross sections for the productionof �He shown in Fig� �� for ��C and in the following �gures for other targets areindependent without a contribution from the progenitor t�

Figs� �� and �� show a comparison of calculated �in and excitation functions forthe production of ��O ��N ��C ��Be �Li ��He ��H n and �� from p��Nwith available experimental data �� For the production ofLi independent and cumulative yields calculated according to Eq� �� are shownseparately�

��

Fig� �� Total inelastic cross section and excitation functions for the the production of��N� ��C� ��C� ��Be� �Be� Li� and Li from p��C� For ��C and ��C� dashed lines show con�

tributions from the channels �p�d�� p�np�� and �p�nd� to the total yields� as indicated� Ex�

perimental data are labeled as� BARASHENKOV�� RI� �� NUCLEX ��

BOD�� AM�� and MI��

��

Fig� �� Excitation functions for the the production of �He� �He� �He� t� d� p� n� ��

�� and �� from p��C� The contribution to the total yields of nucleons and complex

particles from preequilibrium emission� evaporation� and the cascade stage of the reaction

�for nucleons�� as well as the contribution of residual nuclei remaining after all three stages

of the reactions to the total CEM�� yields are shown separately by dashed lines� as indi�

cated� Experimental data are labeled as� NUCLEX �� BA�� and KO��

For �He� �He� and t� predictions of the phenomenological systematics by Korovin et al� �

are shown by thick long dashed lines labeled by ��

�

Fig� �� Total inelastic cross section and excitation functions for the production of��O� ��N� ��C� ��C� ��Be� and �Be from p��N� For �Be� the dashed line shows the results

obtained in Ref� �� with the hybrid model code ALICE LIVERMORE �� using the

Myers and Swiatecki mass formula �� see Fig� � and details in Ref� �� Experimental

data are labeled as� BARASHENKOV�� NUCLEX �� BOD�� MI��

and AM��

��

Fig� �� Excitation functions for the production of Li� Li� �He� �He� t� d� p� n� ��

�� and �� from p��N� For Li� the independent and cumulative yields are shown by solid

and dashed lines� respectively� Experimental data are labeled as� NUCLEX �� and

BA��

The results of calculation of �in and of excitation functions for the productionof ��O ��N ��C ��B ��Be ��Li ��He ��H n and �� from p��Oare compared in Figs� �� with available experimental data �� with results of calculations of ��Be yield using the codes ALICELIVERMORE �� and HETC�KFA �� from Ref� �� in Fig� � and withthe predictions of the phenomenological systematics from Ref� �� for the productionof t in Fig� �

��

Fig� �� Total inelastic cross section and excitation functions for the production of��O� ��O� ��N� ��C� ��C� ��C� and ��B from p��O� For ��O and ��O� dashed lines show

the contributions from the channels �p�d�� p�np�� p�t�� p�nd�� and �p��np� to the total

yields� as indicated� For ��N� ��C� and ��B� the independent and cumulative yields are

shown by solid and dashed lines� respectively �for ��N and ��C� they are practically the

same�� Experimental data are labeled as� BARASHENKOV�� NUCLEX ��

and YI� ��

��

Fig� �� Excitation functions for the production of ��B� ��Be� Be� �Be� Li� �Li� and�Li from p��O� For ��Be� the results from Fig� � of Ref� �� calculated with the codes

ALICE LIVERMORE �� and HETC�KFA� �� are shown by dotted and dashed

lines� respectively� Experimental data are labeled as� YI� �� BOD�� AM��

NUCLEX �� and MI�� The rest of the notation is the same as in Fig� ��

��

Fig� �� Excitation functions for the production of �He� �He� t� d� p� n� �� and ��

from p��O� The contribution to the total yields from cascade� preequilibrium� evaporation

emission� and from residual nuclei after all three stages of the reaction are shown separately

by dashed lines� as indicated� For t� the prediction of phenomenological systematics from

Ref� � is shown by a thick long dashed line marked with an �s�� Experimental data are

labeled as� NUCLEX �� and HON� ��

�

Contributions from the channels �pd� �pnp� �pt� �pnd� and �p np� to thetotal yields are shown in Fig� � for the production of ��O and ��O and from cascadepreequilibrium evaporation emissions and from residual nuclei are shown in Fig� for �He �He t d p and n respectively�

One can see that on the whole the agreement between calculations and exper�imental data is poor for these light targets� Sometimes the CEM reproduces theshapes and for some reactions the absolute values of measured excitation func�tions for not too low incident energies� But for several reactions like ��C�p�p��Be��N�px��C ��N�px��Be ��O�px��N the CEM fails to reproduce correctly the formof experimental data� For other reactions like ��C�px��Be ��N�px��N ��O�px��Bethe form of experimental excitation functions are reproduced satisfactorily but thedi�erence in the absolute values is too large�

As discussed above there are many aspects of the CEM not appropriate to suchlight targets and there are many causes of the observed discrepancies� Neverthelesstaking into account the results presented in Section � we think that such seriousdiscrepancies are caused mainly by poor nuclear masses binding energies and con�sequent Q�values used in CEM� for these nuclides� First we calculate the bindingenergies of preequilibriumand evaporative particles using the Cameron formula ��This formula is old and fails to describe correctly the masses of some nuclides� It ispreferable to use for this purpose the recent experimental mass tables �� and wherethey are absent some new and more reliable mass formulas e�g� from Ref� ��This has been done in a newer version of the CEM and its e�ect will be discussed ina separate paper� A more serious problem for light nuclides are masses and bindingenergies used at the cascade stage of reactions� The Dubna ICM �� used as the�rst stage of reactions in the CEM is a purely classical approach which does notuse any nuclear structure e�ects� The mass of a nucleus is calculated in the ICMsimply as the atomic mass number times the mean mass of a nucleon and a meanseparation energy for nucleons BN � � MeV is used for all nuclides� The last point ispartially justi�ed only for medium and heavy nuclei but for light targets it is oftenstrongly violated� So if ��Be is produced in the reaction ��C�p�p��Be via a consecu�tive emission of three protons the experimental separation energies for these protonsare �� and �� MeV respectively which di�er signi�cantlyfrom the value of � MeV used in the CEM� In the case of the production of ��Cfrom p��O the experimental separation energies of the three consecutively emittedprotons are �� and �� MeV which also di�er greatly from� MeV� We think that this is one of the weaker points of CEM� and of all codesusing �xed values for the mean nucleon binding energy BN of cascade nucleons ifone wishes to describe with these codes yields of nuclides from light targets� Thisincludes all modi�cations of HETC �� using the standard Bertini ICM �� withBN � � MeV HETC��STEP �� BN � � MeV� NUCLEUS �� BN � � MeV�and INUCL �� BN � �� MeV�� Probably it is necessary to use in CEM� andother codes experimental mass tables augmented by new and reliable mass formulasfor the cascade stage of reactions as is already done in some codes like DISCA ��

�

or CASCADE ��For comparison the results of Michel$s group for the production of �Be from ��N

obtained in Ref� �� with the hybrid model code ALICE LIVERMORE �� using the Myers and Swiatecki mass formula �� are shown in Fig� �� and theyields of ��Be from ��O calculated with the codes ALICE LIVERMORE �� and HETC�KFA �� from Ref� �� are shown in Fig� �� One can see thatHETC�KFA �� also fails to reproduce the excitation function ��O�px��Be whileALICE LIVERMORE �� reproduces correctly the production of ��Be from ��Obut fails to describe the reaction ��N�px��Be�

As the CEM reasonably describes the spectra of nucleons pions and compositeparticles from such light targets �� the corresponding excitation functions for theproduction of �He �He t and d agree better with the scarce available experimentaldata and with predictions of phenomenological systematics by Korovin et al� ��Figs� �� and � than do those for production of heavier nuclei� We do notknow of any experimental data for yields of nucleons and pions from these targetsso our results shown in Figs� �� and for these cross sections may serve aspredictions�

When our study was completed two new papers by Michel$s group were pub�lished �� They contain new measurements for these and other targets consid�ered in our work as well as results of calculations with the codes HETC�KFA ��and AREL �� which is a relativistic version of the popular hybrid model code AL�ICE� As a detailed comparison with these new data and calculations is not includedin the present paper let us note only that neither HETC�KFA �� nor AREL ��are able to reproduce correctly the production of ��Be and �Be from carbon nitrogenand oxygen although AREL shows better results for energies below � �� MeV�

�� Target ��Al

Excitation functions from p��Al are some of the best measured and most widelyinvestigated theoretically� Our results for production of ��Si ��Al ��Mg and��Na are shown in Fig� �� for ��Ne ��F and �O in Fig� �� for ��Nand ��C in Fig� and for ��Be Li ��He and t in Fig� �� The CEMindependent yields are shown by solid lines with the corresponding cumulative yieldsby dashed lines� For some nuclides like ��Al ��Mg ��Na ��Ne and ��Fcumulative and independent yields are so close that the corresponding lines on ourplots practically coincide� But for several nuclides like ��Ne and ��Ne cumulativeyields �shown on plots by thick dashed lines� are about one order of magnitudehigher that the independent ones indicating a careful consideration of the properyield calculations is necessary�

��Al is not as light as the previous targets and is already more suitable to be cal�culated with the CEM� One can see that on the whole the agreement of calculationswith measured data is much better than for C N and O although some large

Fig� �� Excitation functions for the production of ��Si� ��Si� ��Al� ��Mg� ��Mg� ��Na��Na� and ��Na from p��Al� For comparison� the results �� of the recent JAERI Bench�

mark �� obtained with the codes ALICE�F �� ALICE�� NUCLEUS ��

and MCEXCITON �� are shown by dashed lines �� and �� respectively� For ��Al� the

results from Fig� � of Ref� �� calculated with the codes ALICE LIVERMORE ��

and HETC�KFA� �� are shown by dashed lines � and �� as indicated� The independent

and cumulative CEM�� yields are plotted by solid and dashed lines which for these reac�

tions are very close to each other� For ��Al� the contributions to the total CEM�� yield

from the channels �p�d� and �p�np� are shown separately by dashed lines� as indicated�

Experimental data are labeled as� NUCLEX �� BOD�� and MI��

�

Fig� �� Excitation functions for the production of ��Ne� ��Ne� ��Ne� ��Ne� ��Ne� ��F��F� and �O from p��Al� For comparison� the results �� of the recent JAERI Bench�

mark �� obtained with the codes ALICE�F �� ALICE�� NUCLEUS ��

and MCEXCITON �� are shown by dashed lines �� and �� respectively� Experimen�

tal data are labeled as� NUCLEX �� BA�� BI� �� GO� �� MI��b ��

and MI��

�

Fig� �� Excitation functions for the production of ��N� ��N� ��C� and ��C from p��Al�

The results �� of the recent JAERI Benchmark �� obtained with the codes ALICE�

F �� and ALICE�� are shown by dashed lines � and �� respectively� Experimental

data are labeled as NUCLEX ��

systematic discrepancies for several nuclides still occur� We believe these discrep�ancies result mainly from two di�erent causes� First the strong overestimation ofthe production of ��Si ��Na ��Ne ��F and the underproduction of ��Mg and ��Nare probably caused by the inaccurate masses and binding energies used in CEM��For example the separation energies of the two neutrons emitted in the reaction��Al�p n��Si are equal to �� and �� MeV in the experimental mass ta�bles �� much di�erent from the value � MeV used in CEM� for cascade neu�trons�

The underproduction of ��C and ��C may be partly be caused for the same rea�son as well as by a second and separate one which may be seen more obviously forfragments ��Be �Be and Li �Fig� �� The CEM does not contain a mechanism offragmentation and does not take into account evaporation and preequilibrium emis�sion of complex particles with A �� All light fragments predicted by the CEMare only residual nuclei remaining after all three stages of reactions� This is only asmall part of the total production of fragments and it is signi�cant only for lightenough targets and high incident energies� To be able to reproduce the productionof fragments the CEM has to be extended by incorporating mechanisms of fragmen�tation of heavy nuclei Fermi breakup of highly excited light nuclei evaporation andpreequilibrium emission of fragments with A � from medium and heavy nuclei�

For comparison the results �� of the recent JAERI Benchmark �� ob�tained with the codes ALICE�F �� ALICE�� NUCLEUS �� and MCEX�CITON �� are shown in Figs� �� for several nuclides and the results for��Al from Ref� �� calculated with the codes ALICE LIVERMORE �� andHETC�KFA �� are shown in Fig� � as well� One can see that on the wholefor these reactions our calculations agree with experimental data better than resultsobtained with these codes� Let us note also that the total inelastic cross sectionspredicted �and used for normalization of all excitation functions� by di�erent codesdi�er up to * at low incident energies �see the lower�right plot in Fig� ��

To understand the CEM production mechanisms for ��Al �Fig� �� the contri�butions to the total yield from the channels �pd� and �pnp� and for �He �He andt �Fig� �� the contributions from preequilibrium emission evaporation and fromresidual nuclei are shown separately� We will discuss these results later in this sectionmaking a comparison with other targets�

For production of �He and t the prediction of phenomenological systematics byKorovin et al� �� is shown in Fig� � for comparison� One can see that the yieldsof �He and t calculated with the CEM� agree well with the experimental data andwith systematics �� But for �He the CEM underestimates the experimental dataand results from Ref� �� The underproduction of �He is another serious problemof the CEM �just as it is for almost all other similar models� which we will discusslater�

�

Fig� �� Total inelastic cross section and excitation functions for the production of ��Be��Be� Li� �He� �He� �He� and t from p��Al� Contributions to the total CEM�� yields of�He� �He� and t from preequilibrium emission� evaporation� and from residual nuclei are

shown separately by dashed lines� as indicated� Inelastic cross sections calculated with the

codes ALICE�F �� ALICE�� and MCEXCITON �� are taken from �les ��

of the recent JAERI Benchmark �� in calculated with the code NUCLEUS �� is

taken from Fig� �� of Ref� � � For production of �He and t� the prediction of phenomeno�

logical systematics from Ref� � is shown by a thick long dashed line marked as KO��

Experimental data are labeled as� NUCLEX �� BOD�� MI�� MI��b ��

BI� �� GO� �� KO�� TA�� BA�� and BARASHENKOV��

�

�� Targets ��P and ��Ca

To our knowledge these targets are less well investigated both experimentally andtheoretically� A few more experimental data for the target element calcium and acalculation of the excitation function Ca�px��Cl with the codes HETC�KFA ��and AREL �� have been presented in a recent paper �� published after ourstudy was completed� these results are not included here�

Our prediction for �in and excitation functions for production of ��P �Mg��Na ��He t d p n �� and �� from ��P are shown in Fig� � togetherwith experimental data from Refs� ��

Figs� �� show a comparison of our results for �in and for excitation functionsof production of �K ��Ar ��Cl �Mg ��Na ��Ne ��N ��C Li ��He ��Hn and �� from p��Ca with available experimental data ��

The general agreement of our results with these data and possible causes of somedisagreements are the same as for the target ��Al discussed above� Let us mentiononly the �dramatic� disagreement between the data and calculations that may beseen for ��Ca�px��Ar� In reality this is a false disagreement and a good exampleof the necessity to take into account in calculations the exact isotopic compositionof the target measured� Above we compared our calculations for ��C ��N and��O with the data not mentioning that the real measurements were performed ontargets with natural isotopic composition� For carbon nitrogen and oxygen thiswas reasonably justi�ed as the percentage of ��C in carbon �� is �� * �andonly ��* for ��C�� For nitrogen and oxygen the corresponding percentage ��is also appropriate� ��N ��* and ��N ��*� ��O ��* ��O ��* and�O �� *� Therefore the comparisons made in Figs� �� were quite justi�edalthough some discrepancies could be partly caused by isotopes of the targets whichwere not taken into account in our calculations�

In the case of calcium a comparison of calculations for ��Ca with data obtainedfor natCa is less justi�ed as the percentage of ��Ca in natural calcium is lower� ��Ca��* ��Ca ��* ��Ca ��*� ��Ca ��* ��Ca ��* and �Ca ��*�

�Ar can be produced from p��Ca interactions only through the rare channel�p p�� or through even more rare channels �pnp �� and �p n�� Thereforeour calculated excitation function ��Ca�px��Ar is di�erent from zero only at energiesabove the pion production threshold and is small in value� The measured yield of�Ar comes mainly from interactions of incident protons with heavier isotopes ofcalcium therefore it is already signi�cant at � MeV and it is much higher than ourresults obtained from ��Ca�

Another large discrepancy between experimental data and our calculations is alsoshown in Fig� � for ��Ar� It probably occurs for the same reason just discussed for��Ca�px��Ar�

�

Fig� �� Total inelastic cross section and excitation functions for the production of ��P��Mg� ��Na� ��Na� �He� �He� t� d� p� n� �� and �� from p��P� Experimental data

labeled as NUCLEX are from Refs� ��

�

Fig� �� Total inelastic cross section and excitation functions for the production of�K� �Ar� �Ar� ��Ar� ��Ar� and ��Cl from p��Ca� Experimental data are labeled as�

BARASHENKOV�� NUCLEX �� BA�� and MI��

��

Fig� �� Excitation functions for the production of �Mg� ��Na� ��Na� ��Ne� ��Ne� and��Ne from p��Ca� Experimental data are labeled as� MI�� NUCLEX �� and

BA��

��

Fig� �� Excitation functions for the production of ��N� ��C� Li� �He� �He� t� d� p� n� ��

�� and �� from p��Ca� Experimental data labeled as NUCLEX are from Refs� ��

�

�� Targets �Fe� ��Fe� ��Fe� ��Fe� and natFe

Excitation functions from iron are also very intensively studied� The majority ofmeasurements were performed on targets with a natural composition of iron there�fore most experimental excitation functions were obtained for natFe� Neverthelessmeasurements were performed on targets enriched with given isotopes of iron andin several measurements with natFe the yields from di�erent isotopes were deducedtaking into account the isotopic composition of target and the estimated cross sec�tions for the competing reactions� Because of this many data on excitation functionsfor many nuclides from natFe are available in the literature while not so many onlyfor incident energies below � �� MeV and for only a few nuclides are available forthe separate isotopes of iron�

Our results for excitation functions for production of ��Co and ��Mn from �Feare compared with experimental data �� in Fig� �� Fig� � shows a compar�ison of calculated and measured excitation functions for production of ��Co and��Mn from ��Fe as well as of ��Mn from ��Fe� Our results for production of ��Co��Fe and ��Mn from ��Fe are compared in Fig� �� with experimental data fromRefs� �� and with results of the recent JAERI Benchmark �� obtained withthe codes ALICE�F �� ALICE�� NUCLEUS �� and MCEXCITON ��To understand the relative role of di�erent channels in the production of several nu�clides the contributions from the channels �pn�� Figs� �� and �� from �p�� and�pnpd� �Fig� � � and from �pnp� �pd� �pn p� �ppd� �p�He� �Fig� �� are shownseparately�

One can see that the e�ect of the target isotopic spin on nuclide yields is verystrong �see also Fig� �� excitation functions for production of the same nuclidesfrom di�erent target isotopes di�er in shape and magnitude up to an order of magni�tude or more� CEM� describes quite well all available data �except the productionof ��Mn from �Fe and ��Fe and ��Mn from ��Fe� and reproduces correctly the isotopee�ect� As one can see from Fig� �� the agreement of our results with all experimentaldata is a little bit better than that of calculations with the codes ALICE�F ��ALICE�� NUCLEUS �� and MCEXCITON ��

The serious disagreement between our results and data for �Fe�px��Mn��Fe�px��Mn and ��Fe�px��Mn is connected with an old problem of the CEM�the model underestimates emission of �He �see e�g� �� We encounter simi�lar disagreements in a limited region of incident energies for all excitation functionswhere emission of ��particles is an important or even the only mechanism for pro�duction of a given nuclide� Unfortunately this is a problem not only of the CEMbut of almost all other codes being used for evaluation of nuclear data at interme�diate energies� therefore it is one of the most important problems which needs tobe solved� A similar but smaller underestimation related to this problem can alsobe seen for ��Fe�px��Mn �Fig� �� One can see that the codes ALICE�F ��ALICE�� and MCEXCITON �� underestimate this excitation function evenmore than CEM� does� Fortunately as one can see from Figs� �� and from

��

Figs� �� and � discussed above the role of complex particle emission in theproduction of nuclides in the spallation region is important only at low incident ener�gies near the corresponding thresholds where this mechanism in a region of incidentenergies may be the main channel� With increasing incident energy the importanceof this channel decreases and the main mechanism for production of nuclides in thespallation region becomes a successive emission of several nucleons� Therefore atincident energies above � �� MeV this problem is no longer of great importance�

Fig� �� Excitation functions for the production of �Co� ��Co� ��Co� and ��Mn from

p��Fe� For ��Mn� the contribution to the total CEM�� yield from the channel �p�n�

is shown by a dashed line� Experimental data are labeled as� NUCLEX �� and

SU��

Our results for �in and for excitation functions for production of ��Co ��Fe��Mn ��Cr ��V ��Ti ��Sc ��Ca ��K ��Ar ��Cl��S ��P ��Si ��Al �Mg ��Na ��Ne �F ��C ��Be ��He ��H nand �� from natFe are compared in Figs� �� with the available experimentaldata as well as with the results of calculations �� with Rudstam$s semiempiricalsystematics �� Figs� �� and �� revised results of JAERI calculations �� ob�tained with the codes NUCLEUS �� and HETC��STEP �� Fig� �� resultsof calculation for ��Cl with the code HETC�KFA �� from Ref� �� Fig� ��results of calculations with the code HETC�KFA �� for ��Al from Ref� �� andfor ��Na from Ref� � �� Fig� �� results of calculations of t yield with the codesDISCA �� CASCADE �� NUCLEUS �� and HETC�KFA �� from Ref�

��

�� Fig� �� and with predictions of phenomenological systematics by Korovin etal� �� for ��He and t �Fig� ��

Fig� �� Excitation functions for the production of ��Co� ��Co� ��Co� ��Mn� and ��Mn

from p��Fe� and for the production of ��Mn from p��Fe� For ��Mn and ��Mn� the

contributions to the total CEM�� yields from the channels �p�� and �p�npd� are shown

by dashed lines� as indicated� Experimental data are labeled as� NUCLEX �� and

SU��

�

Fig� �� Excitation functions for the production of ��Co� ��Co� ��Fe� ��Mn� and ��Mn

from p��Fe� Lines labeled as �� and � are plotted from �les �� with results of the

recent JAERI Benchmark �� obtained with the codes ALICE�F �� ALICE��

NUCLEUS �� and MCEXCITON �� respectively� For production of ��Fe� ��Mn� and��Mn� on the three lower right plots� the contributions to the total CEM�� yields from the

channels �p�np�� p�d�� p�n�p�� p�pd�� p��He�� and �p�n� are shown by dashed lines� as

indicated� On the upper right plot� the thick�dashed line labeled as ALICE�� shows the

results obtained in Ref� �� with the code ALICE�� Experimental data labeled as

NUCLEX are from Refs� ��

��

Fig� �� Total inelastic cross section and excitation functions for the production of �Co��Co� ��Co� ��Co� ��Fe� ��Fe� and ��Fe from p�natFe� Dashed curves labeled as NUCLEUS

and HETC��STEP are plotted from �les with revised results of JAERI calculations ��

obtained with the codes NUCLEUS �� and HETC��STEP �� Here and in all following

�gures� dashed lines marked with �Ru� show results of calculations �� with Rudstam�s

semiempirical systematics �� Experimental data are labeled as� BARASHENKOV��

MI�� MI�� SU�� AL��b �� NUCLEX �� and RU��

��

Fig� �� Excitation functions for the production of ��Mn� ��Mn� ��Mn� ��Mn� ��Mn��Cr� �Cr� and �Cr from p�natFe� Experimental data are labeled as� NUCLEX ��

AL��b �� RU�� MI�� MI�� RA�b �� VI� �� LA� ��

BR�� and RA� �� The rest of the notation is the same as in Fig� ��

��

Fig� �� Excitation functions for the production of �V� �V� ��V� ��Ti� and ��Ti from

p�natFe� Experimental data are labeled as� RU�� VI� �� LA� �� MI��

RA�b �� MI�� AL��b �� NUCLEX �� BR�� and HON� ��

The rest of the notation is the same as in Fig� ��

��

Fig� �� Excitation functions for the production of �Sc� ��Sc� ��Sc� ��Sc� ��Sc� ��Ca��Ca� and ��Ca from p�natFe� Experimental data are labeled as� MI�� BR��

AL��b �� MI�� NUCLEX �� RU�� HON� �� and Fi�� The

rest of the notation is the same as in Fig� ��

��

Fig� �� Excitation functions for the production of ��K� ��K� ��K� ��K� ��K� ��K� �K�

and �K from p�natFe� Experimental data are labeled as� CH� �� HON� ��

RU�� MI�� AL��b �� NUCLEX �� and HON� ��

��

Fig� �� Excitation functions for the production of ��Ar� ��Ar� �Ar� �Ar� ��Ar� and��Ar from p�natFe� Experimental data are labeled as� HON� �� AL��b �� NU�

CLEX �� SCH�� BI� �� and MI��

�

Fig� �� Excitation functions for the production of �Cl� �Cl� ��Cl� ��Cl� �S� ��S� ��P�

and ��P from p�natFe� The dashed line for ��Cl shows results of calculations with the

code HETC�KFA� �� from Ref� �� Experimental data are labeled as� HON� ��

RU�� NUCLEX �� AL��b �� SCH�� CH�� BA�� SCH��

LA� �� RE�� BA�� and LA� ��

��

Fig� �� Excitation functions for the production of ��Si� ��Si� ��Al� �Mg� ��Na� and ��Na

from p�natFe� The results of calculations with the code HETC�KFA� �� are shown with

a dashed line for ��Al �from Ref� �� and with a dotted line for ��Na �from Ref� �� For��Na and ��Na� dashed lines show the results of calculations �� with Rudstam�s semiem�

pirical systematics �� Experimental data are labeled as� HON� �� RUR� �� NU�

CLEX �� RA�� PAI�� HON� �� DE�� MI�� AL��b ��

RU�� BR�� and RU��

��

Fig� �� Excitation functions for the production of ��Ne� ��Ne� ��Ne� �F� ��C� ��Be� and�Be from p�natFe� Experimental data are labeled as� BA�� BI� �� MI��

SCH�� NUCLEX �� HON� �� AL��b �� and RA�b ��

�

Fig� �� Excitation functions for the production of �He� �He� t� d� p� n� �� and

�� from p�natFe� For �He� �He� and t� predictions of the phenomenological systematics

by Korovin et al� � are shown by thick long dashed lines labeled as KO�� For pro�

duction of t� the results of calculations with the codes DISCA� � � CASCADE ��

NUCLEUS �� and HETC�KFA� �� from Ref� � are shown by dashed histograms ��

�� and �� respectively� For �He� �He� and d� contributions from preequilibrium emission�

evaporation� and from residual nuclei to the total CEM�� yields are shown by dashed lines�

as indicated� Experimental data are labeled as� SCH�� BI� �� MI�� and

BAR��

One can see that on the whole CEM� reproduces the experimental data in thespallation region quite well and no worse than the codes cited above or Rudstam$ssemiempirical systematics �� There are nevertheless some disagreements for sev�eral nuclides in this region caused for the same reasons discussed above for previoustargets� One should note that some experimental data shown in these �gures are also

��

questionable �see a good discussion of the experimental situation for iron in Ref� ��But one can also see some serious systematic discrepancies for light nuclides producedin the fragmentation region� As was mentioned above CEM� does not contain amechanism of fragmentation and does not take into account evaporation and preequi�librium emission of complex particles with A � or even coalescence of fragmentsfrom emitted particles as we did in a former version of the CEM �see e�g� �� Allfragments calculated in the present work are only residual nuclei remaining after allthree stages of reactions� therefore for these medium�mass targets they representonly a very small part of the total fragment production�

As one can see from Fig� �� CEM� describes production of �He and t noworse than phenomenological systematics by Korovin et al� �� or than the codesDISCA �� CASCADE �� NUCLEUS �� and HETC�KFA �� do fort� For �He our results are again below the experimental data and prediction of thesystematics �� This is the old problem of the CEM underestimating ��particleemission as discussed above�

�� Target �Co

Since �Co is the single stable isotope of cobalt it is particularly suitable �� fortesting model calculations of nuclear reactions especially as a target for productionof doubly magic ��Ni and magic ��Ni nuclides providing a test of the capability ofmodels to describe nuclide production near closed shells �� We used in our studyall experimental excitation functions for �Co� Let us note here that a recent paperby Michel$s group �� published after our calculations were completed and notdiscussed here� contains many new experimental data for �Co as well as results ofcalculations with the codes HETC�KFA �� and AREL ��

Our results for �in and for excitation functions for production of ��Ni ��Co��Fe ��Mn ��Cr �V ��Sc ��K �Mg ��Na �Be ��He ��Hn and �� are compared in Figs� �� with available experimental data andwith results of calculations with the codes� ALICE� � �� for ��Ni and ��Fefrom Ref� �� Figs� �� and �� ALICE� �� for ��Ni from Ref� �� Fig� ��ALICE�LIVERMORE�� for �Co �Fig� �� Mn ��Cr �Fig� �� V and ��Sc�Fig� �� from Ref� �� HETC�KFA �� for ��Sc from Ref� �� Fig� �� Thecontributions from the channels �pd� �pnp� �pt� �pnd� �p np� �pnt� �p nd��p�np� �pn�p� and �p pd� to the total CEM� yields of �Co ��Co ��Co and��Mn are shown separately in Figs� �� and ��

On the whole CEM� reproduces satisfactorily the shapes of the majority ofmeasured excitation functions and at incident energies above � �� MeV itreproduces correctly the absolute values of most data and agrees with experimentno worse than other codes� But at lower energies especially near the thresholdsCEM� tends to underestimate the data systematically� This is for two di�erentreasons� First CEM� underestimates practically all measured excitation functionsfor p��Co at low energies� This indicates that the total inelastic cross section of this

��

reaction is also underestimated by the model� The few experimental data shown inFig� �� that we were able to �nd for �in in Barashenkov$s compilation �� con�rmthis� At energies below � �� MeV CEM� underestimates the experimental �in from�� to ��*� This is a result of the model employing a geometrical approximation forthe total cross section� Often it is only important to know the relative cross sectionsof the various inelastic channels� For other cases when one needs to know theabsolute cross sections it is possible to calculate the partial cross sections at eachincident energy with �in provided by the model then to perform renormalization ofall partial cross sections using more precise values of �in either from measurementsfrom independent optical model calculations or from systematics�

��

Fig� �� Total inelastic cross section and excitation functions for the production of �Ni��Ni� ��Ni� �Co� ��Co� ��Co� and ��Co from p��Co� For �Ni and ��Ni� predictions of the

code ALICE �� from Ref� �� are shown by lines � and � labeled as �ALICE�� For ��Ni�

results of the code ALICE�� from Ref� �� are shown by the dashed line �� Results

of calculations with the code ALICE�LIVERMORE�� from Ref� �� are shown for�Co by a dashed line labeled as ALICE� For �Co� ��Co� and ��Co� contributions from the

channels �p�d�� p�np�� p�t�� p�nd�� p��np�� p�nt�� p��nd�� and �p��np� are shown by

dashed lines� as indicated� Experimental data are labeled as� BARASHENKOV��

MI�� MI�� MI�� AL�� MI�� and SHV��

��

Fig� �� Excitation functions for the production of �Fe� ��Fe� ��Mn� ��Mn� ��Mn��Cr� and �Cr from p��Co� Dashed lines labeled as ALICE show results of the hybrid

model calculations with a version of the code ALICE�� for ��Fe �from Ref� ��

and with the code ALICE�LIVERMORE�� for ��Mn and ��Cr �from Ref� ��

The contributions from channels �p�n�p� and �p��pd� to the total CEM�� yield of ��Mn

are shown by dashed lines� as indicated� Experimental data are labeled as� AL��

ZA�� MI�� MI�� SHV�� MI�� and MI��

��

Fig� �� Excitation functions for the production of �V� �Sc� ��Sc� ��Sc� ��Sc� and ��Sc

from p��Co� For �V and ��Sc� dashed lines labeled as ALICE show results of calculations

with the code ALICE�LIVERMORE�� from Ref� �� For ��Sc� the dotted line

� labeled as HETC shows results of calculations with the code HETC�KFA� �� from

Ref� �� Experimental data are labeled as� MI�� SHV�� MI�� AL��

and MI��

��

Fig� �� Excitation functions for the production of ��K� ��K� �Mg� ��Na� ��Na� and�Be from p��Co� Experimental data are labeled as� MI�� SHV�� AL��

and MI��

�

Fig� �� Predictions of CEM�� for the production of �He� �He� t� d� p� n� ��

and �� from p��Co� The contributions to the total yields from cascade� preequilibrium

emission� evaporation� and from residual nuclei are shown by dashed lines� as indicated�

The experimental point for �He labeled as BA�� is taken from Ref� ��

��

The second and more serious reason for the large underestimation of the yields ofseveral nuclides like �V ��Sc �Fig� �� at low energies is connected with a poorcalculation by CEM� of nuclear masses and binding energies� In the production ofthese nuclides from p��Co via a consecutive emission of several particles the excitednuclei at intermediate stages pass through or near the region of magic or doubly magicnuclei� Therefore their masses shell and pairing energies and their level densitieshave to be calculated appropriately� If the approaches used for such calculations atthe preequilibrium and evaporation stages of reactions do not do this the �nal resultscan be strongly a�ected� The main problem in the description of reactions involvingnuclei near the closed shells comes from the ICM which does not contain any shelland pairing e�ects and uses a �xed value for the mean binding energy BN � �MeV for all nuclei� A direct con�rmation of this may be seen from comparison ofour results with the hybrid model calculations� At low incident energies the hybridmodel which does not use a classical approach like ICM describes much better allexcitation functions shown in Figs� �� To be able to correctly describe suchreactions the classical ICM has to be extended by using real nuclear masses andshell and pairing corrections in the calculation of the binding energies of emittednucleons�

Discrepancies of another type that can be seen e�g� for ��Fe ��Mn and ��Cr inFig� � are connected with the previously discussed underproduction of �He� Thepeaks of excitation functions for the production of these nuclides in the low energyregion are probably caused by ��emission through the channels �p�n�� pnp��and �pn �� respectively� CEM� underestimates ��emission and as a result thecorresponding peaks in these excitation functions are not reproduced correctly�

The reason for incorrectly predicting the production of �Be fragments �Fig� ��was discussed previously�

A detailed comparison of our results for the production of di�erent nuclides fromp�� GeV��Co with the recent measurements �� and calculations �� withthe codes HETC �� and INUCL �� and with phenomenological systematics�� is given in Table II�

The cumulative yields for all nuclides are calculated using Eq� �� taking intoaccount the precursors shown in the �rst column of the table� To be able to compareadequately our results with predictions of the codes HETC and INUCL we calculatehere according to Eq� �� the cumulative yields predicted by HETC and INUCLusing independent yields given in Tabs� � and of Ref� �� These values aremarked with a ��

��

TABLE IIComparison of cross sections for the production of daughter nuclides from

p�� GeV��Co measured in Refs� �� with predictions of CEM�� and calculationsfrom Ref� �� with the codes HETC �� and INUCL �� and systematics ��

Nuclide Exp� �� Exp� �� CEM�� HETC INUCL �� Ni ��

��

�Co ��

��Co ��Ni� ��

��Co ��Ni� ��

��Co ��

��Mn ��

��Mn ��Fe� ��

��Cr ��Mn� ��

�Cr ��

�V ��Cr� ��

�Sc ��

��Sc ��Ca��K� ��

��Sc ��

��Sc ��Ti� ��

��K ��Ar� ��

��K ��Ar� ��

�Mg ��Na� ��

��Na ��Ne� ��

��Na ��Mg� ��

�Be ��

�

One can see that a general agreement between di�erent calculations and the dataexists� Nevertheless on the whole our results obtained with CEM� are closer toexperiment� To make the result of such a comparison visual the ratio of cumulativeyields predicted by CEM� HETC and INUCL for �Co ��Co��Co ��Mn ��Mn��Cr �V ��Sc ��Sc ��K ��K �Mg ��Na and ��Na to experimental data �� areplotted in Fig� �� as a function of nuclide mass�

Fig� �� Ratios of calculated to experimental �� cumulative yields predicted by the

codes CEM�� HETC �� and INUCL �� for the nuclides �Co� ��Co� ��Co��Mn� ��Mn� ��Cr� �V� ��Sc� ��Sc� ��K� ��K� �Mg� ��Na�

A more detailed comparison of results obtained using the CEM� HETC andINUCL codes with the recent measurements �� of the yields of residual nuclidesfrom interactions of protons of �� MeV and �� GeV with ��Cu ��Cu ��Pb ��Pb��Pb and ��Bi and from p�� GeV��Co may be found in Refs� �� Letus show here part of results from Ref� �� If the coincidence criterion between theexperimental and calculated cross sections is taken to be �� cal��exp � �� theresults of the comparison may be expressed by the ratio of the number of reactionsthat did �coincide� to the total number of reactions compared� Table III shows theresults of such an analysis�

��

TABLE IIIStatistics of coincidence �within a factor of � between calculated and experimental

cross sections for the production of daughter nuclei in the spallation region�adapted from Ref� ��

Target Tp �MeV� HETC INUCL CEM��Co � �� Cu ��

�� Cu ��

�� Pb ��

�� Pb ��

�� Pb ��

�� Bi ��

��

Average �� * �� * �� *

One can see that the results of CEM� when compared with all measured crosssections for all these targets and incident energies agree within a factor of two withthe experimental data for �� * of the reactions the results of HETC agree for ��*of the reactions and the results of INUCL agree for ��* of the reactions�

��

�� Targets �Zr� �Zr� �Zr� �Zr� �Zr� and natZr

Being an important structural material zirconium is well investigated experimen�tally� At present there are excitation functions available for many nuclides from eachstable isotope of zirconium and for natZr� To our knowledge the majority of pub�lished experimental excitation functions were included in the compilation �� There are also experimental data published in Refs� � �� not covered by thecompilation �� We include in our analysis all these data� Many new exper�imental data for Zr were obtained recently by the group of Michel �� but thesemeasurements were reported after we �nished our work� We have however includedin our study several excitation functions required by the Intercomparison �� whosemeasurement was subsequently reported in Ref� �� These results are thus a pre�diction of the CEM�

Our results for excitation functions for the production of ��Nb �Zr �Y ��Se��As ��Ga and ��Zn from p��Zr are compared with experimental data inFigs� � and �� Excitation functions for the production of ��Sr ��Y ��Zr��Rb ��Br ��Se and ��As from p��Zr are shown in Figs� �and yields of ��Nb and Y from p��Zr are shown in Fig� ��

��

Fig� �� Excitation functions for the production of �Nb� �Nb� �Zr� �Y� ��Se� ��As��As� and ��As from p��Zr� The contributions from the channels �p�d� and �p�np� to the

total CEM�� yield of �Zr are shown by dashed lines� as indicated� Experimental data

labeled as NUCLEX are from Refs� ��

��

Fig� �� Excitation functions for the production of ��Ga� ��Ga� ��Ga� ��Ga� and ��Zn

from p��Zr� Experimental data labeled as NUCLEX are from Refs� ��

��

Fig� �� Excitation functions for the production of �Sr� �Sr� �Y� �Y� Y� �Zr� Zr�

and Zr from p��Zr� Experimental data labeled as NUCLEX are from Refs� ��

��

Fig� �� Excitation functions for the production of ��Rb� ��Rb� �Rb� �Rb� �Rb� �Rb�

and �Rb from p��Zr� Experimental data labeled as NUCLEX are from Refs� ��

�

Fig� �� Excitation functions for the production of �Rb� �Rb� �Rb� Rb� Rb� and�Rb from p��Zr� Experimental data labeled as NUCLEX are from Refs� ��

��

Fig� �� Excitation functions for the production of ��As� ��As� ��As� ��Se� ��Se� ��Se�

and ��Br from p��Zr� Experimental data labeled as NUCLEX are from Refs� ��

��

Fig� �� Excitation functions for the production of Y� �Nb� and �Nb from p��Zr�

The contribution from the channel �p�n� to the total CEM�� yield of Y is shown by a

dashed line� Experimental data labeled as NUCLEX are from the compilation ��

Our calculations for the the production of ��Nb ��Zr ��Y ��Sr ��Rb��Br ��Se and ��As from p��Zr are compared with experimentaldata in Figs� �� Excitation functions for the production of ��Nb ��Zr��Sr ��Y ��Rb ��Br ��Se and ��As from p��Zr are shown inFigs� �� Total inelastic cross section �in and excitation functions for the pro�duction of ��Nb ��Zr ��Y ��Sr ��Rb ��Kr ��Br��Se ��As �Ge ��Ga ��Zn ��Co ��Mn ��Cr �V ��Sc ��Ar��Na and �Be from natZr are compared with the available experimental data inFigs� ��

To illustrate the relative role of di�erent reaction channels in the production ofdaughter nuclides the contributions from the �pd� and �pnp� channels to �Zr�px��Zrare shown in Fig� �� the contributions from the �pn�� channel to �Zr�px�Y isshown in Fig� �� the contributions from the �pn�� p n�� p�� pnpd� �p nd��p�np� �pt� �pnd� �p np� and �pn �� channels to the total yields of �Y �YY Zr Zr and �Rb from �Zr are shown respectively in Figs� � and �� thecontributions to the total yields of Zr and Zr from the channels �pt� �pnd��p np� �pd� and �pnp� in the reaction p��Zr are shown in Fig� �� the contribu�tions from the channels �p�� pn�� p n�� p�He� �ppd� and �pn p� to thetotal yields of ��Y are shown in Fig� �� respectively�

�

Fig� �� Excitation functions for the production of �Y� �Y� Y� �Zr� Zr� Zr��Nb� and �Nb from p��Zr� The contributions from the channels �p�n�� p��n�� p��

�p�npd�� p��nd�� p��np�� p�t�� p�nd�� and �p��np� to the total CEM�� yields are shown

by a dashed lines� as indicated� Experimental data labeled as NUCLEX are from the

compilation ��

��

Fig� �� Excitation functions for the production of �Rb� �Rb� �Rb� Rb� �Sr� and�Sr from p��Zr� For �Rb� the contributions to the total CEM�� yield from the channels

�p�n�� and �p�xnyp� are shown separately� as indicated� Experimental data labeled as

NUCLEX are from the compilation ��

��

Fig� �� Excitation functions for the production of ��Rb� ��Rb� �Rb� �Rb� �Rb��Rb� and �Rb from p��Zr� Experimental data labeled as NUCLEX are from the com�

pilation ��

��

Fig� �� Excitation functions for the production of ��Br� �Br� �Br� �Br� �Br� and �Br

from p��Zr� Experimental data labeled as NUCLEX are from the compilation ��

��

Fig� �� Excitation functions for the production of ��Br� ��Br� ��Br� ��Br� ��Br� and ��Br


��

Fig� �� Excitation functions for the production of ��As� ��As� ��As� ��Se� ��Se� and ��Se


��

Fig� �� Excitation functions for the production of �Sr� �Sr� �Sr� �Zr� Zr� Zr�Nb� and �Nb from p��Zr� For Nb and �Nb� predictions of the codes CEM��M ��

ALICE�� ALICE��MOD �� and PEQAQ� �� from the recent Intercompari�

son �� are shown by dashed lines �� and �� respectively� For Zr and Zr� contribu�

tions to the total CEM�� yields from the channels �p�t�� p�nd�� p��np�� p�d�� and �p�np�

are shown by dashed lines� as indicated� Experimental data labeled as NUCLEX are from

the compilation ��

��

Fig� �� Excitation functions for the production of �Y� �Y� �Y� �Y� �Y� and Y

from p��Zr� Predictions of the codes CEM��M �� ALICE�� labeled as ALICE��

and LLNL� for �Y� �� ALICE��MOD �� and of the exciton model with preformed

�particles by Gadioli et al� �labeled as GADIOLI� �� are shown by dashed lines� as

indicated� For �Y� �Y� �Y� and Y� contributions to the total CEM�� yields from the

channels �p�� p�n�� p��n�� p��He�� p�pd�� and �p�n�p� are shown by dashed lines�

as indicated� Experimental data labeled as NUCLEX are from the compilation ��

��

Fig� �� Excitation functions for the production of �Rb� �Rb� �Rb� �Rb� �Rb� �Rb��Rb� �Rb� ��Rb� and ��Rb from p��Zr� Dotted lines labeled as Gadioli�� show predic�

tions of the exciton model with preformed �particles by Gadioli et al� �� Experimental

data are labeled as� NUCLEX �� and KA� ��

��

Fig� � Excitation functions for the production of ��Br� ��Se� ��Se� ��Se� ��As� ��As�

and ��As from p��Zr� Experimental data are labeled as� NUCLEX ��

��

Fig� �� Total inelastic cross section and excitation functions for the production of �Nb��Nb� �Nb� and �Nb from p�natZr� Experimental data are labeled as� BARASHENKOV��

NUCLEX �� and AL��

��

Fig� �� Excitation functions for the production of �Zr� Zr� Zr� and �Zr from

p�natZr� Experimental data are labeled as� NUCLEX �� and AL��

From Figs� �� one can see that all conclusions made above from the analysisof lighter targets are also valid for zirconium� On the whole CEM� reproducessatisfactorily most of the shapes and absolute values of measured excitation func�tions especially at energies above � �� MeV� There are nevertheless some largediscrepancies for several nuclides caused mainly by poor masses and binding energiesused in the calculations of the corresponding nuclides� The CEM does not contain amodel for fragmentation therefore it cannot describe the production of �Be and otherlight fragments from zirconium� the CEM underestimates the production of �He andtherefore underestimates the corresponding parts of some excitation functions where��emission plays an important role�

��

Fig� �� Excitation functions for the production of �Y� Y� �Y� �Y� �Sr� �Sr��Sr� and �Sr from p�natZr� Experimental data are labeled as� NUCLEX �� and

AL��

��

Fig� �� Excitation functions for the production of �Rb� �Rb� �Rb� �Rb� �Kr� �Kr��Kr� and �Kr from p�natZr� Experimental data are labeled as� NUCLEX �� and

AL��

��

Fig� �� Excitation functions for the production of �Kr� �Kr� �Kr� �Kr� �Kr� ��Kr�

and ��Kr from p�natZr� Experimental data are labeled as� NUCLEX ��

��

Fig� �� Excitation functions for the production of ��Br� ��Br� ��Se� ��Se� and ��Se from

p�natZr� Experimental data are labeled as� NUCLEX �� and AL��

��

Fig� �� Excitation functions for the production of ��As� ��As� ��As� �Ge� ��Ga� and��Ga from p�natZr� Experimental data are labeled as� NUCLEX �� and AL��

��

Fig� �� Excitation functions for the production of ��Zn� ��Co� �Co� ��Co� ��Co��Mn� and ��Mn from p�natZr� Experimental data are labeled as� NUCLEX �� and

AL��

��

Fig� �� Excitation functions for the production of ��Cr� �V� ��Sc� ��Ar� �Ar� ��Na� and�Be from p�natZr� Experimental data are labeled as� NUCLEX �� and AL��

��

Let us return once again to the last problem� In our �gures a large underes�timation of ��emission can be seen for the production of Y from �Zr �Fig� ��Y from �Zr �Fig� �� Sr and ��Y from �Zr �Figs� �� and �� and ��Yand �Rb from natZr �Figs� �� and �� Especially impressive are such discrepanciesfor �Zr�px��Y �Fig� �� and �Zr�px�Y �Fig� �� where in a limited region ofincident energies ��emission is the only mechanism for the production of �Y andY from these reactions� CEM� reproduces correctly the position of the peaksconnected with ��emission in these excitation functions but the absolute values ofthe theoretical peaks are about one order of magnitude lower than the experimentaldata� Fortunately as one can see from the experimental data with increasing inci�dent energy the role of ��emission in the production of the �nal nuclides decreasesand at energies above about �� MeV this problem essentially no longer a�ectsthe calculated yields of daughter nuclides�

However if we would like to calculate such excitation functions at lower energiesthis problem has to be solved� As we mentioned above this is a problem not onlyof the CEM but also all other similar statistical Monte Carlo codes currently usedin nuclear data evaluation� therefore it has to be solved before using such codes tocalculate excitation functions at low energies� As an example of how this problemmight be solved consider the Milan group$s approach �� where preformed ��clusters in nuclei are taken into account in a version of the exciton model of nuclearreactions �see a detailed discussion of this approach and many references in the recentbook �� Gadioli et al� �� have analyzed several excitation functions fromp��Zr at energies below �� MeV and their results are shown for comparison forproduction of ��Y in Fig� �� and for ��Rb in Fig� �� One can see that theseresults �� agree very well with the data in the region of energy where ��emissionis important�

An interesting comparison for excitation functions for production of �Nb Nb�Zr and ��Y from p��Zr is shown in Figs� �� and �� For these nuclidesthe results from the �rst step of the Intercomparison �� obtained with the codesCEM� M �� ALICE� �� ALICE �� MOD � �� and PEQAQ � �� are showntogether with the experimental data and our present CEM� calculations� The �rststep of the Intercomparison �� aimed to test the predictive power of di�erent modelsused to describe double di�erential cross sections of secondary nucleons� Apart fromthe required nucleon spectra several contributors have presented as a �byproduct�yields of residual nuclides� Just these �byproducts� published in a tabulated formin the Appendix III of the Report �� are shown in our �gures� To an extent theseresults represent even better the general predictive powers of the compared modelsas they were obtained as a byproduct without a special �tting to the experimentalexcitation functions� Though the Intercomparison �� required results for incidentenergies of only � �� and �� MeV which is not enough to traceall details in the energy dependence of the yields some conclusions may be drawn�First one can see very large discrepancies between results of di�erent codes� Noneof these codes reproduces correctly the peaks connected with ��emission in these

��

excitation functions� The results labeled as CEM� M were obtained in the frame�work of the CEM �� using a �xed value for the level density parameter a � ��Aand a value of &r� � �� fm for the inverse cross sections in Eq� � � �see details inRefs� �� One can see that for ��Nb and ��Y the predictions of CEM� Mare very close to our present results obtained with CEM� while for �Zr and ��Ythe results of CEM� M are about an order of magnitude lower than both the presentCEM� results and the experimental data� This fact con�rms once again the conclu�sions made in Section � that level density parameters inverse cross sections and shelland pairing corrections used in calculations may strongly a�ect theoretical yields ofsome nuclides� therefore well tested approaches for the description of these valueshave to be used in calculations of excitation functions�

�� Target ��Au

For ��Au we have used the compilation of experimental excitation functionsfrom Ref� �� Many new measurements on gold were performed recently byMichel$s group �see Ref� �� but these new results appeared after we had �nishedour calculations� The experimental data on the total inelastic cross section is takenfrom the compilation �� on the �ssion cross section from Table �� of Ref� ��and on cross sections for the production of d t �He and �He from Table � � of thesame book by Barashenkov and Toneev ��

Total inelastic and �ssion cross sections and excitation functions for production of��Hg ��Au ��Pt ��Ir ��Os��Re ��Ta ��Hf ��Lu ��Yb ��Tm ��Er��Ho ��Dy ��Tb ��Gd ��Eu ��Pr ��Ce ��Ba��Xe ��I ��Te ��Sb ��Sn ��Cd ��Ag ��Pd ��Rh ��TcMo ��Nb ��Zr ��Y ��Sr ��Rb ��Kr ��Br ��Se��As ��Ge ��Ga ��Zn ��Cu ��Ni ��Co �Fe ��Mn�V ��Sc ��Ar ��P �Mg ��Na ��Ne �F �Be ��He t d p n �� and �� from p��Au are shown in Figs� ��

It is convenient for us to divide these results depending on production mecha�nisms of the �nal nuclides into four di�erent groups and to discuss them separately�Figures from �� to approximately �� show excitation functions for daughter nu�clides in the spallation region� As an example for production of ��Au ��Au and��Au the contributions from the channels �pd� �pnp� �pt� �pnd� �p np� �pnt��p nd� and �p�np� to the total yields are shown separately in Fig� �� One can seethat as for previous targets �see Figs� �� themain nuclide production mechanism in the spallation region is a successive emissionof several nucleons while emission of complex particles is of importance �and maybe even the single mechanism for production of a given isotope in a limited range ofincident energy as it is shown in Figs� � and �� for Y and �Y� only at low incidentenergies near the corresponding thresholds while with increasing energy its relative

��

role quickly decreases� On the whole CEM� reproduces satisfactorily most of themeasured excitation functions in this region although some large discrepancies canbe seen for several speci�c nuclides caused for the same reasons �poor masses andbinding energies underproduction of �He poor shell and pairing corrections and notwell �tted inverse cross sections or level density parameters� as we discussed abovefor previous targets�

Let us state here another not previously mentioned reason for some possible dis�crepancies� the neglect in CEM� of competition between � emission and evaporationof particles �� ssion for heavy nuclei� at the compound stage of the reactions� Aswas pointed out in a number of recent publications �� the neglect of com�petition between � emission and evaporation in calculations with the hybrid modelcode ALICE� �� of interactions of nucleons with medium and heavy targets leadsto false peaks in the calculated excitation functions near the thresholds� Due to theintranuclear cascade stage of the CEM �absent in the hybrid model� we do not thinkthat this e�ect is of the same importance for CEM� as for ALICE� although aspecial analysis of this problem has not been done yet� Let us note that at the cas�cade and preequilibrium stages of reactions emission of hard photons is also possibleand such a phenomenon has been recently investigated both experimentally and the�oretically � �� We do not take into account such processes in CEM� as the crosssections for gamma emission are very small and we do not expect that the neglect ofsuch processes will a�ect perceptibly the calculated excitation functions although anattempt to take into account such processes in the CEM has been already done � ��

��

Fig� �� Total inelastic and �ssion cross sections and excitation functions for the pro�

duction of ��Hg� ��Hg� ��Hg� ��Hg� ��Hg� and ��Hg from p��Au� Experimental data

are labeled as� BARASHENKOV�� and NUCLEX �� Experimental �ssion

cross sections �points� are taken from Table �� of Ref� ��

��

Fig� �� Excitation functions for the production of ��Au� ��Au� ��Au� ��Au� ��Au��Au� and ��Au from p��Au� For ��Au� ��Au� and ��Au� contributions from the

channels �p�d�� p�np�� p�t�� p�nd�� p��np�� p�nt�� p��nd�� and �p��np� to the total

CEM�� yields are shown by dashed lines� as indicated� Experimental data labeled as

NUCLEX are from the compilation ��

��

Fig� �� Excitation functions for the production of ��Pt� ��Pt� ��Pt� �Pt� �Pt��Pt� ��Pt� ��Pt� and ��Pt from p��Au� Experimental data labeled as NUCLEX are

from the compilation ��

� �

Fig� �� Excitation functions for the production of ��Ir� ��Ir� ��Ir� ��Ir� �Ir� �Ir��Ir� and ��Ir from p��Au� Experimental data labeled as NUCLEX are from the com�

pilation ��

� �

Fig� �� Excitation functions for the production of ��Ir� ��Ir� ��Os� ��Os� ��Os� and��Os from p��Au� Experimental data labeled as NUCLEX are from the compilation ��

��

�

Fig� �� Excitation functions for the production of ��Re� ��Re� ��Re� ��Re� and ��Re

from p��Au� Experimental data labeled as NUCLEX are from the compilation ��

� �

Fig� �� Excitation functions for the production of ��Ta� ��Ta� ��Ta� ��Ta� ��Ta� and��Ta from p��Au� Experimental data labeled as NUCLEX are from the compilation ��

��

� �

Fig� �� Excitation functions for the production of ��Hf� ��Hf� ��Hf� ��Hf� and ��Hf


�

Fig� �� Excitation functions for the production of ��Lu� ��Lu� ��Lu� ��Lu� ��Lu��Lu� ��Yb� and ��Yb from p��Au� Experimental data labeled as NUCLEX are from


� �

Fig� �� Excitation functions for the production of ��Tm� ��Tm� ��Tm� ��Tm��Tm� ��Er� and ��Er from p��Au� Experimental data labeled as NUCLEX are from


� �

Fig� �� Excitation functions for the production of ��Ho� ��Ho� ��Dy� ��Tb� ��Tb��Tb� and ��Tb from p��Au� Experimental data labeled as NUCLEX are from the

compilation ��

� �

Fig� �� Excitation functions for the production of ��Gd� ��Gd� ��Gd� ��Gd� and��Gd from p��Au� Experimental data labeled as NUCLEX are from the compilation ��

��

� �

Fig� �� Excitation functions for the production of ��Eu� ��Eu� ��Eu� ��Eu� ��Eu��Pr� and ��Ce from p��Au� Experimental data labeled as NUCLEX are from the

compilation ��

��

Fig� �� Excitation functions for the production of ��Ba� ��Ba� ��Xe� ��Xe� ��I��Te� ��Sb� and ��Sn from p��Au� Experimental data labeled as NUCLEX are from


��

Fig� �� Excitation functions for the production of ��Cd� ��Ag� ��Ag� ��Ag� ��Ag��Ag� ��Ag� and ��Pd from p��Au� Experimental data labeled as NUCLEX are from


��

Fig� �� Excitation functions for the production of ��Rh� ��Rh� ��Ru� �Tc� �Tc� andMo from p��Au� Experimental data labeled as NUCLEX are from the compilation ��

��

��

Fig� �� Excitation functions for the production of Nb� �Nb� �Nb� �Nb� �Nb� and�Nb from p��Au� Experimental data labeled as NUCLEX are from the compilation ��

��

��

Fig� �� Excitation functions for the production of �Zr� �Zr� Zr� Zr� Y� and �Y


��

Fig� �� Excitation functions for the production of �Sr� Sr� �Sr� �Sr� �Rb� �Rb� and�Rb from p��Au� Experimental data labeled as NUCLEX are from the compilation ��

��

��

Fig� �� Excitation functions for the production of �Kr� �Kr� �Br� �Br� �Br� ��Se�

and ��Se from p��Au� Experimental data labeled as NUCLEX are from the compila�

tion ��

��

Fig� �� Excitation functions for the production of ��As� ��As� ��As� ��As� ��As� ��Ge�

and ��Ge from p��Au� Experimental data labeled as NUCLEX are from the compila�

tion ��

��

Fig� �� Excitation functions for the production of ��Ga� ��Ga� ��Ga� ��Ga� ��Zn��Zn� ��Cu� and ��Cu from p��Au� Experimental data labeled as NUCLEX are from the

compilation ��

��

Fig� �� Excitation functions for the production of ��Ni� ��Ni� ��Co� �Co� ��Co� �Fe��Mn� and ��Mn from p��Au� Experimental data labeled as NUCLEX are from the

compilation ��

��

Fig� �� Excitation functions for the production of �V� �Sc� ��Sc� ��Sc� ��Ar� �Ar� and��Ar from p��Au� Experimental data labeled as NUCLEX are from the compilation ��

��

��

Fig� �� Excitation functions for the production of ��P� ��P� �Mg� ��Na� ��Na� ��Ne��F� and �Be from p��Au� Experimental data labeled as NUCLEX are from the compi�

lation ��

��

Fig� �� Excitation functions for the production of �He� �He� t� d� p� n� �� and

�� from p��Au� The contributions to the total yields from cascade �for nucleons�� pre�

equilibrium emission� and evaporation are shown separately by dashed lines� as indicated�

Experimental data labeled as BAR�� are taken from Ref� ��

��

We show separately for all nuclides the independent and cumulative calculatedyields in our �gures� One can see that for gold in contrast to the previous lightand medium targets the role of contributions from radioactive precursors to themeasured yields is more important� For some nuclides �see e�g� Figs� �� and ��the cumulative yields are up to two orders of magnitude higher than the independentones� Therefore for heavy targets an especially careful calculation of cumulativeyields and their comparison with the measured data are needed�

The next group of lighter nuclides from gold shown in Figs� �� to �� are mainlyproducts of �ssion� CEM� takes into account competition between evaporation and�ssion �see Section � and allows us to calculate �ssion cross sections and nuclear�ssilities� Fig� �� shows a comparison of �ssion cross section calculated according toEq� � �� with the experimental data compiled in Ref� �� These calculations are per�formed with the code CEM� using for the macroscopic �ssion barriers the Yukawa�plus�exponential modi�ed LDM of Krappe Nix and Sierk �� and Cameron$s shelland pairing corrections �� for the ground state and Barashenkov et al� �� correc�tions for the saddle�point masses for microscopic �ssion barriers� the third Iljinov$set al� systematics for the level density parameters �� with shell corrections byCameron et al� �� without taking into account the dependence of �ssion barrierson angular momenta and with the dependence of �ssion barriers on excitation en�ergy proposed in Ref� �� A �xed value of �� is used for the ratio af�an for allincident energies from �� to �� MeV� But to describe the decrease of �ssion crosssection with increasing proton energy at about � GeV with a possible minimum atabout GeV which seems to be observed in experiment �see Fig� �� we have to�t the ratio af�an and the values of �� and �� areused at proton energies of �� and �� GeV respectively�

As one can see from Fig� �� with this set of parameters CEM� reproduceswell the experimental �ssion cross section� But our code does not calculate the pro�cess of �ssion itself and does not provide �ssion fragments and a further possibleevaporation of particles from them� When during the Monte Carlo simulation of acompound stage of a reaction from evaporation and �ssion widths we have to sim�ulate a �ssion we simply remember this event �that permits us to calculate �ssioncross section and �ssility� and �nish the calculation of this event without a real subse�quent calculation of �ssion fragments and a further possible evaporation of particlesfrom them� Therefore our results in Figs� �� show the contribution to the totalyields of these nuclides only from deep spallation processes of successive emissionof particles from the target but do not contain �ssion products� One can see thatthe spallation mechanism for production of nuclides in this region provides only avery small part of the measured yields and only for high incident energies above�� GeV� To be able to describe nuclide production in the �ssion region CEM�has to be extended by incorporating a model of high energy �ssion� For examplethe Fong statistical model of �ssion � �� realized in di�erent Monte Carlo codese�g� at JINR � �� ORNL � �� BNL � �� PINP Gatchina � �� may be usedfor this purpose� A similar approach based on the thermodynamical model of �s�

��

sion was developed in Moscow at ITEP by Stepanov � � and was realized in thecode INUCL �� A more sophisticated and physically grounded but at the sametime more complicated and time consuming approach for this may be the dynamical�Di�usion Model of Fission� � �� realized as a Monte Carlo code at INR Moscowby Mebel with co�authors � � � �� On the other hand several much simpler ap�proaches based on phenomenological distributions of fragments such as Atchinson$smodel � � Nakahara$s model � �� and the recent Rubchenya model � �� are alsoused in a number of codes� Finally in a number of current works high energy �s�sion and fragmentation is calculated in a single statistical model of sequential binarydecays realized in the code GEMINI � ��

Fig� �� shows excitation functions for the third group of nuclides in the regionof fragmentation� These light nuclides are produced either via a very asymmetric�ssion or by fragmentation or sequential �ssion of primary �ssion products� As theCEM does not contain any of these mechanisms of fragmentation it cannot describethese nuclides at all� The vertical bars shown in Fig� �� give an estimate of theupper limit to the total yields of these fragments estimated from a single calculatedcase of deep spallation where such a fragment is produced as a residual nucleusat the end of a reaction� One can see that even this upper limit for the spallationmechanism of fragment production from gold is several order of magnitude lowerthan experimental data� To be able to describe fragment production CEM� hasto be extended by incorporating a model of fragmentation� Good reviews of avail�able models of fragmentation may be found in Refs� �� Letus note here that besides the popular models of fragmentation based on statisticaldecay like the Berlin model � � � the Moscow model of multifragmentation � ��the Copenhagen model � �� or models based on liquid�gas instability like Cugnon$smodel � �� Friedman$s model � �� and other sophisticated approaches reviewed inRefs� � � � �� and widely used in the literature a much simpler sys�tematics based on the liquid�gas phase�transition model was successfully incorporated� �� in the JAERI version of HETC�

It should also be noted that a possible mechanism of light fragment productionfrom medium and heavy nuclei may be evaporation of fragments with A � fromcompound nuclei as was proposed and realized in a number of papers many yearsago �see references in Ref� �� Another similar mechanism which would be simpleto incorporate into CEM� may be the emission of fragments with A � at thepreequilibrium stage of a reaction as was realized recently for �Be in Ref� � �� An�other mechanism not taken into account here for the production of light fragmentsappropriate for medium and heavy targets is the coalescence of fragments from par�ticles emitted at the cascade �and maybe also the preequilibrium� stage of a reaction�As was shown in Ref� �� incorporation in the CEM of the coalescence mechanism ofcomplex particle production improves signi�cantly the agreement of calculated spec�tra with experimental data though it does not provide the total measured yieldsand additional mechanisms of fragment production have to be incorporated in themodel�

��

As a �rst attempt to solve at once both problems of �ssion and fragmentationwe have tried in the present work to use in CEM� after the preequilibrium stageof reactions the well known code GEMINI � �� which has the advantage of treatingthe evaporation fragmentation and �ssion processes in a consistent way� Our �rstpreliminary results on this exercise are unsatisfactory and work in this direction willbe continued�

Fig� �� Mass�yield distributions of residual nuclei from p��Au at �� and �� MeV�

Solid histograms are calculated in the present work� dashed histograms show results of cal�

culations with the Brookhaven National Laboratory and Columbia University version of

the INC realized in the code VEGAS�ISOBAR �� from Ref� �� Experimental data

for cumulative yields of several nuclides labeled as KA�� are taken from Ref� ��

Fig� �� shows the excitation functions for the �th group of the �nal productsi�e� particles emitted at di�erent stages of reaction� One can see that the CEMreproduces satisfactorily the few available experimental yields of d t and �He butas for previous targets it underestimates signi�cantly the production of �He� Toillustrate the relative role of di�erent production mechanisms the contributions tothe total yields from cascade �for nucleons� preequilibriumemission and evaporationare shown in Fig� �� separately� A comparison of these results with similar ones given

��

above for previous targets �Figs� �� and �� shows that the relative rolesof di�erent mechanisms of complex particle production change signi�cantly both withchanging the atomic mass of the target and with increasing incident energy and theseroles are di�erent for di�erent particles� The relative contribution of preequilibriumparticle emission increases with increasing atomic mass of the target for the entireenergy interval� For ��Au the preequilibrium emission provides almost the wholeyield of complex particles in the CEM while evaporation from compound nuclei isstrongly suppressed by the Coulomb barrier and does not provide even ��* of thetotal yields� The situation is just the opposite in the case of light targets like ��C�Fig� �� and ��O �Fig� �� Besides for light targets so much spallation takes placethat a signi�cant contribution to the total yields of complex particles comes fromresidual nuclei remaining after emission of other particles at the end of reactions� Sofor targets of ��C �Fig� �� and ��O �Fig� � this mechanism becomes predominantfor the production of �He even at quite low energies� It is interesting to note thatthis �residual nucleus� mechanism does not decrease very quickly with increased masstargets� Even for Fe �Fig� �� and Co �Fig� �� one can see small contributions fromsuch processes to the total yields of complex particles�

Fig� �� Mass�yield distributions of residual nuclei from p��Au at � and � GeV�

Solid histograms are calculated in the present work� dashed histograms show results of

calculations with the Brookhaven National Laboratory and Columbia University version

of the INC realized in the code VEGAS�ISOBAR �� for Tp � � GeV� and with the

Oak Ridge National Laboratory version of the INC �� for Tp � � GeV� from Ref� ��

Experimental data for cumulative yields of several nuclides labeled as KA�� are taken from

Ref� ��

��

A general summarizing overview on the capability of CEM� to describe nuclideproduction from gold is given in Figs� �� and �� where mass�yield distributions ofresidual nuclei at �� and �� GeV calculated in the present work are com�pared with the results of calculations with the Brookhaven National Laboratory andColumbia University version of the INC realized in the code VEGAS�ISOBAR � ��with the Oak Ridge National Laboratory version of the INC � �� and with ex�perimental data from Ref� � �� One can see that for all these energies CEM�describes quite well the data in the spallation region providing a better agreementwith the measured cross sections than VEGAS�ISOBAR � �� or Bertini$s INC � ��does� But with decreasing masses of measured nuclides and passing into the �ssionregion the disagreement with the data increases and CEM� has to be extended byincorporating a model of high energy �ssion to be able to describe nuclide productionin this region as well�

Of course many other reasons not discussed above might also cause some of theobserved discrepancies� Di�erent features of the CEM and of other similar modelsmay be improved which could result in a signi�cant change of their predictions� Letus enumerate here several possible improvements of the CEM and further problemsto be solved�

� use accurate nuclear densities and potential energy functions in the ICM

� model the e�ects of refraction and re ection on the cascade particles as theymove from one potential zone of the nucleus into another

� use realistic velocity�dependent potentials

� take into account not only the coordinates of elementary interactions but alsotheir times

� account for �trawling� �local reduction of nuclear density� of nuclei by fastcascade particles

� incorporation of clusters in the ICM �see e�g� � � ��

� model knock�out and pick�up processes

� use of new more precise experimental data for the cross sections of the elemen�tary interactions

� take into account nuclear medium e�ects on the properties of hadrons and theirinteractions inside a nucleus �see e�g� Ref� � ��

� take into account explicitly resonances �such as ! etc�� as cascade participants

� � � �

��

All these problems are very complicated and interconnected and have yet to beincluded together in a complete study as fragmentary results obtained previously inthe literature are often unexpected and�or contradictory� Unfortunately inclusionof a separate re�nement in nuclear models used in ICM calculations does not alwayslead to improved agreement with experimental data� So Chen et al� �� have foundthat for incident energies below �� MeV especially for medium and heavy nucleithe agreement with experimental data was better when refraction and re ection ofcascade nucleons were neglected than when these e�ects were included �see the thirdpaper in Ref� �� Further the same authors have found �see the second paperin Ref� �� that the introduction of a velocity�dependent potential consistent withoptical�model analyses of nuclear data does not lead to greatly improved agreementbetween intranuclear cascade calculations and experimental data� Only when in afollowing study �see the �rst paper in Ref� �� when the authors have includedin their ICM e�ects of short�range nucleon correlations along with refraction andre ection at potential boundaries together with a velocity�dependent potential wasthe agreement with experimental data improved�

��

�� Summary

We have performed detailed analyses of more than �� excitation functions forinteractions of protons with energies from �� MeV to GeV with nuclei of ��C ��N��O ��Al ��P ��Ca ��Fe ��Fe ��Fe �Fe natFe �Co �Zr �Zr �Zr �Zr �ZrnatZr and ��Au in the framework of an extended version of the cascade�excitonmodel of nuclear reactions� We have compared our results with all reliable experi�mental data available to us and with predictions of other models realized in severalcodes� ALICE LIVERMORE �� HETC�KFA� �� ALICE�� LA�HET �� ALICE�F �� NUCLEUS �� MCEXCITON �� ALICE� ��DISCA �� CASCADE �� HETC �� INUCL �� ALICE� � �� AL�ICE LIVERMORE � � �� ALICE �� MOD � �� PEQAQ � �� ALICE� ��CEM� M �� with the Milan version of the exciton model of nuclear reactions withpreformed ��clusters in nuclei �� and with calculations using phenomenologicalsystematics from Refs� ��

Our analyses have shown that several di�erent mechanisms participate in the pro�duction of most �nal nuclides� Their relative roles change signi�cantly with changingatomic mass of targets with increasing incident energy and are di�erent for di�erent�nal nuclides� The main nuclide production mechanism in the spallation region isthe successive emission of several nucleons while emission of complex particles is im�portant �and may be even the only mechanism for production of a given isotope in alimited range of incident energy� only at low incident energies near the correspondingthresholds while with increasing energy its relative role decreases quickly�

For medium and especially for heavy targets the contribution from radioactiveprecursors to the measured yields of many nuclides is very important� The cumulativeyields of some nuclides are up to two orders of magnitude higher than the independentones� Therefore for heavy targets an especially careful calculation of cumulativeyields and their comparisons with the measured data are needed�

Our analyses have shown that nuclear structure e�ects are very important in pro�duction of some nuclides and manifest themselves strongly even at an incident energyof GeV� Therefore reliable and well �tted approaches for shell and pairing correc�tions level density parameters and especially for nuclear masses and consequentbinding energies and Q�values have to be used in calculations�

The extended version of the cascade�exciton model realized in the code CEM�describes satisfactorily with a �xed set of input parameters the shapes and absolutevalues of the majority of measured excitation functions for production of nuclidesin the spallation region and for the emission of secondary nucleons and complexparticles� We feel that the yields of both nuclides in the spallation region and sec�ondary particles of A � � predicted by CEM� are at least as reliable and in manycases more so than those of the models and phenomenological systematics mentionedabove�

For target nuclei from ��Al to ��Au CEM� describes the majority of experimen�tal excitation functions in the spallation region to within a factor of � For lighter

��

targets than ��Al the agreement with the experimental data is worse and the CEMlike the majority of other models has to be improved to be able to describe excita�tion functions from light targets� CEM� does not contain a special mechanism forfragmentation underestimates production of �He and does not include a model ofhigh energy �ssion� These mechanisms of nuclear reactions should be incorporatedinto the CEM�

In rare cases in the same spallation region CEM� underestimates or overesti�mates some individual measured excitation functions sometimes up to an order ofmagnitude� This is mainly a result of the poor nuclear masses and binding ener�gies used in CEM�� Other possible causes of such discrepancies were discussed inSections � and ��

One may conclude that the extended version of the cascade�exciton model realizedin the code CEM� is suitable for a rough evaluation of excitation functions in thespallation region� But for a better description of the measured yields in this regionand for an extension of the range of its applicability into the �ssion and fragmentationregions it should be developed further� Among improvements of the CEM which areof highest priority we consider the following�

� incorporation of recent experimental nuclear mass tables and new reliable the�oretical mass formulas for unmeasured nuclides

� development and incorporation of an appropriate model of high�energy �ssion

� modeling the emission of gammas competing with the evaporation of particlesat the compound stage

� treating more accurately ��emission at the preequilibrium stage

� incorporation of a model for fragmentation of medium and heavy nuclei andthe Fermi breakup model for highly excited light nuclei

� modeling the evaporation of fragments with A � from not too light excitednuclei �incorporation of such processes at the preequilibrium stage may also beimportant�

� modeling the coalescence of light fragments from fast emitted particles

� improvement of the approximations for inverse cross sections and

� use of new more precise experimental data for the cross sections of elementaryinteractions at the cascade stage�

Such a development and improvement of the CEM is possible and work in thisdirection is already in progress� We hope that a proper incorporation of the aboveimprovements in the code will not destroy the present wholeness of CEM� and itsgood predictive power for the spectra of secondary particles�

��

There are a number of other possible and desirable improvements of the CEMdiscussed in Section � justi�ed from a physical point of view� Unfortunately in�clusion of separate re�nements in nuclear models used in ICM calculations does notalways lead to improved agreement with experimental data�

The problems discussed above are typical not only of the CEM but also for allother similar models and codes where they are not solved yet� Excitation func�tions are a very �di�cult� characteristic of nuclear reactions as they involve to�gether the di�erent and complicated physics processes of spallation evaporation�ssion and fragmentation of nuclei� A lot of work is still necessary to be doneby theorists and code developers before a reliable complex of codes able to sat�isfactorily predict arbitrary excitation functions in a wide range of incident ener�gies�projectiles�targets��nal nuclides will be available� At present we are still veryfar from the completion of this di�cult task�

In the meantime to evaluate excitation functions needed for science and appli�cations it is necessary to use and analyze together the available experimental dataand for each region of incident energies�projectiles�targets��nal nuclides the predic�tions of phenomenological systematics and the results of calculations with the mostreliable codes� Our present study has shown that for proton�induced reactions in thespallation region not too low incident energies and not too light targets CEM� issuch a reliable code�

Acknowledgements

We wish to thank N� M� Sobolevsky for kindly supplying us with experimentaldata from the compilation �� We are very grateful to T� Fukahori for provid�ing us with results of calculations of excitation functions with the codes ALICE��ALICE�F MCEXCITON and NUCLEUS from the JAERI Benchmark �� andwe thank H� Takada for sending us new more re�ned �� results of calculations withthe codes NUCLEUS and HETC��STEP �as compared to those published in ��It is a pleasure to acknowledge M� Blann V� P� Eismont L� M� Krizhansky R� MichelP� Nagel and Yu� E� Titarenko for useful discussions on spallation physics which havestimulated us to carry out this research� One of the authors �S� G� M�� thanks CEABruy(eres�le�Ch)atel and ORNL Oak Ridge for kind hospitality and excellent condi�tions during his work in February�August �� at Bruy(eres�le�Ch)atel and in July�August �� at Oak Ridge where most of this study was done� He is also grateful toM� B� Chadwick R� E� MacFarlane D� G� Madland P� M�oller R� E� Prael L� Watersand P� G� Young of LANL for fruitful discussions and support�

This study was completed under the auspices of the U�S� Department of Energyby the Los Alamos National Laboratory under contract no� W��ENG��

�

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�� S� G� MASHNIK and V� D� TONEEV �MODEX , the Program for Cal�culation of the Energy Spectra of Particles Emitted in the Reactions of Pre�Equilibrium and Equilibrium Statistical Decays� JINR Communication P�� Dubna ��

�� T� ERICSON �The Statistical Model and Nuclear Level Densities� Adv� inPhysics � � ��

�� F� C� WILLIAMS Jr� �Intermediate State Transition Rates in the Gri�nModel� Phys� Lett� B � ��

�� F� C� WILLIAMS Jr� Particle�Hole State Density in the Uniform SpacingModel� Nucl� Phys� A � ��

��

�� I� RIBANSKY P� OBLOZINSKY and E� BETAK �Pre�Equilibrium Decayand the Exciton Model� Nucl� Phys� A ��

�� G� MANTZOURANIS H� A� WEIDENM�ULLER and D� AGASSI �Gener�alized Exciton Model for the Description of Preequilibrium Angular Distribu�tions� Z� Phys� A ��

�� E� BETAK �Complex Particle Emission in the Exciton Model of Nuclear Re�actions� Acta Phys� Slov� ��

�� J� R� WU and C� C� CHANG �Complex�Particle Emission in the Pre�Equilibrium Exciton Model� Phys� Rev� C � ��

�� E� GADIOLI E� GADIOLI ERBA and J� J� HOGAN �Preequilibrium Decayof Nuclei with A � �� at Excitation Energies to �� MeV� Phys� Rev� C ��

�� E� GADIOLI and P� E� HODGSON Pre�Equilibrium Nuclear Reactions Ox�ford University Press New York ��

�� V� F� WEISSKOPF and D� H� EWING �On the Yield of Nuclear Reactionswith Heavy Elements� Phys� Rev� ��

�� N� BOHR and J� A� WHEELER �The Mechanism of Nuclear Fission�Phys� Rev� ��

�� A� V� MALYSHEV Level Density and Structure of Atomic Nuclei �in Russian�Atomizdat Moscow ��

�� A�V� IGNATYUK G� N� SMIRENKIN and A� S� TISHIN �Phenomenolog�ical Description of the Energy Dependence of the Level Density Parameter�Yad� Fiz� � �� Sov� J� Nucl� Phys� � ��

�� A� V� IGNATYUK M� G� ITKIS V� N� OKOLOVICH G� N� SMIRENKINand A� S� TISHIN �Fission of Pre�Actinide Nuclei� Excitation Functions forthe �� f� Reaction� Yad� Fiz� � �� Sov� J� Nucl� Phys� � ��

�� E� A� CHEREPANOV and A� S� ILJINOV �Statistical Calculation of NuclearLevel Densities� �in Russian� Preprint INR AS USSR P�� Moscow ��Nucleonika ��

�� A� S� ILJINOV M� V� MEBEL N� BIANCHI E� De SANCTISC� GUARDALO V� LUCHERIINI V� MUCCIFORA E POLLI A� R� RE�OLON and P� ROSSI �Phenomenological Statistical Analysis of Level Densi�ties Decay Width and Lifetimes of Excited Nuclei� Nucl� Phys� A ��

��

�� A� G� W� CAMERON �A Revised Semiempirical Atomic Mass Formula�Can� J� Phys� ��

�� J� W� TRURAN A� G� W� CAMERON and E� HILF �Construction of MassFormulas Designed to be Valid for Neutron�Rich Nuclei� Proc� Int� Conf� onthe Properties of Nuclei Far From the Region of Beta�Stability Leysin Switzer�land �� v� � p� ��

�� W� D� MYERS and W� S� SWIATECKI �Anomalies in Nuclear Masses�Ark� Fysik� ��

�� S� G� MASHNIK �Statistical Model Calculations of Nuclear Level Density withDi�erent Systematics for the Level Density Parameter� Acta Phys� Slovaca� ��

�� V� S� BARASHENKOV A� S� ILJINOV V� D� TONEEV andF� G� GEREGHI �Fission and Decay of Excited Nuclei� Nucl� Phys� A ��

�� V� S� BARASHENKOV and F� G� GEREGHI �Systematics of Fission Barri�ers� �in Russian� Communication JINR� P�� Dubna ��

�� H� C� PAULI and T� LEDERGERBER �Fission Threshold Energies in theActinide Region� Nucl� Phys� A ��

�� H� J� KRAPPE and J� R� NIX �Modi�ed De�nition of the Surface Energy inthe Liquid Drop Formula� Proc� �rd IAEA Symp� on the Phys� and Chemistryof Fission Rochester New York �� IAEA�SM�� Vienna �� v� �p� ��

�� H� J� KRAPPE J� R� NIX and A� J� SIERK �Uni�ed Nuclear Potential forHeavy�Ion Elastic Scattering Fusion Fission and Ground�State Masses andDeformations� Phys� Rev� C ��

�� A� J� SIERK �Macroscopic Model of Rotating Nuclei� Phys� Rev� C ��

�� V� M� KUPRIYANOV K� K� ISTEKOV B� I� FURSOV andG� N� SMIRENKIN �Simple Description of the Dependence of the FissionBarriers and the Ratio "n�"f on the Nucleonic Composition for TransuraniumNuclei� Yad� Phys� �� Sov� J� Nucl� Phys� ��

�� V� S� BARASHENKOV A� S� ILJINOV V� D� TONEEV andF� G� GEREGHI �Inelastic Interactions of High Energy Nucleons with HeavyNuclei� Nucl� Phys� A ��

��

�� G� SAUER H� CHANDRA and U� MOSEL �Thermal Properties of Nuclei�Nucl� Phys� A ��

�� V� M� STRUTINSKI.I �Form of the Fissioning Nucleus at the Saddle Pointand the Liquid�Drop Model� Yad� Fiz� � � �� Sov� J� Nucl� Phys� ��

�� S� COHEN and W� J� SWIATECKI �The Deformation Energy of a ChargedDrop� Part V� Results of Electronic Computer Studies� Ann� Phys� �N�Y��

�� S� G� MASHNIK �Optimal Systematics of Single�Humped Fission Barriers forStatistical Calculations� Acta Phys� Slovaca � ��

�� A� S� ILJINOV and V� D� TONEEV �Calculation of Successive Particle Emis�sion from a Highly Excited Nucleus with High Angular Momentum�Yad� Fiz�� Sov� J� Nuc� Phys� � �� see also �Analysis of ExcitationFunctions in Heavy Ion Reactions� �in Russian� Acta Phys� Polonica B ��

�� A� S� ILJINOV E� A� CHEREPANOV and S� E� CHIGRINOV �Probabilityof Nuclear Fission Induced by Moderate�Energy Particles� Yad� Fiz� �� Sov� J� Nucl� Phys� ��

�� E� A� CHEREPANOV �Statistical Model for Calculating the Characteris�tics of Heavy Ion Nuclear Reactions Based on the Monte�Carlo Method�Proc� Int� Symp� on In�Beam Nuclear Spectroscopy Debercen Hungary May�� p� ��

�� I� DOSTROVSKY Z� FRANKEL and G� FRIEDLANDER �Monte CarloCalculations of Nuclear Evaporation Processes� III� Application to Low�EnergyReactions� Phys� Rev� � ��

�� M� TRABANDT W� SCOBEL M� BLANN B� A� POHL R� C� BYRDC� C� FOSTER and R� BONETTI �Preequilibrium Neutron Emission in theReactions �Zr ��Pb�p� xn� with �� MeV Projectiles� Phys� Rev� C ��

�� A� A� COWLEY A� VAN KENT J� J� LAURIE S� V� FORTSCHD� M� WHITTAL J� V� PILCHER F� D� SMIT W� A� RICHTER R� LIND�SAY I� J� HEERDEN R� BONETTI and P� E� HODGSON �Preequilib�rium Proton Emission Induced by �� and � � MeV Protons Incident on �Zr�Phys� Rev� C � ��

�� P� W� LISOWSKI A� GAVRON W� E� PERKER J� L� ULLMANNS� J� BALESTRINI A� D� CARLSON O� A� WASSON and N� W� HILL

��

�Fission Cross Sections in the Intermediate Energy Region� Proc� of a Spe�cialists Meeting on Neutron Cross Section Standards for the Energy RegionAbove �� MeV Uppsala Sweden May �� p� ��

�� V� P� EISMONT A� V� PROKOFYEV A� A� RIMSKI�KORSAKOVA� N� SMIRNOV H� COND-E K� ELMGREN S� HULTQVIST J� NILS�SON N� OLSSON E� RAMSTR�OM T� R�ONNQVIST and E� TRAN-EUS�Neutron�Induced Fission Cross Sections of ��Bi and ��U in the IntermediateEnergy Region� pp� �� in Ref� ��

�� H� COND-E K� ELMGREN S� HULTQVIST J� NILSSON N� OLSSONT� R�ONNQVIST E� TRAN-EUS V� P� EISMONT A� V� PROKOFYEV andA� N� SMIRNOV �A Facility for Measurement of Fission Cross Sections atIntermediate Energies� Uppsala University Neutron Physics Report� UU�NF��/� January ��

�� R� E� PRAEL and H� LICHTENSTEIN �User Guide to LCS� The LAHETCode System� LA�UR�� Los Alamos National Laboratory �Septem�ber �� see also R� E� PRAEL �A Review of Physics Models in theLAHETTM Code� pp� �� in Ref� �� see also L� S� WATERS �Statusof the LAHETTM Code System� Simulating Accelerator Radiation Environ�ments � �SARE�� proceedings CERN Geneva October �� see alsoR� E� PRAEL and M� BOZOIAN �Adaptation of the Multistage Preequilib�riumModel for the Monte Carlo Method �I�� LA�UR�� Los Alamos Na�tional Laboratory �September �� see also R� E� PRAEL �LAHET Bench�mark Calculation of Di�erential Neutron Production Cross Sections for �� and � MeV Protons� LA�UR�� Los Alamos National Laboratory ��see also R� E� PRAEL �LAHET Benchmark Calculation of Neutron Yield fromStopping�Length Target for �� MeV and � MeV Protons� LA�UR�� Los Alamos National Laboratory �� see also R� E� PRAEL �LAHETTM

Benchmark Calculation of Di�erential Neutron Production Cross Sections for�� and �� MeV Protons� LA�UR�� Los Alamos National Laboratory�� see also R� E� PRAEL �Model Cross Section Calculation Using LA�HET� LA�UR�� Los Alamos National Laboratory �� the majorityof documents on LAHET are presently available on the Web at� http��www�xdiv�lanl�gov�XTM��

�� R� MICHEL F� PEIFFER and R� ST�UCK �Measurement and Hybrid ModelAnalysis of Integral Excitation Functions for Proton�Induced Reactions onVanadium Manganese and Cobalt up to �� MeV� Nucl� Phys� A ��

�� O� V� SHVEDOV Yu� E� TITARENKO E� I� KARPIKHIN I� V� FE�DOROV V� D� KAZARITSKY V� F� BATYAEV Yu� V� KOCHEVALIN and

��

N� V� STEPANOV �Experimental and Calculating Research of Deep Spalla�tion Reactions on �Co Induced by �� GeV Protons� Chapter � CalculatedResults� Preprint ITEP �� Moscow ��

�� A� P� VINOGRADOVA� K� LAVRUKHINA and L� D� REVINA �in Russian�Geokhimiya � ��

�� A� K� LAVRUKHINA L� D� REVINA V� V� MALYSHEV and L� M� SA�TAROVA �Spallation of Fe Nuclei Induced by �� MeV Protons� JurnalExp� Teor� Fiz� ��

�� G� RUDSTAM P� C� STEVENSON and R� L� FOLYER �Nuclear Reactionsof Iron with �� MeV Protons� Phys� Rev� � ��

�� Yu� V� ALEKSANDROV S� K� VASILJEV R� B� IVANOV L� M� KRIZHAN�SKY and V� P� PRIKHODTZEVA �Cross Section for the Production of Ra�dionuclides from an Iron Target Irradiated with �� MeV Protons� �in Rus�sian� Int� Conf� on Nucl� Spectroscopy and Nucl� Structure St��PetersburgJune �� Book of Abstract St� Petersburg �� p� ��

�� M� HONDA and D� LAL �Spallation Cross Sections for Long�Lived Radionu�clides in Iron and Light Nuclei� Nucl� Phys� � ��

�� Yu� N� SHUBIN V� P� LUNEV and A� Yu� KONOBEEV �Role of NuclearLevel Density in Description of Cross Sections of Nuclear Reactions with Multi�ple Emission of Particles�� in Russian� Proc� Int� Conf� on Nucl� Phys� �XLVIMeeting on Nucl� Specrtoscopy and Structure of At� Nucl�� Moscow June �� Book of Abstracts St� Petersburg �� p� �� and to be publishedin Bull� Russian Acad� Sci�� Physics�

�� N� V� KURENKOV V� P� LUNEV and Yu� N� SHUBIN �In uence of NuclearLevel Density on Calculations of Excitation Functions for the Production ofRadionuclides Cs Xe I Pb Tl and Bi� �in Russian� Preprint FEI� ��Obninsk ��

�� V� A� KONSHIN �Neutron Cross�Section Calculations Using Optical Statis�tical and Pre�Equilibrium Models� Workshop on the Computation and Anal�ysis of Nuclear Data Relevant for Nuclear Energy and Safety Trieste Italy ��February�� March �� H��SMR ��

�� M� BLANN �ALICE � � pp� �� in Ref� �� see also LLNL ReportUCRL�JC�� November ��

�� A� V� IGNATYUK �Contribution of Collective Motions in the Density of Ex�cited States of a Nucleus� Yad� Fiz� � � �� Sov� J� Nucl� Phys� � �� see also A� I� BLOKHIN A� V� IGNATYUK A� B� PASHCHENKO

��

Yu� V� SOKOLOV and Yu� N� SHUBIN �Analysis of Excitation Functionsof Threshold Reactions in the Generalized Super uid Model� Izv� AN SSSR�Ser� Fiz� � �� see also A� I� BLOKHIN A� V� IGNATYUK andYu� N� SHUBIN �Vibrational Enhancement of the Level Density of Nucleiin the Iron Region� Yad� Fiz� �� Sov� J� Nucl� Phys� � �� see also A� V� IGNATYUK J� L� WEIL S� RAMAN and S� KAHANE�Density of Discrete Levels in ��Sn� Phys� Rev� C � ��

�� T� FUKAHORI �Review of Evaluation in the Medium Energy Region�pp� �� in Ref� ��

�� V� S� RAMAMURTHY M� ASGHAR and S� K� KATARIA �Mean Distribu�tion of Single�Particle Levels in Thin�Skinned Potential Wells and the Macro�scopic Level Density Parameters of Nuclei� Nucl� Phys� A ��

�� T� NISHIDA and Y� NAKAHARA �Analysis of Spallation Product Yields forProton�Induced Reactions� pp� �� in Ref� ��

�� T� NISHIDA Y� NAKAHARA and T� TSUTSUI �Development of aNuclear Spallation Simulation Code Calculation of Primary SpallationProducts� JAERI�M�� in Japanese�� see also T� NISHIDAH� TAKADA and Y� NAKAHARA �NUCLEUS� pp�� in Ref� ��see also H� TAKADA Y� NAKAHARA T� NISHIDA K� ISHIBASHI andN� YOSHIZAWA �Microscopic Cross Section Calculations with NUCLEUSand HETC��STEP� pp� � �� in Ref� ��

�� K� J� Le COUTEUR �The Evaporation Theory of Nuclear Disintegrations�Proc� Phys� Soc� �London� A��

�� T� NISHIDA Y� NAKAHARA and T� TSUTSUI �Analysis of the Mass For�mula Dependence of the Spallation Product Distribution� JAERI�M��

�� R� MICHEL G� BRINKMANN H� WEIGEL and W� HERR �Measurementand Hybrid Model Analysis of Proton�Induced Reactions on V Fe and Co�Nucl� Phys� A ��

�� Yu� V� ALEKSANDROV A� I� BOGDANOV S� K� VASILJEV R� B� IVAN�OV M� A� MIKHAILOVA T� I� POPOVA and V� P� PRIKHODTZEVA�Cross Section for the Production of Radionuclides from Interaction of � GeVProtons with Medium Atomic Number Nuclei� Izv� AN SSSR� Ser� Fiz� � ��

�� N� G� ZAITSEVA C� DEPTULA O� KNOTEK KIM SEN KHAN S� MIKO�LAEWSKI P� MIKEC E� RURARZ V� A� KHALKIN V� A� KONOV and

��

L� M� POPINENKOVA �Cross Sections for the �� MeV Proton�Induced Nu�clear Reactions and Yields of some Radionuclides Used in Nuclear Medicine�Radiochimica Acta � � ��

�� V� S� BARASHENKOV Cross Sections of Interaction of Particles and Nu�clei with Nuclei �in Russian� JINR Dubna �� see also the Web page at�http��www�nea�fr�html�dbdata�bara�html�

�� F� YIOU M� BARIL J� DUFAURE DE CITRES and P� FONTES �Mass�Spectrometric Measurement of Lithium Beryllium and Boron Isotopes Pro�duced in ��O by High�Energy Protons and some Astrophysical Implications�Phys� Rev� ��

�� B� S� AMIN S� BISWAS D� LAL and B� L� K� SOMAYAJULU �Radiochem�ical Measurements of ��Be and �Be Formation Cross Sections in Oxygen by ��and � MeV Protons� Nucl� Phys� A ��

�� S� SUD-AR and S� M� QAIM �Excitation Functions of Proton and DeutronInduced Reactions on Iron and Alpha�Particle Induced Reaction on Manganesein the Energy Region up to MeV� Phys� Rev� C ��

�� R�W� MILLS M� F� JAMES and D� R� WEAVER �The JEF Fission ProductYield Evaluation� Proc� of a Specialists Meeting on Fission Product NuclearData Tokai Japan May � � �� NEA�NSC�DOC�� p� �� see alsoH� O� DENSCHLAG �Measurement of Cumulative and Independent FissionYields� ibid� pp� �� see also A� C� WAHL �Nuclear�Charge Distribu�tion and Delayed�Neutron Yields for Thermal�Neutron�Induced Fission of ��U��U and ��Pu and for Spontaneous Fission of ��Cf� At� Data and Nucl� DataTab� ��

�� N� G� GUSEV and P� P� DMITRIEV Radioactive Chains� Handbook �in Rus�sian� d Edition Energoatomizdat Moscow ��

�� C� M� LEDERER and V� S� SHIRLEY Table of Isotopes �th Edition JohnWiley New York �� see also E� BROWNE and R� B� FIRESTONE Tableof Radioactive Isotopes V� S� SHIRLEY Ed� John Wiley + Sons New York��

�� P� CLOTH D� FILGES R� D� NEEF G� STERZENBACH C� REULT� W� ARMSTRONGB� L� COLBORN B� ANDERS and H� BR�UCKMANN�HERMES A Monte Carlo Program System for Beam�Material Studies�KFA�Report KFA�IRE�EAN� �� J�ul� �� see also �HETC�KFA �pp� �� in Ref� ��

�� A� Yu� KONOBEEV Yu� A� KOROVIN and V� N� SOSNIN �Neu�tron Displacement Cross�Sections for Structural Materials Below �� MeV�

��

J� Nucl� Materials � �� see also �A Nuclear Data Library forStructural Material Radiation Damage Calculation at High Energies� Kern�technik �� see also A� Yu� KONOBEEV and Yu� A� KOROVIN�The Cross Section Library �BISERM� for Calculation of the Helium Hy�drogen Production and Damage Rate in Structural Materials Irradiated withNucleons at the Energies from � MeV to �� MeV� �in Russian� VoprosyAtomnoi Nauki i Tekhniki� Series� Yadernye Konstanty � ��

�� V� S� BARASHENKOV LE VAN NGOK L� G� LEVCHUK Zh� Zh� MUSUL�MANBEKOVA� N� SOSNIN V� D� TONEEV and S� Yu� SHMAKOV �CAS�CADE Program Complex for Monte�Carlo Simulation of Nuclear Processes Ini�tiated by High Energy Particles and Nuclei in Gaseous and Condensed Matter��in Russian� JINR Preprint P �� Dubna ��

�� Th� SCHIEKEL R� R�OSEL U� HERPERS I� LEYA M� GLORISR� MICHEL B� DITTRICH�HANNEN P� W� KUBIK H��A� SYNAL andM� SUTER �Cross Sections for the p�Induced Production of Longlived Ra�dionuclides for the Interactions of Cosmogenic Nuclides� pp� �� inRef� ��

�� B� DITTRICH U� HERPERS H� J� HOFMANN W� W�OLFLI R� BODER�MANNM� L�UPKE R� MICHEL P� DRAGOVITSCH and D� FILGES �AMSMeasurements of Thin�Target Cross Sections for the Production of ��Be and��Al by High�Energy Protons� Nucl� Instrum� Methods B ��

�� E� M� RIMMER and P� S� FISHER �Resonances in the �pn� Reaction on ��C�Nucl� Phys� A � ��

�� M� BLANNAlice Livermore �� Code Private Communication �� Citationunder Ref� ��

�� G� AUDI and A� H� WAPSTRA �The �� Atomic Mass Evaluation�I�� Atomic Mass Table� Nucl� Phys� A �� see also �The ��Update to the Atomic Mass Evaluation� Nucl� Phys� A ��

�� P� M�OLLER J� R� NIX W� D� MYERS and W� J� SWIATECKI �NuclearGround�State Masses and Deformations� Atomic Data and Nuclear Data Ta�bles �� see also J� DUFLO and A� P� ZUKER �Microscopic MassFormulas� Phys� Rev� C �� R � ��

�� T� W� ARMSTRONG and K� C� CHANDLER �HETC , A High EnergyTransport Code� Nucl� Sci� Eng� � ��

�� G� A� LOBOV N� V� STEPANOV A� A� SIBIRTZEV and Yu� V� TRE�BUKHOVSKI �Statistical Simulation of Interaction of Hadrons and LightNuclei with Nuclei� Intranuclear Cascade Model� �in Russian� ITEP Preprint

��

ITEP�� Moscow �� see also A� A� SIBIRTZEV N� V� STEPANOVand Yu� V� TREBUKHOVSKI �Interaction of Particles with Nuclei� Evap�oration Model� �in Russian� ITEP Preprint ITEP�� Moscow �� seealso N� V� STEPANOV �Statistical Simulation of High�Excited Nuclei Fis�sion� I� Model Formulation� �in Russian� ITEP Preprint ITEP�� Moscow�� see also N� V� STEPANOV �Statistical Simulation of High�ExcitedNuclei Fission� II� Calculation and Comparison with Experiment� �in Rus�sian� ITEP Preprint ITEP� Moscow ��

�� Th� SCHIEKEL F� SUDBROCK U� HERPERS M� GLORIS H��J� LANGEI� LEYA R� MICHEL B� DITTRICH�HANNEN H��A� SYNAL M� SUTERP� W� KUBIK M� BLANN and D� FILGES �Nuclide Production by Proton�Induced Reactions on Elements �� Z � �� in the Energy Range from ��MeV to �� MeV� Nucl� Instr� Meth� B ��

�� M� BLANN AREL Code Private Communication �� Citation underRef� ��

�� T� FUKAHORI had kindly supplied S� Mashnik with �les� �pub�he�benchmark�uptogen�calc�al�alice�f� al�alice�� fe�alice�f� fe�alice��mcexciton� and nucleus with results of the recent JAERI Benchmark ��

�� T� FUKAHORI �ALICE�F Code System� pp�� in Ref� �� see alsoT� FUKAHORI �ALICE�F Calculation of Nuclear Data up to � GeV� JAERI�M �� see also S� PEARLSHTEIN �Medium�Energy NuclearData Libraries� A Case Study Neutron� and Proton�Induced Reactions in��Fe� Astrophys� J� �� Alice Livermore �� Code Private Com�munication �� Citation under Ref� ��

�� ALICE� Code Private Communication �� Citation under Ref� ��

�� N� KISHIDA and H� KADOTANI �On the Validity of the Intranuclear�Cascadeand Evaporation Model for High�Energy Proton Induced Reactions� pp� � �� in Ref� �� see also Y� NAKAHARA and T� NISHIDA �Monte CarloAlogarithms for Simulating Particle Emission from Preequilibrium States Dur�ing Nuclear Spallation Reactions� JAERI�M ��

�� F� BAROS and S� REGNIER �Measurement of Cross Sections for ��Na��Ne and ��Ar in the Spallation of Mg Al Si Ca and Fe ProductionRatios of some Cosmogenic Nuclides in Meteorites� J� Phys� �Paris� � ��

�� R� H� BIERI and W� RUTSCH �Erzeugungsquerschnitte f�ur Edelgase ausMg Al Fe Ni Cu und Ag bei Bestrahlung mit �� MeV Protonen�Helv� Phys� Acta ��

��

�� K� GOEBEL H� SCHULTES and J� Z�AHRINGER �Production Cross�sections of Tritium and Rare Gases in Various Elements� CERN�� Geneve��

�� R� MICHEL F� PEIFFER S� THEIS F� BEGEMANN H� WEBBERP� SIGNER R� WIELER P� CLOTH P� DRAGOVITSCH D� FILGES andP� ENGELERT �Production of Stable and Radioactive Nuclides in Thick StonyTargets �R�� and cm� Isotropically Irradiated with �� MeV Protons andSimulation of the Production of Cosmogenic Nuclides in Meteorites� Nucl� In�strum� Methods B � ��

�� Y� TAKAO Y� KANADA S� ITADANI T� TAKAHASHI H� EIFUKUM� MORINAGA and A� IWASAKI �Measurements of Helium ProductionCross Sections of Aluminum Irradiated by Protons� pp� �� in Ref� ��

�� O� F� NEMETS and Yu� V� GOFMAN Handbook of Nuclear Physics �in Rus�sian� Naukova Dumka Kiev ��

�� M� C� LAGUNAS�SOLAR and R� P� HAFF �Theoretical and ExperimentalExcitation Functions for Proton Induced Nuclear Reactions on Z � �� toZ � � Target Nuclides� Radiochimica Acta ��

�� M� BLANN and T� A� KOMOTO �Alert I and II Hauser�Feshbach Codes forNuclei at High Excitation and Angular Momenta� LLNL Report / UCID��

�� H� TAKADA Y� NAKAHARA T� NISHIDA K� ISHIBASHI andN� YOSHIZAWA �Microscopic Cross Section Calculations with NUCLEUSand HETC��STEP� pp� � �� in Ref� ��

�� Dr� H� TAKADA had kindly sent S� Mashnik �les with new and revised results�as compared with the ones published in Ref� �� of calculations with thecodes NUCLEUS �� and HETC��STEP ��

�� R� L� BRODZINSKI L� A� RANCITELLI J� A� COOPER and N� A� WOG�MAN �High�Energy Proton Spallation of Iron� Phys� Rev� C � � ��

�� G� V� S� RAYUDU �Formation Cross Sections of Various Radionuclides fromNi Fe Si Mg O and C for Protons of Energies Between �� and �� MeV�Can� J� Chem� � ��

�� G� V� S� RAYUDU �Formation Cross Sections of Various Radionuclides fromNi Fe Si Mg O and C for Protons of Energies Between �� and �� GeV�J� Inorg� Nucl� Chem� ��

�� M� HONDA and D� LAL �Spallation Cross Sections for Long�Lived Radionu�clides in Iron and Light Nuclei� Nucl� Phys� � ��

��

�� D� FINK M� PAUL G� HOLLOS S� THEIS S� VOGT R� STUECKP� ENGLARD and R� MICHEL �Measurements of ��Ca Spallation Cross Sec�tions and ��Ca Concentrations in the Grant Meteorite by Accelerator MassSpectrometry� Nucl� Instr� Meth� B ��

�� K� F� CHACKETT �Yields of Potassium Isotopes in High Energy Bom�bardments of Vanadium Iron Cobalt Nickel Copper and Zinc� J� In�org� Nucl� Chem� ��

�� O� A� SCHAEFFER and J� Z�AEHRINGER �High�Sensitivity Mass Spectro�metric Measurements of Stable Helium and Argon Isotopes Produced by High�Energy Protons in Iron� Phys� Rev� � ��

�� A� CHENG Thesis Stony Brook ��

� �� M� BAKLOUTI Thesis Bordeaux ��

� �� S� REGNIER M� BAKLOUTI M� SIMONOFF�LAGARDE and G� N� SI�MONOFF �Production of ��Cl by High Energy Spallation� Phys� Lett� B � � ��

� � � A� K� LAVRUKHINA R� I� KUZNETSOVA and L� M� SATAROVA �Rate ofFormation of Radioactive Isotopes in Chondrites by Cosmic�Ray Reactions�Geokhimya � � �� Geochemistry International � ��

� �� M� L�UPKE R� MICHEL B� DITTRICH U� HERPERS P� DRAGOVITSCHD� FILGES H� J� HOFMANN W� W�OLFLI �Proton�Induced Spallation Be�tween �� and �� MeV� pp� �� in Ref� ��

� �� G� M� RAISBECK C� MENNINGA R� BRODZINSKI and N� WOGMAN�Cross Sections for the production of ��Al from Targets of Si Al and Fe Ir�radiated by Protons of �� MeV� Proc� �th Int� Cosmic Ray Conf� PlovdivBulgaria August �� vol� p� �� Bulgarian Academy of Science��

� �� P� PAILLARD �Production of ��Al by Spallation of Fe Si Al Nuclei��in French� Thesis �D� �e Cycle� Centre d$Etudes Nucleares Bordeaux��Univ� ��

� �� J� DEDIEUX �Cross Section Measurements for Long�Lived Isotopes and theirInterest in Astrophysics� �in French� Thesis �D� �e Cycle� Centre d$EtudesNucleares Bordeaux�� Univ� ��

� �� M� BLANN Overlaid ALICE Code CCO�� Rochester ��

� �� M� BLANNAlice Livermore �� Code Private Communication �� Citationunder Ref� ��

��

� �� M� BLANN and V� P� LUNEV �ALICE �� pp� �� in Ref� �� see alsoReports UCID�� UCID� ��

� �� E� BETAK �PEQAG �extended�� pp� �� in Ref� �� see also ReportINDC�CSR��LJ IAEA Vienna �� see also Report FU SAV ��Inst� Phys� Bratislava ��

� �� M� V� KANTELO and J� J� HOGAN �Charged�Particle Emission in Reac�tions of �Zr with �� MeV Protons� Phys� Rev� C �� seealso M� V� KANTELO Ph� D� Thesis McGill University Montreal QuebecCanada ��

� � � Yu� V� ALEKSANDROV S� K� VASILJEV R� B� IVANOV L� M� KRIZHAN�SKY M� A� MIKHAILOVA T� I� POPOVA V� P� PRIKHODTZEVAV� P� EISMONT A� F� NOVGORODOV and R� MISIAK �Cross Sectionfor Spallation Production of Radioactive Nuclides by �� MeV Protons�Izv� Rossiiskoi Akad� Nauk� ser� �z� �� Bull� Russian Acad� Sci��Physics �� see also Yu� V� ALEKSANDROV V� P� EISMONTR� B� IVANOV L� M� KRIZHANSKY M� A� MIKHAILOVA T� I� POPOVAV� P� PRIKHODTZEVA S� K� VASILJEV A� F� NOVGORODOV andR� MISIAK �Cross Section for the Production of Residual Radionuclides byProton�Induced Spallation at �� MeV Protons� pp� �� in ��

� �� M� BLANN V� P� LUNEV V� S� MASTEROV and Yu� N� SHUBIN �E�ectof Gamma Emission Competition on the Excitation Function Description forthe Reactions Induced by Medium Energy Nucleons� pp� �� in Ref� ��

� �� H� NIFENECKER and J� A� PINSTON �High Energy Photon Production inNuclear Reactions� Annu� Rev� Part� Sci� � �� see also �High En�ergy Gamma�Ray Production in Nuclear Reactions� Prog� Part� Nucl� Phys��

� �� S� G� MASHNIK Ye� S� GOLUBEVA and A� S� ILJINOV �Gamma Emis�sion Calculations in the Cascade�Exciton Model� Proc� Int� Conf� on Perspec�tives for the Interacting Boson Model on the Occasion of its ��th AnniversaryPadova Italy June �� R� F� CASTEN A� VITTURI A� B� BAL�ANTEKIN B� R� BARRETT J� N� GINOCCHIO G� MAINO and T� OT�SUKA Eds� World Scienti�c Singapore �� p� � ��

� �� P� FONG Statistical Theory of Nuclear Fission Gorgon and Breach SciencePublishers New York ��

� �� V� D� TONEEV �Interaction of Fast Nucleons with Nuclei� III� Calculation ofNuclear Fission� �in Russian� JINR Report B �� Dubna �� see alsoV� S� BARASHENKOV V� M� MALTSEV and V� D� TONEEV �Interaction

��

of Fast Protons with Heavy�Nuclei� Izv� AN SSSR� ser� �z� �� Bull� USSR Acad� Sci�� Phys� Ser� �� see also �Calculation ofFission of Nuclei Induced by Fast Particles� Izv� AN SSSR� ser� �z� �� Bull� USSR Acad� Sci�� Phys� Ser� ��

� �� V� S� BARASHENKOV and S� Yu� SHMAKOV �Nuclear Fission Induced byHigh�Energy Protons� JINR Communication E�� Dubna ��

� �� F� S� ALSMILLER R� G� ALSMILLER Jr� T� A� GABRIEL R� A� LILLIEand J� BARISH �A Phenomenological Model for Particle Production fromthe Collisions of Nucleons and Pions with Fissile Elements at Medium En�ergies� Nucl� Sci� Eng� �� see also R� G� ALSMILLER Jr�T� A� GABRIEL J� BARISH and F� S� ALSMILLER �Neutron Produc�tion by Medium�Energy �� GeV� Protons in Thick Uranium Targets�Nucl� Sci� Eng� ��

� �� H� TAKAHASHI �Analysis of Neutron Yields from High�Energy Proton Bom�bardment of Uranium Targets� Nucl� Sci� Eng� � ��

� �� M� M� NESTEROV V� F� PETROV and N� A� TARASOV �The Role ofShell E�ects in Fission of Nuclei by Fast Protons� Yad� Fiz� �� Sov� J� Nucl� Phys� ��

� � N� V� STEPANOV �Statistical Simulation of Fission of Excited Atomic Nu�clei� I� Model Formulation� Institute of Theoretical and Experimental Physics�ITEP� Preprint � Moscow �� in Russian�� see also �Statistical Simula�tion of Fission of Excited Atomic Nuclei� II� Calculation and Comparison withExperiment� ITEP Preprint �� Moscow �� in Russian��

� �� G� D� ADEEV I� I� GONCHAR V� V� PASHKEVICH N� I� PISCHASOVand O� I� SERDYUK �Di�usion Model of Formation of Fission�Fragment Dis�tributions� Fiz� Elem� Chastits At� Yadra � � � �� Sov� J� Part� Nucl�� see also I� I� GONCHAR �Langevin Fluctuation�DissipationDynamics of Fission of Excited Atomic Nuclei� Fiz� Elem� Chastits At� Yadra�� Phys� Part� Nucl� ��

� �� G� D� ADEEV A� S� BOTVINA A� S� ILJINOV M� V� MEBEL N� I� PIS�CHASOV and O� I� SERDYUK �Method of Calculation of Mass�Energy Dis�tributions of Fragments of Fission of Nuclei by Intermediate Energy Particles�Preprint INR � �� Moscow ��

� � F� ATCHINSON �Spallation and Fission in Heavy Metal Nuclei under MediumEnergy Proton Bombardment� Proc� Meeting on Targets for Neutron BeamSpallation Sources KFA J�ulich Germany June �� Report J�ul�Conf�� see also �A Treatment of Fission for HETC� pp� �� inRef� ��

��

� �� Y� NAKAHARA and T� TSUTSUI �NMTC�JAERI A Simulation Code Sys�tem for High Energy Nuclear Reactions and Nucleon�Meson Transport Pro�cesses� JAERI�M �� JAERI �� in Japaness�� see also Y� NAKA�HARA �Evaluation of Computational Models for Fission and Spallation Re�actions Used in Accelerator Breeding and Transmutation Analysis Code�J� Nucl� Sci� Technol� ��

� �� P� P� JAUHO A� JOKINEN M� LEINO J� M� PARMONEN H� PENTTIL�AJ� �AYST�O K� ESKOLA and V� A� RUBCHENYA �Isotopic Product Distri�butions in Near Symmetric Mass Region in Proton Induced Fission of ��U�Phys� Rev� C � ��

� �� R� J� CHARITY M� A� McMAHAN G� J� WOZNIAK R� J� McDONALDL� G� MORETTO D� G� SARANTITES L� G� SOBOTKA G� GUAR�INO A� PANTALEO L� FIORE A� GOBBI and K� D� HILDENBRAND�Systematics of Complex Fragment Emission in Niobium�induced Reactions�Nucl� Phys� A � ��

� �� J� CUGNON �Nuclear Multifragmentation� Antiprotons versus Protons andHeavy Ions� Yad� Fiz� �� Phys� At� Nucl� ��

� �� D� H� E� GROSS and K� SNAPPEN �Statistical Multifragmentation� Com�parison of Two Quite Successful Models� Nucl� Phys� A ��

� �� J� P� BONDORF A� S� BOTVINA A� S� ILJINOV I� N� MISHUSTIN andK� SNEPPEN �Statistical Multifragmentation of Nuclei� Phys� Rep� ��

� � � D� H� E� GROSS �Statistical Decay of Very Hot Nuclei , the Production ofLarge Clusters� Rep� Progr� Phys� ��

� �� A� S� BOTVINA A� S� ILJINOV and I� N� MISHUSTIN �MultifragmentationBreakup of Nuclei by Intermediate�Energy Protons� Nucl� Phys� A ��

� �� J� P� BONDORF �Chaotic Fragmentation of Nuclei� Nucl� Phys� A � � c��

� �� J� CUGNON �Possible Fragmentation Instability in a Nuclear Expanding Fire�bale� Phys� Lett� B ��

� �� W� A� FRIEDMAN �Rapid Massive Cluster Formation� Phys� Rev� C ��

� �� N� SHIGYO T� NAKAMOTO and K� ISHIBASHI �Fragmentation Cross Sec�tions by HETC� pp� � � �� in Ref� �� see also �Systematics of Fragmenta�tion Reaction and their Incorporation into HETC� pp� �� in Ref� �� see

��

also J� Nucl� Sci� Technol� �� see also N� SHIGYO K� ISHIBASHIand Y� WAKUTA �Systematics of the Fragmentation Cross Sections for Inci�dent Proton Energies up to � GeV� pp� �� in Ref� �� see also S� SAK�AGUCHI K� ISHIBASHI T� NAKAMOTO Y� WAKUTA and Y� NAKA�HARA �Systematics of the Fragmentation Cross Section for �� GeV ProtonInduced Spallation Reactions� pp� �� in Ref� ��

� �� A� Yu� KONOBEEV and Yu� A� KOROVIN �Emission of �Be from Nucleiwith Atomic Number Z � �� by Intermediate Energy Protons� Kerntechnik��

� �� K� CHEN Z� FRAENKEL G� FRIEDLANDER J� R� GROVERJ� M� MILLER and Y� SHIMAMOTO �VEGAS� A Monte Carlo Simulationof Intranuclear Cascades� Phys� Rev� �� see also G� D� HARPK� CHEN G� FRIEDLANDER Z� FRAENKEL and J� M� MILLER �In�tranuclear Cascade Studies of Low�Energy Pion�Induced Nuclear Reactions�Possible E�ects of the Finite Lifetime of the �� Isobar� Phys� Rev� C �� see also J� N� GINOCCHIO �Deep Inelastic Pion�Induced NuclearReactions in the Isobar Model� Phys� Rev� C � ��

� �� S� B� KAUFMAN and E� P� STEINBERG �Cross�Section Measurements ofNuclides Formed by the Reaction of �� GeV Protons� Phys� Rev� C ��

� �� H� W� BERTINI �Nonelastic Interactions of Nucleons and � Mesons withComplex Nuclei at Energies Below � GeV� Phys� Rev� C � ��

� � � K� ISHIBASHI H� TAKADA T� SAKAE Y� NAKAHARA and T� NISHIDA�Improvement on Intranuclear Cascade Model Calculation for an Energy Range�� MeV� pp� �� in Ref� ��

� �� E� SUETOMI N� KISHIDA and H� KADOTANI �An Analysis of the Intranu�clear Cascade Evaporation Model with In�MediumNucleon�Nucleon Cross Sec�tions� Phys� Lett� B ��

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