SUPPLEMENTO AL VOLU][E II, 8ER1E X N. 1, 1 9 5 5

DEL NUOVO CIM:ENTO 2 ~ S e m e s t r e

Search for the ~Decay of the Pion. (*)

~. LOKANATHAN a n d J . ~TEINBERGER (**)

Nevis Cyclotron Laboratories, Columbia U'Mversity Department o] Physics . New York

1 . - I n t r o d u c t i o n .

1"1. Theoretical . - Normal ly the charged pion decays into ~ muon and a

light neut ra l particle, usually assumed to be the neutrino. The possible com- peting' decay into electron and neutr ino is not wi thout interest , and we recall

here some theoretical points:

a) Connect ion with nuclear ~-decay. - YUKAWA postula ted the meson ~-dec~y in ~ two step theory of nucleon ~-decay. This hypothesis fails on the one hand because the t ransi t ion ra te of pion-eleetron decay if non-zero, is a t any ra te too small to account for the nuclear ~-lifetimes, and on the other hand because the observed propert ies of ~-decay require FERMI couplings (1) which

are not a consequence of a two step theory with pseudoscalar mesons. The artz'ument m a y be reversed, and it m a y be supposed tha t the pion can

t ransform into an in te rmedia te nucleon-~mtinucleon pair which annihilates

with normal ~-de<'ay:

(1) ~ - - ~ p + n - - > e + ~ -~ .

The pion being pseudoscalar, this t ransi t ion is forbidden except in pseudo- scalar and axial vector ~-coupling theories. I t m a y then be recalled tha t it

is possible to account for the bulk of ,3-decay dat~ using only scalar and tensor

(*) This research was supported by the Joint Program of the Atonfie Energy Commi~-sion and the Office of Naval Research.

(**) Lecture given by J. STEI~-BERG~g. (7) See for instance, S. J. Wt~: Proceedi~gs o/tl, e 1954 Glasgow Confere~we o~ Nuclear

a~d Me,~'o~ Pl~y,~ic~" (l~ondon, 1955).

152 s. LOKANATHAN and J. STEINBERG]~R

in terac t ions (1). The smallness of ~:-electron decay is therefore not in conflict with experiment. I t is however in principle possible to learn about the pos- sible role of pseudoscalar coupling in ~-theory from pion-~-deeay. Unfortun- ately the computat ion of process (1) not only involves divergent integrals, bu t different cutoff procedures have led to transit ion probabilities which differ by several orders of magni tude (2.3).

b) Symmetrical coupling o / p i o n to rouen and electron. - If the pion were coupled symmetr ical ly to muon and electron, ei ther directly, or by means of an intermediate nucleon anti-nucleon pair, then the relative transit ion pro- b~bility (~ --> e + ~)/(~: --> ~ +.~) depends only on kinematical factors (masses), field theoretical uncertainties cancel. One then obtains (~.3) for pseudoscalar coupling of the fermions

" 2 2 2 -~e + ~ _ IM~-- Me]

and for axial vector coupling

�9 2 2] Z r: ---> e + ~ I M p - - M e .M~ 1

- - 2 2 71A-2 ~ - -

The pseudoscala~ result is roughly equal to the ratio of phase space. I t favors --> e decay and is well known to be wrong. The axial vec tor coupling how-

ever discriminates strongly against low mass particles. If i t could be estab- lished experimental ly tha t the ratio (~-->e)/(~:-->~) is indeed less t han 1/8 000, it would be possible to rule out the possibility of symmetrical coupling of the

pion to the muon and electron.

1"2. Experimental. - In previous a t tempts to find this decay (4), photo- graphic plates were exposed to well collimated meson beams close to the cyclo- t ron target which was bombarded by high energy protons. I t was concluded as unlikely tha t the electron decay of the pion should account for more than one in a thousand pion decays, gecen t l y external meson beams of reasonable in tens i ty have made i t possible to use counters as detectors and obtain greater sensitivity. The pion beam is stopped in absorber and the decay electron

detected in a counter telescope. The chief experimental problem is tha t of distinguishing between ~-decay

(~) M. RUDERMAN and R. FI~T~ELST~I~ �9 Phys. Rev., 76, 1458 (1949). (3) j . ST:aI~BERGER: .Phys. Rev., 76, 1180 (1949) (4) H. L. F~IE])MA~ and J. RAINWATER" Phys. Rev., 84, 684 (1949).

SEARCtl FOR TIlE ~-])ECAY OF TIlE PION 153

electrons and wdeeay electrons. This is accomplished by making the detector

sensitive to the shorter lifetime and higher energy of the ,-:-decay electron.

2. - Experimental Procedure.

The experimental arrangement is shown in Fig. 1. The 60 MeV =+ beam

of the Columbia University Nevis Cyclotron is collimated trod monitored by

counters no. 1 and no. 2.

Counter no. 1 is a plastic

scintillator 41 inches in

diameter and ~ inches

thick and counter no. 2

is a stilbene crystal 2�89

inches in diameter and 1

inches thick. The beam

is fur ther collimated by

a 2 inch diameter aper-

ture in a 2 inch thick lead

shield directly preceding

counter no. 2 and is slo-

wed by carbon absorbers

inserted between no. 1

~md no. 2.

The tarR'et is a ,~ inch

carbon absorber ~ \

de~ector counter~

Fita'. 1. - Arrangement of counters and absorbers.

thick piece of polyethylene (1.T R'/cm ~) mounted at

approximately 30 ~ to the incident beam. Of the order of 500 pions stop in

the target per second and this represents somewhat more than half of the

pulse former �9 M

$cJntdlotion wide bridge type pulse width comcidence counters bond ClrCWf5

zmp#h~cs

Fig'. 2. Block diagram of circuits.

MDs

~D

1-2 rate. Of these

roughly I in 300 will

decay with the char-

ged decay product

within the aeeep-

tance angle of the

detector. This de-

tector consists of

four plastic scintil-

lators, each 4�89 in-

ehes in diameter,

tile first three ~ in-

ches thick and the

last 4 ~ inch thick.

The counters no. 3,

154 S. LOKANATHAN ~ n d J . STEINBERGER

4, 5 and 6 are arranged so tha t it is possible to insert 1 inch thick sheets of

absorber between each pair of counters and an additional 6 inches in f ront

of counter no. 3.

A block diagram of the electronics is shown in Fig. 2. The following events

arc recorded:

M

D ~

MD I =

M D s ~- -

Monitor coincidences 1-2.

Detector coincidences 3, 4, 5, 6 with a resolving time of 10 -s s .

~ Fast ~ coincidences MD when D occurs within 10 -7 s

after the arrival of M.

((Slow~) coincidences MD when D occurs within

1.8.10-6 s after the arrival of M.

Of the ~+-mesons which stop in the target, and decay with a mean life

of 2.6-10-Ss (s), the vast major i ty produce ix-mesons. The muons have a

range of 2 mm in the polyethylene, about ~ of its thickness. Approximately

95 percent of these ~-mesons therefore stop and decay in the same target

piece. The mean-life of this decay is 2.2.10 -6 s (6), two orders of magni tude

longer than the parent process, and results in a continuous ~-spectrum with

53 MeV maximum energy (7).

With ~mall absorber thicknesses therefore the events D are due to the

ix-electrons. Of these 56 percent ~ 1 - - e x p [--1 .8/2.2] are expected to be counted with the long gate of MD~. Between 4 percent and 31 percent of

these are counted in the short gate, MD~. The rate D may therefore be used

to determine the product of the rate of stopping ~:'s multiplied by the accep-

tance solid angle of D. The ratios MD~/D and MD~/D may be used to deter-

mine the effective gate width of these channels.

Two sets of observations were made. In run no. 1 rates were observed

with thicknesses of polyhethylene in 1 inch steps from zero arbsorber thickness

(in addition to the counters and target) to 9 inches of absorber. I n run no. 2

only 3 inches and 9 inches of polyethylene were used. I n both runs data were

obtained with and without the target, and the bulk of the observation was

m,~de with 9 inches of absorber. This latter thickness corresponds to an energy

(5) C. WIEGA]ND: Phys. Rev., 83, 1085 (1951). (6) 3i•" E. BELL and E. P. HI~CKS: Phys. Rev., 88, 1424 (1952). (3) See for instance, P. SARaEN~, M. RI~EttART, L. LEDERMAN and K. ROGERS:

in press.

SEARCH FOR THE .~-DECAY OF THE PION 155

loss for r e l a t i v i s t i c pa r t i c l e s of 55 MeV due to i on i z a t i on alone, bt-decay

e lec t rons c a n n o t p e n e t r a t e th i s a b s o r b e r ; howeve r , some a re ne ve r the l e s s det-

ec ted t h r o u g h the conve r s ion of t h e i r b r e m s s t r a h l u n g . The g e o m e t r y of

coun te r s a n d a b s o r b e r s in D is chosen to m i n i m i z e th i s effect. E x p e r i m e n t a l l y

we f ind 1/500 of t he d e c a y s p e c t r u m d e t e c t e d in th i s m a n n e r . This is a r a t e

which m i g h t r e a s o n a b l y be e x p e c t e d for b r e m s s t r a h l u n g convers ion . The

b~-deeay b a c k g r o u n d in MDs wi th 9 inches of p o l y e t h y l e n e is t he re fo re a p p r o x -

i m a t e l y .04 .1 /500 - 8 . 1 0 5 of t he t o t a l b~-decay ra te .

3. - E x p e r i m e n t a l R e s u l t s .

The e x p e r i m e n t a l r e su l t s were o b t a i n e d in 2 t h r e e - d a y runs a n d are pre-

s en t ed in T a b l e I ' tnd I I a n d in F ig . 3.

t \ !

SPECTRUM FRO" ~T,-- e IF PRESEIV7 " ~ . t[

: I I ~ f ' - ~ I I ' i / [ \ , I IONIZATION LOSS I ' I I "

0 1(3 20 3'0 40 5~7) /__ 60/ ", 70

Fig. 3. Countino' rates 3II)~ and MDj as a function of tlle absorber thickness in the detector D, obtained in run no. 1. The rates MD s have been mult ipl ied by the factor 25.6 so that the t~vo curves coincide for small absorber thicknesses. The solid curve is the expected range dependence of l~.-decas electrons (�89 = ~). The dotted curve is the expected ~ - - e rang'e dependence, aud sl[ould be compared with the di//erence

be(ween the exl)erimental curves ][Df and MD=.

156 s. LOKANATHAN and J. STEINBERGER

TABLE I.

Absorber

. . . . L ~ / / " Thickness Total of CH2 ionization �9

in inches loss in MeV

0 7.5 1 12.5 2 17.5 3 22.5

4 27.5 5 32.5 6 37.5

7 42.5 3.07 8 47.5 3.07 9 52.5 fi9.4

Target in

106 D MD 1 I

4.26 14453 541 4.10 11 964 468 3.07 7510 274 3.07 5602 212

3.08 3 878 143 3.07 2318 78 3.07 1 257 45

471 23 122 3 606 15

TABLE If .

Target out

~ I . 1 ; ' D M D I

1.54 364 ! 1 1.54 149 1 1.54 94 3 1.54 6 6 [ 2 I

1.54 37 4 1.54 28 0 1.54 29 1

1.54 23 0 1.54 21 1

15.5 206 2

Net Monitor Counts per 10 6

D ! MDf

2 811 113 2 389 87 1 787 68

1246 44 738 25 392 14

139 7 26.1 8

7.3 .38: 16

Absorber

J Total ioni- : zation loss Mr.

inches in Mev

Target in

1o, D Thickness of CH2 in

1.38 23.6

1 957 238

56 1 021 6 61

Tar et out I Net Monitor _ g _ Counts per _106

/M'_ 10 6 D MD I MD~_. D__ MD 1_ MD~_

0 28 97 0 8 1320 46 741

4. - A n a l y s i s of the D a t a .

4"1. Product K 01 stopped meson flux and detector solid angle. - K is o b t a i n e d

by e x t r a p o l a t i n g t h e o b s e r v e d r a t e D f r o m smal l abso rbe r th ickness to zero

abso rbe r th ickness , as d iscussed in t h e i n t r o d u c t i o n . F o r run no. 1 th is can

be done us ing Fig . 3, and K , = 3 330 ~- 50 per 106 m o n i t o r counts . F o r r u n

no. 2 we m u l t i p l y t he r a t e o b s e r v e d w i t h 3 inches of p o l y e t h y l e n e b y t h e r a t io

of coun t s D e x t r a p o l a t e d to zero abso rbe r to counts D w i t h 3 inches of poly-

e t h y l e n e as d e t e r m i n e d in Fig . 3. This r a t io be ing 2.0, K2 = 2 640 • 50 per

106 m o n i t o r counts .

b) Acceptance time ~ /or the detection o] decay positrons in MDs. - This

can be d e t e r m i n e d f r o m the c o u n t i n g ra tes of t h e ~ -decay pos i t rons us ing sma l l

S E A R C U F O R T I l E ~ - I ) E C A u O F T I l E P I O N 157

a b s o r b e r t h i cknes s :

W e find

Z = )b.-~ exp [h, (D/(D . M D I) ) ] .

~ = 8.6"10 S s for run no. 1,

2~ 6.7"10 ~s for run no. 2.

c) Detectio~, probability o] positro~s ]rom the decay o] r~+---> e + + v.

These p o s i t r o n s will h a v e an e n e r g y of 71 MeV, one ha l f of t h e res t ene rgy

of t he p ion . W i t h 9 inches of p o l y e t h y l e n e , t h e a v e r a g e i o n i z a t i o n loss of a

n f i n i m u m ionizing' p a r t i c l e is 45 MeV in t h e 21 g /e ra 2 of p o l y e t h y l e n e , a b o u t

7 MeV in t he fou r d e t e c t i o n - c o u n t e r s (3.5 g / cm 2 CH~) ~nd 2.5 MeV in one ha l f

of t he m e s o n s t o p p i n g t a r g e t (1.1 g/era ~ CH2) for a t o t a l loss of 54.5 MeV

t h r o u g h ion iza t ion . I n t h e a p p e n d i x we c a l c u l a t e t h e p r o b a b i l i t y w i th which

e lec t rons of g iven energ ies wi l l pe-

n e t r a t e a b s o r b e r s of ?.'iven ioniza- ,o~ t ion loss t a k i n g r a d i a t i o n a n d mul - : Z / ~ ~ ~ ~ ' '

9 absorber " ' "

t iple scat tering" int, o a,ccoun~. I~rolI] 8 / rooOo , r / / . . / / ~ ]

FIR'. 4, we i n t e r p o l a t e t h a t 71 MeV ; 30 M~v ? - : i

e lec t rons will be d e t e c t e d wi th a 6 . . . . eV i

p r o b a b i l i t y E - - 0 . 4 8 when 9 in- ~

3 | t " / " / " / ' / / i" / 7 ~ P~eV t

ftl ehes of p o l y e t h y l e n e a re p re sen t .

H o w e v e r , th i s wil l no t be qu i t e

t r u e in t he ease of p o s i t r o n s for

these can a n n i h i l a t e in f l ight . This

is in l a rge m e a s u r e b a l a n c e d b y a

s inf i lar effect on t h e p o s i t r o n s f rom

the F-e d e c a y wlfieh serve as cali-

b ra t ion . W e e s t i m a t e t h a t th is

effect r educes the p r o b a b i l i t y E

b y a b o u t 2 to 3 p e r c e n t a n d

the re fo re use t h e va lue E - - .46.

0 10 20 30 40 50 60 70 80 90 100 e l e c t r o n e n e r g y MeV

Fig. 4. - Smooth emwe presentation of the results of the Monte Carlo eMeulations. Dete- ction probabi l i ty vs. energy in polyethylene. The range parameter is given in units of MeV ionization loss.

d) Correction ]or tt~c F-decay positrons. - Tile w d e c a y pos i t r ons which

are c o u n t e d in MDj with 9 inches of a b s o r b e r t h r o u g h t h e conve r s ion of t he

b r e l m l s s t r a l u n g r a d i a t i o n a re d i r e c t l y d e t e r m i n e d f rom t h e r a t e s D or MD~ which are a h n o s t e n t i r e l y due to th is effect.

Thus t i le u m n b e r which has to be s u b t r a c t e d f rom M D s is

(1 - - e x p [ (2 /2 .2) . 10-6]) - - (MDs),i,,cho, (l exp [ - - 0 . 8 / 2 . 2 ) - 1 0 - q ) '

158 s . LOKANATIIAN a n d J. STEINBERGER

o r

We find

(~ = (D),i~ch~. (1 - - exp [ - - (~/2.2).10-6]).

5 ~ (.18 • .025) per 106 moni tor counts for run no. 1,

~ (.089 :~ .02) per 106 moni tor counts for run no. 2.

e) Correction ]or inverse photomeson production and charge exchange scat- tering. - The t a rge t is t r aversed by a flux of pions measured in M. Only one

half of these actual ly stop in the target , the average energy in the t a rge t m a y

be approx ima te ly 25 MeV, and the average thickness of carbon t raversed is 1.5 g /cm 2. The meson has a finite p robabi l i ty for nuclear in teract ion with

subsequent y-emission, ei ther f rom the inverse of pho tomeson production, or f rom charge exchange scattering. The former process m a y be es t imated to have a cross-section of 2 =L 1 mb in this energy range, f rom observat ions (s)

on the react ion y + C - r 2 4 7 7:+, which shows a cer tain resemblance to its

inverse. The ~,-rays emi t ted are of the order of 130 YleV and will have a detect ion probabi l i ty of app rox ima te ly 0.35 in D. The count ing ra te due to

this effect is therefore approx imate ly :

M D ~ / M = (2 ! 1)'10-2v'[1.5"6"102~/12]'[.049/4~z] ".35 --~ (2.2 ~= 1.1).10 .7 .

The charge exchange cross-section in carbon has not been measured, how- ever, i t appears to be less t han 1 mb for posit ive pions under 30 McV (9). The efficiency for detect ing these y-rays is somewhat less, because of the lower energy; it is approx imate ly 0.2. The corresponding ra te should therefore be

M D I / M < 2.1-1027. [1.5.6.10~3/12] .[.049/4n]. 0.2 : 1.25.10 -v .

The charge exchange correction is therefore less t han one half of the inverse

photo process correction, bu t will not be made, since only an upper l imit for

this correction exists.

]) .Fraction o/ r:'s decaying to electrons. - The net count ing ra te MD1/M af ter subt rac t ion for ~-decay electrons and inverse photoprocess is

(.38 :[: .16) - - (.18 i .025) - - (.22 :[: . 1 1 ) : ( - - .02 ~- 21)

per 10 G moni tor counts for run no. 1.

(s) j . ST]~I~TB]~RGER and A. S. BISHOP: Phys. Rev., 86, 171 (1952). (9) j . TIN-LOT: private communication.

SEARClI FOR THE ~-DJECAY OF TIlE PION 159

and

(.254 _~ . 1 0 ) - - (.089 -~ .02) -- (.22 -L: .11) ( - - .055 ~_ .15)

per 10 ~ moni tor counts for run no. 2.

The fract ion of ~-mesons underg'oing" ,~-decay is

( M D j 'M) ......... te(I" 1/K" J / E - - ]

]~ ... . .13 1.36"10 -a for run no. 1 ,

] 2 : - . 4 5 q _ l . 2 3 . t 0 4 for run no. '2.

Combining" these two results, ore' exper iment yields the rat io:

7 ~ e

7u~ -->LL - I - - (--.a :5.9) .1o- , .

The quoted error is the s tandard deviat ion and includes the stat is t ical

uncer ta in ty as well as an es t imate of the error in the subtract ion for the inverse photomeson production.

I t is therefore not likely tha t the actual = - ~ e decay fract ion is grea ter than .6-10-* or one in 17000. The exper immlt is approx imate ly twen ty

t imes more sensitive than previous a t t em p t s to find this decay mode, but no

posit ive evidence is obtained. I t seems therefore improbable tha t the pion is coupled symmetr ica l ly to the muon.

A P P E N D I X

Straggling of Electrons with Energies of the Order of the Critical Energy.

In this energy range the straggling" is pr imar i ly due to radia t ion a.nd mul- tiple scattering. This problem has not been solved analyt ical ly, a l though the processes are well understood. We have solved the prob lem with an accuracy sufficient for our purposes by mak ing Monte Carlo calculations for the radia t ion straggling and combining these with similar calculations (1) on the reduct ion in range due to the i r regular i ty of the t ra jec to ry (multiple scattering) chiefly near its end.

The radiat ion stra.g~'ling ealcula.tions were carried out, a t 6 energies: E = 25, 35, 50, 70, 85 and 100 MeV. The Bethe-Hei t le r radia t ion loss formula is app rox ima ted by the form which corresponds to unifornl energy loss over the spec t rum :

d X ( E ) / d x - - 1 , , E X .

160 s. LOKANATHAN a n d a. STEINBERGEI~

TABLE I I I . -- Results o] the Monte Carlo calculations on the ranges of electrons in poly- ethylene. 100 triaTs are presented ]or each o] six energies. The ranges in the column

(c Range Interval )) are given in units o] ionizations loss in MeV.

R a n g e I n t e r v a l

2 . 5

5

7.5

10

12.5

15

17.5

20

22 .5

25

27 .5

30

32.5

35

37.5

40

42.5

45

47 .5

50

52.5

55

57.5

60

62.5

65

67.5

7O

72.5

75

77.5

8O

82.5

85

87.5

90 +

92.5 +

95 +

97.5 +

E 25

0 + 2 . 5

+ 5

+ 7.5 1

+ 10

+ 12.5 3

+ 1 5 3

+ 17.5 6 + 20 11

- - 22 .5 7

+ 25 69

+ 27 .5

+ 30

+ 32 .5

+ 35

+ 37.5

-.'- 40 - - -

+ 42 .5

+ 45 + 47 .5

+ 50 + 52.5 - - 55

+ 57.5 + 6O

+ 62.5

+ 65 - -

+ 67 .5

+ 70

+ 72.5

+ 75

+ 77.5

+ 80

+ 82.5

+ 85

+ 87.5

+ 90

92.5

95

97.5

1 0 0

35

1

2

5 4

6

3

8

6 65

- - i

50

2

2 1

1

1

1

5

5

6

5

8

8 17

38

70

2

1

5 2

3

i

6

2

4

3

4

6

4

6

8

6

6

10

12

85 100

1

1

2 1

1 1

2 1

1 2

1

1 3

1 1

1

3 1

5 3 2

2 3

3 1

3 1 2 1

6 1

3 2

5 2 4 3

4 4

6 3

5 5

5 5

5 1

5 7

8 3

7 5

7 3

- - 6

- - 5

- - 5

- - - 7

- - 7

- - - 5

SEARCI[ FOR TIlE ~ DECAY OF THE PION ](il

X(E) is the n u m b e r of quan ta of energy E radia ted per unit energy interval and X is the radia t ion length; in our case of CH2 this is 65 g/cmL The ab- sorber is then divided into sections of 5 MeV ionization loss. In CH2 the ioniz~tion loss of m i n i m u m out-going particles is 2.18 MeV/e 2, so tha t each section corresponds to .0354 radia t ion length. The radia t ion loss probabi l i ty distr ibution is then divided into 100 regions of equal p robabi l i ty and two dio'it r andom numbers are chosen for each interwd. The calculat ion proceeds by allowing a tr ial electron to pene t ra te to the center of the first section by losing 2.5 MeV through ionization. I t then radigtes according to the loss picked from the radia t ion probabi l i ty dis t r ibut ion by the r andom n u m b e r of the section, loses 5 3[eV by ionization to get to the center of section two, radiates according to its luck in this section and so on. We calculate for 100 trajectories a t each of the six energies. The results are t~bulated in Table I I I .

In Fig. 4 these results are p lo t ted af ter the stgtist ical irregularities are smoothed. In the same figure we also show the results of folding the mult iple

a[ L ? ~"

i

I : ~ 20 40 50

I I

~ ---RADMTIONANDSCATTERINO 5T#AGOLIN6

"~" "~ i PARAMETER LABELLINO CURVE5 25 - ~ ~ ELECTRONENERSY/NMeV

\ \ \ \ \ \ \ i

\ \ \ , x \ , \ , \

\ \x [

:, I \

---I I' " x ' - - \,

50 70 80 90 lOG RANOE fN MeV IONIZATION L055

Fig. 5. - Smooth curve presentation of the results of the Monte Carlo range calculations : I)eteetion Probability vs. Range in Polyethylene.

scatterfilg dis tr ibut ion into these results (~o). The range is Given in units of ionization loss. For the purposes of the exper iment it is necessary to know the detect ion probabi l i ty (probabil i ty tha t the range be in excess) as a function of energy for different absorber thicknesses, and this i~ p lo t ted in Fig. 5. The data of Fig. 5 are derived f rom Fig. 4.

(~o) "[he multiple ~catteri[~g affe(ts the trajectory chiefly near the end. We neglect the energy dependence of this straggling, and use the calculations made earlier for the nlultiple seatteril~g of 50 MeV electrons; J. STEIXBEt{GER: Phys. Rer., 75, 1135 ,(1949).

11 - ~%'upplemenl . (d A w ) v o C i m e n l o .

162 S. LOKANATPIAN all~ J. 8TEINBEI~GER

We wish to point out here that the results presented in Table I and Figs. 1 and 2 may also be used to predict the behavior in other materials, if the energy scale is converted by the factor:

f/I,

where I is the ionization loss per radiation length, in this ease 142 ~eV. The computations have received some confirmation by comparing the

observed ~--> e range curve with a computation of this range distribution using the calculated electron ranges and a spectrum for the decay electrons given by Michel's parameter ~ ~---�89 (7). This is shown in Fig. 3.