IL NUOVO CIMENTO VOL. XI, N. 4 16 Febbraio 1959

A Note on the Trident Process.

P. K. ADITYA (*)(**)

Physics Honours School, Pan]ab University - Chandigarh

(ricevuto il 2 Dicembre 1958)

Summary. - - The mean free p~th for direct pa~r production by high energy electrons has been found for electrons of mean energy 20 GeV and 80 GeV. Electrons were obtained from high energy electromagnetic cascades recorded in nuclear emulsion stacks. Pair energies have been determined by using a modified relation for the p~ir opening angle. The cascade theory has been used to find the correction for spurious tridents. The trident mean free path values obtained ~t mean energy 20 GeV and 80 GeV are 10.4 :~ 1.2 and 7.7 ± 1.9 respectively, measured in terms of the cascade unit. The results are in agreement with the theoretical predictions.

I n r ecen t years, some obse rva t ions on the a b n o r m a l d e v e l o p m e n t of cascade

showers (~) ~nd ~he presence of a, l~trge n u m b e r of t r i den t s in t h e m ~nd ~long

cores of high energy disintegr,~tions (') had r~ised d o u b t on the v a l i d i t y of the

q u a n t u m e l e e t r o d y n a m i c theory . We have carr ied ou t an i n v e s t i g a t i o n in

this field and in this no t e describe our m e t h o d of approach ~nd the resul t s

obt~fined thereof. A de ta i led su rvey (:~) of all the d a t a k n o w n to us reveals

(*) Formerly known as l ' rem Kmnar. (**) At present at tile Inst i tute for Theoretical Physics, University of Copenhagen. (1) M. SCHF~IN, D. M. HASKIN and R. G. GLASS]~R: Phys. Rev., 95, 171 (1954);

A. D~B~Da~TTI, C. M. GAR~LI,I. L. TAI.LONE and M. VIGONE: NUOVO Cimento, 2, 220 (1955); 3, 226 (1956); 4, 1151 (1956); G. WATACmlN: Proc. Rochzster ConJerence (Feb. 1955); L. BARBANTI-SILVA, C. BONAClNI, C. DE PIET:aI, R. PERILLI-FEDELI and A. Rov]~RI: Nuovo Cimento, 3, 1465 (1956).

(~) P. S. F~E~E~ and J. E. NAU~;~: Pl~ys. Rev., 92, 1086 (1953); M. KOSmBA and hi. F. KAPLO~- : Phys. Rev., 97, 193 (1955); E. LOHR~ANN: Nuovo, Cime~tto 3, 820 (1956).

(3) To be published separately.

A NOTE ON THE T R I D E N T PROCESS 547

tha t the observed discrepancies arose due to limitations of the experimental

approa.ch. Two parameters entering into the determinat ion of the tr ident mean free

path are a) the energy estimation of the parent electrons and b) the elimi-

nation of spurious tridents. The following has been our method of approach.

~) Energy estimation: Since multiple Coulomb s~atterin~ measurements

have a limited reliability (up to about 5 GeV for the normally available 500 izm

cell size and 0.~ ~m noise level), we resorted to the use of pair opening angle

versus photon energy relation, taking into ac(.ount the fact that , for high energy

pairs of which the separation is not measurable in the first few mm from

origin, the contribution due to multiple Coulomb s(.attering may not a priori be neR'lected (*). Assuming equiparti t ion of encrR'y between the two ele(,trons

we have (,ombined the relative scatterint~ contribution to the true opening~

using the most probable value giv(~n by Bors(qlino's relation (~). Since the

separation due to scattering varies as the ~ power of the distance from origin~ it

predominates over the true opening for all distan(.es beyond 250 Fro; at, which

the two contributions are equal. A few typi(.al enerR'ies, plotted m Fig. 1~

50,-- Pair energy(GeV) --~

::il JJ2 20 7/777/

777/7/, " .05 0.1

.2 .4 .6.8.1 /

i l L ~ 10

2 3 4 5 10 2(

10 Distonce from pa/r orig/n (mm)

//•/60 80"100 200 GeV

30O 400

500

100 200

Fig. 1. -- Variation of pair separation with distance from pair origin, for pairs of various energies.

(~) 11t two brief communications (1% the energy e~timation was done on these lines, when our attention was drawn to similar arguments alrea4y published independently by E. [~OIIRMANN (N'ttOVO Cimen.to, 2. 1029 (1955)). We shall therefore not enter into details.

(5) A. BOI~SELLI-N-O: Phys. Rev., 89, 1023 (1953).

54:8 P. l~, ADITYA

show the curves between pair opening and distance from origin. One t hen needs to find pair separation ~t regular intervals, the interval depending upon

pair energy aad available length. In general up to ten such readings o/ire a

good estimate of the energy. For most par t of the energy range we are inte-

rested in at present, the re]iabi]ity of the method has been checked by com-

p~ring the energy spectruln of secondary electrons with tha t theoretically

predicted (~). Our results are shown in Fig. 2. The availability of a few

3ff N

10

5 ,~~t=O.5c.u. 2

10

Q

o

N ~

N j

50

20

10

5

2

N~ 5O

2O

10

5

'2

11 Y

Fig. 2. - Mean number N, of secondary electrons of energy greater th~n E,,, against y, where y=ln (Eo/E,,,), E o being the energy of ~ primary electron. Points beyond y=7

are derived from cascades of p r i m a r y energy greater than 100 GeV.

alternate methods in tile high energy region have enabled us to extend the

compa, rison to energies even of the pr imary order. For six casc~des of ~vhbh

(6) H. J. BtIABHA and S. K. C, IIAKRABAI~TY: .Phys. Rev., 74, 1352 (1948). We ,~re thankful to Professor CtlA~ICABARTY for the communicated advice a.nd some of his later cMculations.

A NOTE ON THE T R I D E N T PROCESS 549

t h e e n e r g y cou ld be f o u n d b y t h r e e or m o r e m e t h o d s , t he c o m p a r a t i v e s t a t e -

m e n t is g iven in Tab le I . F o r t he l o n g i t u d i m d d e v e l o p m e n t we h a v e e m p l o y e d

t h e ea l ( .u l~t ions of BItABItA a n d CHAKRA:BAR.TY and CHAKm~AR'rY (~). E a c h

of the cascades was fo l lowed for more t h a n 2.5 <.ascade un i t s (one e . u . = 2 . 9 c m

of n u c l e a r emuls ion) . I n o rde r to c o m p e n s a t e for t he d e t e e t i o n ineff ic iency of

low e n e r g y pa i r s (since t he re is no such effe<.t in ( 'ase of t r i de n t s ) , ~tu a .pp ropr i a t e

'l'aBI.~ I. - Energy o] the primary .pairs (GeV). obtained by various methods.

Shower Longitudinal Lateral Decrease of Present designation development, development ionization method

K., ¾ N3 N: NlO N3

1 200 300 600 300 250 100 150

1 000 300

300

800 ± 100 25O ± 5O 50O ± 8O 250 ± 50 25(I ~ 50 100 ± 3O 100 ± 3O

> 600 200- - 300 5O0 - 600

250 -- 300 80 - 100

100 + 150

(.ut-off for t he m i n i n m m a c c e p t a b l e e n e r g y was app l i ed , e.g., a t y - - l n (E,)/E,,) 7

for p r imaTy energies a r o u n d 100 GeV. The l a t e r a l d e v e l o p m e n t of t h r e e

showers which were g e o m e t r i c a l l y f a v o r a b l e was p l o t t e d a n d the ene rgy

e s t i m a t e d a f t e r t h e m e t h o d of PINKAU (7). The ene rgy e s t i m a t e of six pa i r s

was also o b t a i n e d f rom t h e dec rease in i o n i z a t i o n n e a r t he pa i r or igin (s), b y

c o m p a r i n g the e x p e r i m e n t a l v a l u e of t he dis tan( .e a t wh ich the ion iza t ion

t e n d e d a s y m p t o t i c a l l y to t he v a h i e for two i n d e p e n d e n t e lec t rons , w i th t h a t

e x p e c t e d t h e o r e t i c a l l y . The e n e r g y vah les o b t a i n e d b y us c o m p a r e r e a s o n a b l y

well a lso w i th t hose o b t a i n e d f r o m r e l a t i v e s ( .a t te r ing , as was i nd i ca t ed b y

LOHI~5~NN (s), who found , us ing our curves , an ene rgy of 70 to 75 GeV for

some of t he pa i rs , for which he h a d o b t a i n e d a va lue of ,50 ~_.,~5 GeV by scat -

t e r ing . I n r e g a r d to T a b l e I~ i t n m y be m e n t i o n e d tha.t t he p r e s e n t m e t h o d

m a y no t g ive a r e p r e s e n t a t i v e e n e r g y v a l u e for a n y i n d i v i d u a l pai~', h u t s ince

i t is our a i m to f ind the a v e r a g e e n e r g y of e l ec t rons classif ied in to a g roup ,

t he i n d i v i d u a l u n c e r t a i n t y does n o t m a t t e r , espec iMly since t he e r ror would

dec rease w i t h t h e inc rease of s t a t i s t i c s .

b) Correction ]or sy,urious tride~ts: Theore t i ( . a l ly i t is poss ib le to corn-

(~) K. PINKAU: NUOVO Cimento, 3, 1285 (1956). (3) D. H. PERKINS: Phil. Mag., ~6, 1146 (1955); G. YEKUTI]gLI: N~O~)O Cimento,

5, 1381 (1957). (9) E. LOH~AN~-: pr ivate communicat ion (June 1956). Thanks are due Dr. LOHm

MANN for t h e measurements and useful comments.

5 5 0 P . K . A D I T Y A

pute the fraction F of bremsstrahlung pairs (B.P.), which would materialize

within the least resolvable distance (0.2 ~m in projection and 0.4 ~m in dip)

from an electron track and give rise to a spurious tr ident (S.T.). Results of

such a calculation made by KI%6 et al. (~o) ~nd by KAPLO~ et al. (~5), indicate

I00

60

3£

o

E oy:7~ Experl~nental

x y : 8 points I

+y:9/

D/stance (c.u.) ~.

Fig. 3. - Mean number of electrons observed at various distances along the shower axis against distance in cascade units. Theoretically predicted curves are included for values of y from 7 to 9. y= ln (Eo/E~), E o being the energy of a primary electron, ~nd E,,~ the minimum acceptable energy for a secondary electron. Points for y = 8 and 9 are derived from cascades of primary energy

greuter than 100 GeV.

that , for energies ~--J00 GeV,

more than 70% of the observed

tridents are spurious. Accordina'

to Kaplon 's procedure that has

been widely used , number of

S.T. = F / ( 1 - - F) times observed

B.P., tha t appear resolved from

electron tracks. GREISE~- (H)

has however suggested the

advantnge of finding the cor-

rection not from the observed

number of resolved B.P., bu t

entirely from the electromag-

netic theory, i . e , compute the

bremsstrahlung spectrum and

expected number of both re-

solvable and unresolvable l~airs.

This method, though it ac~.epts

the measurement of energy and computa t ion of F, is less sen-

sitive to errors, because F would

enter linearly rather than as

F / ( 1 - Y). We have obtained

our experimental material from

two stacks of stripped emulsions

exposed in the stratosphere

over India (r.,). Out of a large

number of scanned showers, in

all 20 cascades of favorable

geometry were selected for detailed investigation. Plots of showers at various

stages were made for each cascade. In Fig. 3, the observed development is

(10) M. M. BLOCK and D. T. KING: Phys. Rev., 95, 171 (1954); 96, 1627 (1954). (11) K. GREISEN: private communication (August 1956). We are gTateful to Pro-

fessor GREISEN for his excellent suggestions. (12) D. LAL, YASH PAL and B. PETERS: ])roe. I~d. Acad. Sci., 38, 277 (I953);

R. R. DANIEL, G. FRIEDMAN, D. LAL, YASH PAL and B. P~T~RS: ])roc. Ind. Acad. Sci., A 40, 151 (1954). We are indebted to Professor PETERS for the loan of a stack and for the facilities of his laboratory where part of this work was done.

A NOTE ON THE TRID:ENT t~ROC]~SS 5 5 1

plotted over tha t predicted theoretically (~). But for:~small though apparent

deviation (':~) within the first 0.5 c.u., the agreement appears to be good. We

have not observed any case depicting abnormal beh'~viour. In fact, what we

observed was a slightly too small number of resolved pairs and a large number of tridents, bu t the correct total.

In earlier brief communications (~4) using the present method of energy esti-

mation, we h~Ld corrected for S.T. according to K.xPLON ~t ~d. (15). Using an along-

the- t rack following" procedure, a total of ]25 pairs and 49 tridents (including

spurious and genuine) were observed along 3.83 metre of emulsion length.

The electron track was sel)arated into two energy g'roups of (1+10) GeV and

(10 +100) GeV, obtaining the mean free path values ((i.] +"~i~) c.u., and (4.0:~i~) c.u.,

respectively. (A cascade unit was there taken equal to 3.0 cm of emulsion).

In view of the ~bove approach to the correction for S.T., it ~ppeared useful

to reconsider our previous data as well as to include some more cascades F rom the facsimile drawing of 20 showers an electron track length of 70 c.u.

was accumulated for an average energy of 20 GeV. In this length 68 pos-

sible tridents were observed. Using an appropriate factor F, the proportion

of B.P. which would appear as tridents was calcnlated at 61.3, leaving an

excess of 6.7 tr idents as genuine.

Reconsideration by KI~'G et al. (~0) of the theoretical cross-section for trident

processes calculated by BHABHA (~6), has shown it to be ill agreement with tha t

of I~ACAH (17). Aecordingly, the mean free path for 'tn average energy of

20 GeV is 35 cm, such tha t in 70 c.u. one expects 5.8 true tridents. This

number is in fair ~greement with our experiment~fl value of 6.7, which gives

~T = (10.4 ~: 1.2) c.u. at 20 GeV

With a view to find the cross-section at still higher energies, we considered

separately tim pr imary pairs tip to a, distance of 0.5 c.u. from the origin. Such

a cut-off has a further advantage, since the number of tridents increases linearly

with t, while the correction goes as t 2. J6 possible tridents were observed alon~"

18.5 c.u., of average energy 60 GeV. The calculated number of S.T., equal

to 13.6, left an excess of 2.4 true tridents, leading to a mean free path of

(7.7 2:1.9) c.u., as compared to 8.9 c.u. expected theoretically. Since the small

statistics does not allow stress to be laid on this result, our value of 20 GeV

(53) It may be possible to account for part of this deviation on the basis of a gelmine trident contribution likely to be present while the electrons have not lost their pri- mary energy.

(14) p . KUMA~: Proc. Ind. Sei. Cottg., III-3 (n. 18, 1955; n. 61, 1956); Proc. Cosmic Ray Symposium (Bombay, March 1957, unpublished).

(~5) M. KOSHIBA and M. F. KAPLON: Phys. Rev., 100, 327 (1956). (1~) H. J. BHABHA: Proc. Roy. Soc., A 152, 559 (1935). (57) G. RACAH: Nuovo Cimento, 14, 93 (1937).

552 P . K . ADITYA

sugges t s in gene ra l t h a t t he t h e o r e t i c a l c ross - sec t ion is n o t in e r ro r a n d t h a t

t he o b s e r v e d d i sc repanc ies a r i se as a consequence of t he m e t h o d s app l i ed .

I t is a p l e a s u r e to t h a n k P ro fes so r B. M. ANAND for his keen i n t e r e s t

d u r i n g t h e course of t h e w o r k a n d for g r a n t i n g l eave of absence t h e T a t a

I n s t i t u t e of F u n d a m e n t a l Resea rch , B o m b a y . F i n a n c i a l a s s i s t ance of t h e Go-

v e r m n e n t of I n d i a , D e p a . r t m e n t of A t o m i c E n e r g y , is g r a t e f u l l y a c k n o w l e d g e d .

R I A S S U N T O (*)

s ta to t rova to il cammino libero medio per la produzione di eoppie di elet troni di media energia (20 GeV e 80 GeV) da par te di elet t roni 4i a l ta energia. Gli elet troni sono s ta t i o t tenut i da caseate elet t romagnet iche di a l ta energia registrat i in pacchi di emulsioni nucleari. L 'energia delle coppie (~ s ta ta determinata servendosi di una relazione per l 'angolo d 'aper tura della coppia modificata. Lu teoria della cascara ~ s t a t s ut i l izzata per t rovare la co1~rezione pei t r ident i spuri. I valori dei cammini liberi medi dei t r ident i o t tenut i alle medie energie di 20 GeV e 80 GeV espressi in unit~ di cascata sono l ' ispettiYamente 10.4 ~ 1.2 e 7.7 ± 1.9. I r isul ta t i si accordano colle previsioni teoriche.

(*) T r a d u z i o n e a cura del la Redaz ione .