REVIEWS OF MODERN PHYSICS VOLUME 20, NUMBER 1 JANUARY, 1948

. . .xe use oI.' Coincic ence Counting .V. :et.woe s in:3etermining, b'uc. .ear .3isintegration Sc.iemes

ALLAN C. G. M ITCHELL

Indiana University, Bloomington, Indiana

I. INTRODUCTION

~ OR some years the author and his collabora-tors'* have been using coincidence counting

techniques as an aid in the determination ofnuclear disintegration schemes. The informationobtained by this method, when taken togetherwith that obtained with the help of a magneticanalyzer —magnetic lens or 180' type magneticspectrograph —is at present one of the bestmethods of obtaining nuclear disintegrationschemes, or the energy levels of radioactivenuclei. A comparison of the two methods givesa picture of the advantages and disadvantagesof each.

Any magnetic analyzer, to be sure, has muchgreater resolving power than does the coin-cidence method. In principle, a resolution(AHp/Hp) in momentum of the electrons meas-ured of i—2 percent can be obtained. Measure-ment of gamma-ray energies can be obtained toan accuracy of 1 to 5 percent by measuring theenergy of photoelectrons produced in someradiator, such as lead. It is not difhcult to meas-ure the energies of the electrons ejected from theZ and I. shell by some gamma-ray and therebyobtain the energy of the gamma-ray. In addition,one can measure the momentum distribution ofCompton electrons produced in an element ofIow atomic number, say copper or aluminum,by the gamma-rays under investigation. Thismethod can serve as a check on gamma-rayenergies obtained by the photo-effect and isparticularly useful in the two cases: (I) whenthe energy of the gamma-ray is so high that theprobability of production of photoelectrons be-comes small; and, (2) when two gamma-rays areso situated that the I- line of one is superimposedon the X line of the other, for some particularradiator.

The energy of gamma-rays can be measuredwith considerable accuracy by this method,

*References are to be found in the bibliography at theend of this article.

provided sources of high activity are available.The problem is to determine the energy levelscheme from this information which is, at thesame time, consistent with the spectrum of thedisintegration electrons.

The determination of the momentum distribu-tion of the disintegration electrons (beta-rayspectra) poses a somewhat different problem.The thickness of the source and the materialupon which it is mounted influence the shapeof the distribution especially at the low energyend of the spectrum. One is therefore forced touse sources of very high specihc activity in orderto obtain the best results. When the distributionis measured, a "Fermi Plot" is made of the re-sults, and a decision made as to whether thespectrum is simple or complex. If the spectrumconsists of two groups, a determination of thetwo end points can be made with fair accuracy.If more than two groups are present, the ac-curacy of determining the end points of thelower energy groups is considerably less.

With the help of the information from thegamma-ray spectra and that of the beta-rayanalysis, including the occurrence of internalconversion lines, one attempts to draw up aself-consistent energy level diagram. This methoddoes not allow one to be certain that the mostenergetic beta-ray leads to the ground state ofthe product or that a beta-ray of a given energyis followed by one or more gamma-rays exceptin so far as it is consistent with a reasonableenergy level scheme. Great accuracy can be ob-tained, certainly, in the measurement of gamma-rays but, on the other hand, sources of highactivity are needed.

Up to the present, in most experiments inwhich coincidence counting techniques have beenused, instruments of high resolving power formeasuring beta-ray and gamma-ray energieshave not been used. The energy of beta-rayshas been determined by absorption methods andthat of the gamma-rays by a determination of

96

the range of sec:ondary electrons produced in aradiator. Nevertheless, it has been possible tomake a correct determination of energy levelschemes by this method. Since no high resolvingpower apparatus is employed, it follows thatsources of low activity will be sufhcient for thistype of work. The principle of the method is toplace two counters near the radioactive sourceand then measure coincidences between (1) theseveral gamma-rays which may be emitted, and

(2) between the gamma-rays and beta-rays ofvarying energy. In this manner one can ascer-tain (a) whether there is more than one gamma-ray per disintegration, (b) whether the lowestenergy beta-ray leads to the ground state of theproduct, and (c) whether there are any low

energy groups of electrons associated with addi-tional gamma-ray transitions.

G. ARRANGEMENT OF APPARATUSAND PROCEDURE

Coincidence counting apparatus' is usuallyused in two different modi6cations for the pur-poses of (1) measuring coincidences betweenbeta- and gamma-rays; and (2) of determiningthe energy of gamma-rays by measuring therange of Compton electrons produced by themin aluminum.

The first arrangement is shown in I'ig. 1. Thetwo counters are in the same horizontal planewith the source placed midway between them.If coincidences between gamma-rays are to beobserved, enough aluminum is placed on eitherside of the source to prevent any beta-rays fromreaching the counters. If beta-gamma coin-cidences are to be observed, thin sheets ofaluminum, whose thickness can be varied, areplaced between the source and one of thecounters. In this manner the number of beta-gamma coincidences, can be measured as afunction of the energy of the beta-rays.

The arrangement for measuring the energy of

t:he gamma-rays is shown in Fig. 2. Gamma-raysfrom the radioactive source, 5, eject Comptonelectrons from the aluminum radiator R. Theseelectrons then pass through both counters, beingrecorded as coincidences. Sheets of aluminumare then placed at the point A between thecounters to absorb the electrons, and the numberof coincidences per minute is measured as afunction of absorber thickness.

The energy of the maximum energy gamma-ray may be determined by measuring the rangeof the Compton electrons in aluminum. By com-paring the range thus determined with a curvepublished by Curran, Dee, and Petrzilka, ' whichgives the range of Compton electrons ejected bygamma-rays of known energy, the energy of thegamma-ray in question may be found.

Another method, 6rst devised by Becker andBothe is applicable in determining the gamma-ray energy when only one gamma-ray is present.This depends on a measurement of the amountof absorber necessary to decrease the number ofCompton coincidences to one-half and to one-quarter of their value when no absorber ispresent. If D~~„ is this value, then the energyof the gamma-ray, E, may be calculated fromthe relation

Dgg„= Cgg„r (B/mpc')'/(E/mpc'+1) g. (1)Here the constant C&~„may be determined bymeasuring D&~„ for a gamma-ray of known en-ergy and computing C&~„. The constant C&~„ isnearly independent of energy, and has a value0.0630 g/cm' for I=2 and 0.110 g/cm' for n=4for the 2.62 Mev line from ThC". A measure-ment of 8 calculated from D~~2, D~~4, and therange gives an indication of how many gamma-rays are present. If they differ and the gamma-ray energy, as calculated from D&~2, D&~4, and therange, appears to increase, there are probablyseveral gamma-rays. Bleuler and Zunti4 haveworked out a method for determining the indi-

6-H tube

Ftc. l. Arrangement for meas-uring beta-gamma and gamma-gamma coincidences.

ijjgyypygy/////6-M kvbe arnpltf &er

~R

selector +co, l & nQ

c irc viet eCOr del,

FM. 2. Arrangement for measuring energY of gambia-rays.

vidual gamma-ray energy, when there are severalpresent, from an analysis of these curves.

1Vlost workers in this field have, in the past,been satisfied to measure the range of the beta-rays in aluminum and to calculate the maximumenergy of the beta-ray spectrum from theFeather relation,

R(gm/cm') = 0 571F(Mev) —0.161, (2)

since it was felt that whether the spectrum wascomplex or not could be determined more easilyby measuring beta-gamma coincidences. Featherand Bleuler and Ziinti' have proposed a methodof determining the shape and complexity of abeta-spectrum from an analysis of the absorptioncurve alone.

III. USE AND ANALYSIS OF THECOINCIDENCE METHOD

(A.) Beta Ray S-pectrum Simple, OneGamma-Ray jper Disintegration

In using the coincidence method, the firststep is to determine the range of the beta-

particles. This gives at once the end point of thebeta-ray spectrum and at the same time showswhether there are any gamma-rays present. Thesource is then investigated for coincidences be-tween gamma-rays by making use of the ap-paratus as shown in Fig. I. Enough aluminum isplaced between the source and each counter tostop all beta-rays. If there are no gamma-gamma coincidences, it is clear that there isonly one gamma-ray per disintegration, and itremains to determine whether the highest energybeta-ray leads to the ground state or whetherthe spectrum is complex.

The number of beta-gamma-coincidences isnow investigated in the same apparatus. Thethick aluminum absorber is removed from be-tween the source and one of the counters andthe number of beta-gamma coincidences meas-ured as the thickness of the absorber is changed.If the number of beta-gamma-coincidences perdisintegration is independent of the beta-rayenergy, it is clear that the beta-ray leads to anexcited state of the product, from which thegamma-ray follows. If, on the other hand, thenumber of beta-gamma coincidences decreasesas the thickness of absorber increases and reachesa zero value at a range corresponding to anenergy less than the end point of the beta rayspectrum, it follows that the spectrum is com-plex. The energy, beyond which there are no

l.5 MeV

~/Np

X la~, t2-

I.O

0.5

$f

A~98 l98

Au Hg

Fro. 3. Coincidences in Au" .

04~

0, 2

Total Absorber (ym/cm2)

COINCIDENCE COUN TING METHOnS

5.0

4.0- 25%

]4.0 MV

3.0

Fly. 4.3.0 .2.0-

I

l.o-/

/

4 6

Hp xtO

l.51

io

beta-gamma coincidences, is the end point ofthe lower energy group.

In order to get an expression for the numberof coincidences and single counts in each counterlet Xo be the number of disintegrations persecond, &op and co& the solid angle subtended bythe beta-counter and gamma-counter, respect-ively. Let Np&, Np, and N& be the number ofbeta-gamma coincidences per second and thenumber of counts per second recorded in thebeta- and gamma-counters, respectively. Finally,let e& be the efficiency of the gamma-ray counterand F;(x) be the fraction of electrons in the ithgroup entering the counter after passing throughan absorber of thickness x.

For the case in which the number of beta-gamma coincidences is independent of the en-

ergy, the following relations hold.

ments by Jurney failed to find gamma-gammacoincidences, showing that there is only onegamma-ray. Magnetic spectrograph measure-ments made by Siegbahn' and Peacock andWilkinson" show that there is one beta-ray ofenergy 0.92 Mev and one gamma-ray of energy0.41 Mev.

Np=¹(op [Fg(x)+F2(x)],

N~ = Npco~e„

Np, NoF, (x)~p~——,e, .

(7)

(8)

(9)

Hence,

(B.) Beta-Ray Spectrum Complex, OneGamma-Ray per Disintegration

If the number of beta-gamma coincidences isdependent on the energy, the equations become

Np = Np(vpF(x),

N~ =Xpor~e~,

Np, No&~F(x) e——, ~,.

It follows then that

(3)

(4)

(g)and

Np~ Fg(x)~~e„

Np Fg(x) +Fg(x)

Np~ = Fg(x)a)p.

(10)

= e~v~.

It will be seen at once that e&, the eKciency ofthe counter for the gamma-ray in question, canbe determined from (6). An example of this typeof disintegration is that of Au'", shown inFig. 3. Coincidence measurements have beenmade by Norling, ' Clark, 7 and Jurney. ' Allauthors 6nd that the number of beta-gammacoincidences per beta particle is independent ofthe energy of the beta particles, indicating onlyone group of beta-rays. The most recent measure-

F~(x) is zero for a value of x equal to or greaterthan the range of the first group, so that theend point of the lower energy group is deter-mined from measuring Np~/Np as a functionof x. A measurement of Np~/N~ gives the ab-sorption curve of the lower energy group. Ex-trapolation of these measurements to x =0, anda comparison with Np at x=0 gives the relativeintensity of the two electron groups, F&/(F&+ F2).Several cases of disintegrations of this type havebeen found. Among them are Sb"', investigatedby Mitchell, Langer, and Mcoaniel, ' K" in-vestigated by Siegbahn and Johansson, " and

I

0" Na" by Bleuler and ZCinti " however, thecoincidence method was not used to establishthe latter two cases. Siegbahn and Johanssonused coincidence counting in conjunction with amagnetic lens spectrometer and Fig. 4 shows theresults of their investigation. Here the numberof beta-gamma coincidences is plotted as afunction of IJp, and it mill be seen that the in-terior end point is well established at 1.92 Mev,while the end point of the most energetic groupis 3.58 Mev.

Since the energy of the gamma-ray can bedetermined by measuring the range of secondaryelectrons emitted from aluminum, the end pointof the spectrum for the most energetic group ofbeta-rays by absorption, and that of the lowerenergy group by one of the methods discussedabove, the disintegration scheme can be de-termined.

(C.) Beta Ray -Spectrum Simple, More Than OneGamma-Ray per Disintegration

If gamma-gamma coincidences are present,the analysis becomes more complicated. Onewishes to determine the number and energy ofthe gamma-rays and whether they are in cascadeor in parallel. The simplest case to discuss isthat in which the number of beta-gamma co-incidences per disintegration is independent ofabsorber thickness. As an example, consider thecase of Na'4. This isotope was investigated firstby Langer, Mitchell, and McDaniel" and morerecently by Wiedenbeck" with substantially thesame results.

The beta-ray end point of the Na'4 spectrumis 1.39 Mev. '5 The coincidence experimentsshowed that there were both beta-gamma andgamma-gamma coincidences. The number ofbeta-gamma coincidences per recorded beta-count was found to be independent of the energy.Figure 5 shows the results of the experiment ofLanger, Mitchell, and McDaniel, in whichNp~/Xp is plotted as a function of the thicknessof absorber, in grams/cm' between source andcounter. This shows at once that all beta-raytransitions lead to the same excited state of theproduct, and the beta-spectrum is simple. Thecareful work of Lamson" and Siegbahn" on thebeta-spectrum indicates that there is only onegroup.

The gamma-ray spectrum of Na" has beeninvestigated by various observers with con-victing reports. What appear to be the mostreliable measurements give two gamma-rays-one at 1.38 Mev and one at 2.76 Mev, of prac-tically equal intensity. The inference to be drawnfrom the gamma-gamma coincidence measure-ments is that these two gamma-rays are incascade. The level system which results requiresthat the energy of Na" be 5.53 Mev above theground state.

Recently Sachs" pointed out that the highenergy of Na24 was in disagreement with a valueoriginally predicted by Barkas, " but since re-vised. " He proposed an alternative schemewhereby the 1.39-Mev beta-ray was followed bytwo gamma-rays of 1.38 Mev in cascade andalso a 2.76-Mev gamma in parallel mith these.In order to obtain equal intensities for the

Np~„)oNp

3.0 I I I- 6.0MV

. 5.0

„' 4.0

2.0-'~jttoNy

276.. 2.0

I.O-

O.l 0.20.8

0.3 04MY

0.5 0.6 Gm/ cm

~ 2400

FK:. 5. Coincidence measurements and disintegration scheme of Na'4.

COINCI DENCE COUNTING METHODS

2.0

FIG. 6. Coincidence measure-ments and disintegration schemeOf Iniie (54 min. ).

lr6

l,2

0,8

(i ~ r r ~

1l6

(54 min)

Irs

- 5.0 %IV.

- 2.0

.l. 0

O. i0 0.200.8

050l,2 MV

0.40 050 |'m/ce

1.0,i 0.57Oo

567O.l7

Ne =N proc F(x),

N, =Npep, (ei 4+eg 8), . .

Np~ = NppppF(pp)4d, (e1.4+eg. g),

X~~ = 2%0~p'&i. «~.8

(12)

(

observed 1.38 Mev- and 2.76-Mev gamma-rays abranching ratio of 1:2 has to be assumed.

This question has been resolved by Cook,Jurney, and Langer. "Their experiments appearto show that the gamma-ray of 2.76 Mev is incascade with a lower energy gamma-ray, pre-sumably one of 1.38 Mev. This experiment con-sisted in showing that an absorption curve in

lead, taken with a single counter, had the sameshape as an absorption curve of the coincidences,when lead absorbers were placed symmetricallybetween the source and each counter.

A somewhat diferent approach to the sameproblem, but leading to the same result, hasbeen made by Wiedenbeck. 14 His argument isbased on the fact that the efficiency of a counterfor gamma-rays increases with the energy of thegamma-ray. Consider the energy level scheme inwhich the 1.38-Mev and 2.76-Mev gamma-raysare in cascade and no other gamma-rays arepresent. In the usual notation, the various count-ing rates are given by

It therefore follows that

Xp~4dy (el.4+ e2. 8)

Xp

Xpp 8y, 48~. 8=2 GO

(e1.4+e2. 8)

The ratio

N„/N, e, ,e, .—=2Ne„/Ng (e1.4+e2.8)'

On the other hand, if there are two 1.4-Mevgamma-rays in cascade, and one 2.8-Mev gammain parallel with these, the value of R becomes

R =3(e1.4)'/2(e1. 4+e2.8)'.

If R is plotted as a function of e2, 8/e1. 4, forvarious values of e2.8/e1. 4, from approximately0.5 to 2, then for case (1), R 0.5 over theentire range, but for case (2), R decreasesvery rapidly for e2.8/e1. 4 going from 0.5 to 2.0.Wiedenbeck measured the values of R forcounters of various materials, for which theefficiency ratio eg. g/e1. 4 should change markedlyand found that E. was approximately constantand roughly equal to 0.5. He, therefore, con-cludes that there are only two gamma-rays

302 ALLAN C. G. M I TCHELL

4/VFe

2.8l

7 206

0.822

0

P's|-, 7, Energy levels of Mn".

(2.76 Mev and 1.38 Mev) and these are incascade.

Another element with a disintegration schemeof this type, but somewhat more complicated, isIn"' (54 min. ). Beta-gamma and gamma-gammacoincidences have been investigated by Langer,Mitchell, and McDaniel" who established thatthere was only one beta-ray which goes to anexcited state of Sn"' followed by transitions tothe ground state involving several gamma-rays.Curtis and Richardson" have investigated thespectrum of the beta-rays and gamma-rays,with the help of a cloud chamber, and give thedisintegration scheme shown in Fig. 6. The dis-integration scheme is so complicated that it isclearly not possible to determine the number ofgamma-rays from coincidence methods alone.

(D.) More Complicated Types of Disintegrations

If two or more beta-ray groups and severalgamma-rays are present, the analysis becomesmuch more complicated. It is possible to ascer-tain, however, whether the highest energy beta-ray group leads to the ground state or to anexcited state of the product, except in caseswhen a high energy group leading to the groundstate is of Iow intensity.

As an example, consider the case of Mn".Coincidence measurements on this element havebeen made by Dunworth, "Langer, Mitchell, andMcDaniel, "Elliot and Deutsch, "and Siegbahnand Johansson" with identical results. For elec-trons of energy greater than about 1.0 Mev, theratio of the number of beta-gamma coincidencesper beta-count is a constant independent of ab-

sorber thickness, showing that the highest energybeta-ray does not go to the ground state of theproduct and that the beta-spectrum is complex.In addition, gamma-gamma coincidences arefound, indicating several gamma-rays.

The actual energy level scheme of Mn" hasbeen worked out by Elliot and Deutsch and alsoSiegbahn and Johansson, with the use of a mag-netic lens. The latter authors also used coin-cidence counting apparatus in connection withthe lens, measuring coincidences between gamma-rays and the resolved beta-ray beam. The spec-trum as given by these authors is shown in

Fig. 7. It will be seen that the highest energybeta-ray does not lead to the ground state andthat the beta-ray spectrum is complex, consistingof three groups. The number of beta-gamma co-incidences per beta-ray should be constant be-yond I.04 Mev and should increase below thisvalue, in agreement with the coincidence meas-urements. In addition, the observed gamma-gamma coincidences are accounted for.

IV. MEASUREMENT OF INTERNALCONVERSION ELECTRONS

In certain cases the internal conversion co-e%cient of a partially converted gamma-ray canbe determined by coincidence counting. Themethod was used by the author" during thewar for the determination of the total number ofconversion electrons per disintegration. It isparticularly useful for cases in which the specificactivity is not large enough to use magneticanalysis of the beta-ray spectrum. The methodconsists in measuring coincidences between in-ternal conversion electrons and disintegrationelectrons, called particle-particle coincidences.

Since internal conversion electrons are of low

energy, it is necessary to use thin walled counters—window thickness a few mg/cm'. In addition,care must be taken to eliminate scattered elec-trons. For this reason it is best to mount thecounters side by side, with the source above. Itis also necessary to place a shield between thetwo counters so that an electron which makes acount in one counter cannot produce a secondarywhich counts in the other.

Consider the situation, for simplicity, of asubstance like Au'" whose spectrum has beenworked out. This substance has one beta-ray and

COI N CI DENCE COUNTI NG M ETHODS

one internally converted gamma-ray. Let N~ bethe number of particles per disintegration, dis-integration electrons and internal conversionelectrons; let N» be the number of coincidencesper second between disintegration electrons andinternally converted electrons; and let n be theinternal conversion coeS.cient. Then

Ele-ment Radiations

P 2.75T 1.80

Half- Energy levelsLife Type product

2.4 min. I 1.80

References

Mn '

0 835~4 K 310d I os35 (27)

TABLE I. Disintegration schemes of isotopes worked outwith help of coincidence methods.

N„=Np(1+u)(opF(x),

N„~ = Np(op'nF'(x),

cepF(—x)N„(1+n)

(20)

(21)

(22)

e+ 0470KT 0.805

Au 198 P 0.920.41

e 3.58,2.071.51

72d I OS05

2.8d I 041

12.4h II 1.51

(27)

(8), (9), (1o)

(12)

Here F(x) is a function denoting the absorptionof the electrons as a function of the thickness.In the low energy region it is assumed 'that F(x)for both disintegration and conversion electronsis the same and experiment shows that F(x)

The procedure is to measure both N„andN»/N~ as a function of the thickness (belowthat necessary to stop the internal conversionelectrons), plot the results on semi-log paper,and extrapolate to zero thickness. In the experi-ments of the writer, the two curves were parallel,justifying the assumption concerning F(x) madeabove. Extrapolation of these curves to zerothickness gives

Sb1»

Na'4

Co't'

Qr82

Inll6

Sbn4

e 1.191.770.568

e 1.391.38,2.76

e+ 1.50T 0.845,

1.26

e 0.4651.35,0.787,0.547

e 0.851.8, 1.41.0, 0.570.36, 0.17

e 2.32, 1.58,0.98, 0.63,0.472.064, 1.7080.714, 0.6500.603, 0.121

2.8d II 0.568 (1), (35), (36), (37)

14,8h III 1.38, 4.14 (13), (14), (15), (16), (20)

III 0.845, 2.11 (25)

34h 1.35, 2.142.69 (28)

III 0.17, 0.57i.O, 2.4 (21), (22)

0.606, 1.33, 1.97 (1) (36) (37)2.32, 2.43

Xpy A~pF(0).N„1+a (23)

e 0.595I»1 T 0.080,

0.367 .

8.0d III 0.080, 0.447 (29)

(24)

(25)Np, = No(1 —n)(opF(x)(o„e, .

In order to determine ~pF(0), it is necessary toobtain a source which gives a known number ofbeta-particles/sec. , measure the number ofcounts/sec. from it as a function of absorberthickness in the same geometry, and extrapolatethis result to zero thickness. A thin source con-taining a weighed amount of U308 is convenientfor this purpose. From these two pieces of in-

formation it is clear that 0. can readily be de-termined.

Since, in the case under consideration, beta-gamma coincidences can also be measured, thefollowing additional equations hold.

N, = Np(1 —cx)(u,e„

S 4, e 0.36, 1 9 85d0.88, 1.12 IV 0;88, 2.00

e 0.75, 1.04Mnw 2.81

0,822,1.77, 2.06

e 0.260,re» 0.460

1.30, 1.10

1.10, 1.3060 e 0.308

2.5h IV '"""2.88

IV 1.10, 1.30

IV 1.10, 2.40

Ga»

e 3.09, 2.20.79 andothers0.64, 0.71,0.84, 2.2and others

Not com-plete

14h IV

IV

A87$

e 1.29, 2.49

055 120 268h IV 055 171.75

(12), (24), {25)

(30)

(33)

Unfinishe

Unfinishe

(.l), (31)

Hence,Np, (1—n)

N, ) (1+n)(26)

e 0.61, 1Agq0.537,0.667, 0.7440.417

0,744, 1.411, (32)1.948, 2.364

304 ALLAN C. G. M I TCHELL

for x small enough to allow conversion electronsto enter the counter. In addition, the relation

Npp/X7 Xp(—o—p Ji (x) (2&)

can be combined with (22) and e obtaineddirectly.

However, a more accurate result is obtainedif the first method is employed since, in thesecond method, errors which arise on accountof the use of both Xp& and N» are inherentlylarger than if only one of these is used along withthe singles count of the Usos source.

Methods for more complicated schemes canbe worked out along the lines suggested in thediscussion of beta-gamma coincidences.

BIBLIOGRAPHY

(1) A. C. G. Mitchell, L. M. Langer, and P. W. McDaniel,Phys. Rev. 57, 1107 (1940).

(2) S. C. Curran, P. I. Dee, and V. Petrzilka, Proc. Roy.Soc. 169, 269 (1938).

(3) H. Becker and W. Bothe, Zeits. f. Physik 76, 421(1932).

V. SUMMARY OF WORK TO DATE

'I'he examples given in the text above werechosen as being illustrative of each type of dis-integration under discussion. Altogether, dis-integration schemes have been worked out forat least 21 radioactive isotopes with the help ofcoincidence counting methods. The results ofthe measurments can best be summarized in atable. For use in understanding Table I, thedisintegration schemes are divided into types asfollows: Type I, beta-ray (or positron) spectrumsimple, followed by one gamma-ray, no particleemission to ground state (this includes Ecap-'ture followed by a single gamma-ray); Type II,beta-ray (or positron) spectrum consisting oftwo groups, one of which leads to the groundstate of the product, one gamma-ray; Type III,beta-ray (or positron) spectrum simple followed

by more than one gamma-ray; Type IV complexbeta- and gamma-spectra. The actual energylevels which have been worked out for theseelements can be found in the references cited.

(4) E. Bleuler and WV. Ziinti, Helv. Phys. Acta XIX, 375(1946).

(5) N. Feather, Proc. Camb. Phil. Soc. 34, 599 (1938).(6) F, Norling, Ark. f Mat. Ast. och Fys. B27(3), 9

(1941).(7) A. F. Clark, Phys. Rev. 61, 242 (1942}.(8) E. T. Jurney, Phys. Rev. , in press.(9) K. Siegbahn, Proc. Roy. Soc. A, 189, 52/ (1947).

(10) C. L. Peacock and R. G. Wilkinson, in press.('11) K. Seigbahn and A. Johansson, Ark. f Mat. Ast. och

Fys. 34A, No. 10 (1946).(12) E. Bleuler and W. Zunti, Helv. Phys. Acta XX, 195

(1947).(13) L. M. Langer, A. C. G. Mitchell, and P. W. McDaniel,

Phys. Rev. 56, 962 (1939).(14) M. L. Wiedenbeck, Phys. Rev. '72, 429 (1947).(15) K. Siegbahn, Phys. Rev. '70, 127 (1946).(16) J. L. Lawson, Phys. Rev. 56, 131 (1939).(17) R. G. Sachs, Phys. Rev. 70, 572 (1946).(18}W. H. Barkas, Phys. Rev. 55, 691 (1939).(19) W. H. Barkas, Phys. Rev. 72, 346 (1947).(20) C. S. Cook, E. T. Jurney, and L. M. Langer, Phys.

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