IL NUOVO CIMENTO VOL. XIII , N. 5 1 ° Settembre 1959

Electromagnetic Processes at High Energies. P A R T I . -- A n o m a l o u s S h o w e r s .

P. K. A1)ITX'A (*)

_Physics Houours School, Pan, jab Universily - Cha~digarh

(ricevuto il 15 Giuzno 1959)

Summary. - - The problem of anomalous showers has been discussed with a view to compare their fluctuations with those for two other samples of electromagnetic cascades. I t is concluded that the observed discrepancies result on account of the individuality of the events and that the fluctuations are similar to those for normal cascades. In general the fluctuations are found to be not very much larger than those for a Poisson distribution.

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

In reeent years , the s tudy of e lec t romagnet ic processes has assumed a

new importan( 'e , since some exper imenta l findings ind ica ted marked depar-

tures from theory. F r o m observat ions made in nuclear emulsions, on the

deve lopmen t of e lec t ron-photon showers and the presence in them of an ab-

norm~flly large number of t r idents , i t appea red t h a t the exis t ing theories on

easeade deve lopment and t r i den t p roduc t ion were inadequa te to expla in the

phenomena a t high energies. On account of the m a n y advan tages of s t r ipped

emulsions over other t ype of de tec tors most of the cascade theory problems

have been in l a te r years t ack led wi th renewed ~pproach. Inves t iga t ions at

high energies are l imi ted on account of the r a r i t y of such events and so a t t e m p t s

are somet imes made to derive as much in format ion as possible f rom events

found under different exper imen ta l condit ions. As ~ resul t a wide va r i e ty of

d a t a has accumula ted , some indica t ing accordance with theore t ica l predict ions

and other po in t ing out large discrepancies. In view of the l imits of error in-

(*) At present a~ the Institute for Theoretical Physics, University of Copenhagen, Denmark.

1014 P.K. AmTra

volved in the exper imenta l procedure and wide f luctuations allowed by the

theory, a s t ra ight forward in te rpre ta t ion of the exper imenta l da t a has not.

a lways been possible. ]in a recent communica t ion (~), i t was ment ioned t h a t

during the course of t ha t invest igat ion no shower depicting abnorma l behaviour

was observed. This conclusion was in fact based upon our hav ing recognized

the large f luctuat ions intrinsic in the na ture of the process. Howe~-er, if we had selected, out of our mater ia l an individual event and neglected all the others

(the s i tuat ion is somewhat similar to our hav ing accidentally observed only

one par t icular event) it could possibly be classified as an anomalous shower.

I n order to clarify this point , we propose to discuss in this article the prob lem

of the so-called (~ Anomalous showers ~) and consider in t h a t con tex t the var ious

events known to us and t ry to find out whether the observed anomalies have

been apparen t or genuine.

2. - S t a t e m e n t of t h e p r o b l e m .

in a systematic investigation, the electron-photon showers are normally

picked up by scanning for bunches of minimum ionization tracks. Each bunch

is then followed through the stack either to the point of m'~,terialization of the

primary photon or to the point of entry of the electron or electrons into the

stack. Such events which m a y be called isolated showers are the subject of

the present discussion. (In some cases, the following back migh t lead to a high energy disintegrat ion f rom which the soft componen t emerges as a result of the decaying high energy ~°-mesons. These showers called re la ted cascades shall not be considered a t present.) In mos t of tile cases however a sys temat ic inves t igat ion is not carried out wi th a view to pick up tile cascades bu t dur ing a scanning for some other exper iment , a soft cascade is picked up a t random. i~ is evident t h a t in such a case there is a very s t rong bias in favor of those events being picked up more f requent ly which have high mul t ip l ica t ion either due to ve ry high energy of the p r i m a ry or to some anomalous processes

h i ther to unknown. Unless a significant number of these so-called anomalous

events are obta ined in a sys temat ic invest igation, any conclusions on the

na tu re and f requency of these r andom events might be misleading. The sit-

ua t ion is much worse when only a single event is observed and compared

wi th the theoret ical ly predicted behaviour .

Theoret ica l ly it is possible to es t imate the a.verage n u m b e r of e lectrons

expected a t a certain dep th measured with respect to the origin of the shower. A soft shower m a y be called anomalous if the number funct ion i.e., the distri-

but ion of the various electron t racks in regard to the longitudinal development.

(1) p. K. ADITYA: NUOVO Cime~to, l i , 546 (1959).

E I . E C T R O M A ( ~ N E T I C P R ( ) ( : E S S E S AT l l l ( ; l l E N E R G I E S - I l ( ) ] , ~

and/or lateral spread n~ture of the process. following sources:

are beyond the wide f luctuations allowed by the

The observed a.n(mm:lies can arise possibly f rom the

1) indefiniteness of the nature and number of p r imary part icles;

2) un( .er tainty in energy es t imat ion t)f the wtrious components of the

shower ;

3) eontr ibut ion to the shower deveh)pinont by I)ro('esses other t h a n

the conventional ;

4) fluctuations.

2"]. - a) P h o t o n i n i t i a t e d s h o w e r s : I f the origin of a cascade is a pa i r

of two t racks originating in the emulsion it is na tura l to assume tha t the pri-

m a r y has been a photon and the point of mater ia l iza t ion is considered as the

origin of the ('ascade. I t is however not possible to say wi thout doubt whe ther

the photon has been single or is aeeompa| | ied by one or more other i)hotons. Be(,~use of l~he conditions of the exper iment there exists nlso a finite proba- bi l i ty of a parti(,ul,/r shower 's existing in the sta(.k in such a way tha t the

tra(,k of the paren t electron which emi t t ed the l)hoton or photons by the con-

vent ional b remss t rah lung pro('ess cannot t)e observed. This probabi l i ty (te-

ponds strona'ly upon the exper imenta l fa('tors, such as the steepness of the

event , the [.larity of the emulsions and the level of min imum ionization. The

single electr(m might ha.ve gol hig'hly seattere(l af ter a sudden radiat ion loss

of the major par l of its energy and appear :,.t such a steel)angle as to be easily missed. Fai lure lo (Ieteet the sint~le ele(~tron in the v M n i l y of one or more high energy pairs e 'm lead to :m (,vent anomalous in regard to either or 1)oth of c'~seade development and lateral sI)read. Assuming tha t the exper imenta l conditions are ideal and t ha t th(, (,as(,ade development is found to be much more rapid than t ha t expec ted for a sin~'le ldmton, or if the lateral sprea.d of the shower is impossil)le to be ext)eeted f rom a single photon, om~ is left to assume ~ larger number of photons 1)(,il~ l)resent. These photons eonhl

result f rom the followintz pro(,ess'.~s:

i) Up to two photons can be associated with the deeay of a ~°-meson,

bu t one meets with the difficulty of findin~ a, nea rby source of ~°-mesons.

In spite of the t ime di la ta t ion a t very high energies, the =°-meson because of

its very short life t ime ( ~ 10 ~5 s) is not expected to travel large distances.

A loeM source such as a high energy disintegr,/t ion is not difficult to detect,

unless it is a rare collision be tween a high energy pro ton (or neutron) and a, mwleon of the emulsion, involving p r o d u d i o n of only neutral pa.rtMes.

1016 P . K . AI)I~['YA

ii) There could be some other unst~ble particles of hmg life t ime de-

caying into ~(-rays. At the present s ta te of knowledge the existence of such a

par t ic le is not known.

iii) Two or more photons can be produced in an amlihi lat ion process

be tween a p ro ton-an t ip ro ton or an electron-positron. (~ORINAL1)ESI (2) ] las

es t ima ted the probabi l i ty for p+-p: annihilat ion and in order to explain as m a n y as 20 photons, suggestive of the anomalous event observed b y SOHE~"

ct al. (3) needed an energy of ~ 1052 eV. In view of the an t ipro tons being

rare, and the impossibi l i ty of having energies of t ha t order, the probabi l i ty

of such a process being responsible for the large number of observed anomalous

events is negligible. GUPTA (4) and JOSEPH (5) have es t imated t ha t in e+-e -

:mnihilat ion a t ve ry high energies the probabi l i ty of mult iple photon product ion

of up to 4 or 5 photons is comparab le to t h a t for the normal two photon pro-

duct ion. Since in cascades, high energy positrons are in equal number as

electrons, the remote possibility of a very high energy posi t ron get t ing anni- h i la ted may not be neglected, t Iowever , according to ~{EITLER (6), e v e n at very high energies the posi trons are more likely to loose their energy before

get t ing annihilated, so t ha t the contr ibut ion to cascade deve lopment by this

process can be only negligibly' smM1. I t m a y be ment ioned tha t in emulsions,

such a process cannot be direct ly identified, since it is not possible to detect

a s topping m i n i m u m ionization th ick and. associate it with a cascade t h a t

s ta r t s developing far ahead. However , if it occurs in an a l ready developed

shower it is possible to recognize a t rack s topping in flight~ bu t the annihi lat ion photons when mater ial iz ing cannot be distinguished f rom the normal brems- s t rahlung photons. For some events of this k ind which show much too large later ' t l spread of the pairs and for which the probabi l i ty of having missed the

asso('iated electron t rack or t racks is small, e ~ -e- annihilat ion seems to be a fea-

sible explam~tion.

2'1. - b) Electron init iated showers: I f a cascade when followed back lends

to a single t rack a t m i n i m um ionization it is mos t l ikely to be due to an

electron because the cross-section for b remss t rah lung by he,~vier particles is

known to decrease very rapidly' with increasing mass. I t is a t first absolutely

essential to follows such a t rack to its point of entry into the stack, because

unless t h a t is done the origin of the cascade cannot be precisely defined. I t

m a y be possible to judge the potent ia l lang'e of such a track, if it is not con-

(2) lff,,. CORINALDlgSI: ~'UOVO CimeMo, t2, 571 (1954). (8) M. SCH•IN, D. M. HASKIN and R. G. GLASSJ~R: Pl~ys. Rev., 95, 855 (4) S. N. GUPTA: Phys. Rev., 98, 1502 (1955). (5) j . JosneH: Phys. Rev., 103, 481 (1956). (6) W. I-IEITLEtt: Quantum Tl~cory o] Radiation (Oxford, 1954), p. 271.

(1954).

E L E C T R O - ~ [ A G N E T I C P R O C E S S E S A T H I G H E N E R G I E S - I 1 0 1 7

ven ien t to follow it back bu t such a procedure is likely to introduce an unknown

bias against some low energy pairs t h a t might have mater ia l ized in the un-

followed length and do not show up now at the point one finds apparen t ly

only one t rack. I t is known to every exper imenta l i s t th'~t the following back of a single t rack a t m i n i m u m ionization involves apa r t f rom great care also

some uncer ta in ty . Assuming tha t the single t rack has been followed to the

point of its en t ry into the stack, it is (,onventional to assume tha t point as

the origin of the cascade and consider the electron to be alone. This is a reasonable assumpt ion for mos t of the c~ses, b u t might no t be so in t h a t rare

case when some ((bremsstrahlung ,> has been emi t t ed in the packing mater ia l

beyond the sensit ive volume of the s tack or even some created a l i t t le outside

the stack. Because such photons are likely to mater ia l ize at any stage, on

or near the p r i m a r y t rack these can give rise to an anomalous event with an

~pparen t ly fas t growth and wide aper ture . The si tuat ion is par t icular ly bad

in the ease of emulsions, because only a l imited port ion of the cascade near

its origin can be observed. I t appears therefore unsafe to derive conclusions

on the anomalousness of an event t h a t is ini t ia ted b y one or more electrons enter ing the s tack f rom the outside. Considerations as above will apply to a pair of t racks enter ing the s tack (see for example the event due to SCHEIS" et al. (~)) or even to those events in which the p r ima ry photon materializes very soon af ter en t ry into the stack.

2"2. - Uncertainty in energy estimation. Apar t f rom predict ing the average

n u m b e r of electrons expected a t a certain depth in the absorber, the cascade

theory foresees a certain energy spec t rum of the secondary electrons. Bo th

the cascade deve lopment and energy spec t rum can be specified provided the energy of the p r i m a ry can be es t imated. For mos t of the anomalous events, the anomalies d isappear if the es t imated energies are allowed uncer ta in t ies in some cases of ve ry large order. I t is felt t h a t energies are a lmost a lways underes t imated. The underes t imat ion of p r imary energy leads one to classify

a cascade as depict ing an anomalous ly rapid growth, while an underes t imat ion of secondary energies gives rise to a discrepancy between the exper imenta l ly observed and theoret ical ly predic ted energy spectra. The si tuat ion is equally

bad if different techniques are used for es t imat ing energies in the various energy

ranges, so t h a t discrepancies arise in the development , or in the energy spectra

or p a r t l y in both. At present a num ber of methods of vary ing meri t are

avai lab le for energy es t imat ion, wi th a drawback tha t not one of them can

be employed for the entire region one needs to explore. These are:

i) mult iple Coulomb scat ter ing;

ii) opening angle of the pair ;

6 6 - II Nuovo Cime~do.

1018 P . K . ADITYA

iii) suppression of ionization near pair origin (7);

iv) lateral spread of the shower (8);

v) h)ngitudinal cascade development.

A detailed consideration of all these methods nmy preferably be postponed for a la ter discussion, bu t a few useful remarks may be made in the eoatext . Pr imary energies ~ 100 GeV can be determined equally well by using any of the methods iii), iv) and v) wherever applicable. The first method i.e., suppression of ionization is part icularly useful for those events which cannot be followed for sufficient length in the stack. Nei ther of these methods oan

be used to est imate ener~'ies of the secondary order. The first two methods i.e., multiple scattering and opening angle may ill some c'~ses be used for pr imary pairs of small energy bu t are suited more for the low energy secon-

dary pairs. On account of emulsion distortion, microscope stage-noise~ personal reading

error and above all spurious scattering, energy nleasurements by multiple scat ter ing at a few GeV or more cannot always be relied upon, whereas a neglect of the multiple scat ter ing while est imating energies from the opening angle of the pair would almost alw'tys lead to energy underest imation. F rom our experience with this work it appears tha t p~ir energies can be es t imated

to a fairly good approximation, if the t rue opening angle between the two par tners is ex t rac ted from the observed opening af ter taking into account the

influence of the relative scat ter ing of the tracks (~.*).

2"3. - Processes other than conventional: I n the deveh)pmeut of showers, the t lmory takes into account only the usual emissions by the electron of bremsstrahlung photons and their subsequent materialization. If the growth of the shower is too rapid with respe(.t to tha t predicted, it is natural to think tha t apar t f rem conventional processes there might be some contr ibut ion due

t o other phenomena. I t has been known (9) tha t electrons c'm directly produce a negatron-

positron pair in a one step process (in emulsions known as the t r ident process),

bu t since the cross-section of this process has been theoretically i)redi(,ted to be negligibly small ' t t the energies commonly dealt with, no account of the t r ident process has been taken in cascade theory calculations. The exper imental ob- servation of a large number of events looking like tridents, ini t iated a contro-

versy, (~whether the t r ident cr0ss-section is in fact much higher than t h a t

(') P. K. AOlTYA: Ind. J. Phys., (under publ icat ion) . (7) j . IWADARF,: Phil.Mag., 3, 680 (1958). (8) K. PINKAU: P]dl. Mag., 2, 1389 (1957). (9) It . J. BHAm~A: Proc. Roy. Soc., A 152, 559 (1935).

ELECTROMA(~NETIC PROCESS]~S AT IIIGH ]tSNERGIES - I 1019

predicted )). I f so it is possible tha t such a phenomenon should mater ia l ly (.hange

tile sha.pe of the. shower a t least in the initial stages, tim magni tude of the

depar ture increasillff with incre~sing primary energy. Wi thou t ~ critical cousi-

der ' t t ion of the present s i tuat ion (whi('h it is not our aim to discuss here) it migh t appea r unsafe to make a precise s t~tement . However in view of the

proba.bility of bremss t rah luu~ photons material izing accidental ly within the

least resolw~ble distance from electron tr't(,ks, there has 1)een growing a ge- neral belief t ha t most of the ot)served t r idents are (( spurious )) and th:lt tit(,

number of t rue t r idenls is not far from that; predicted. Though numerical

results of some theoretic:fl a t t e m p t s (1,,.ii) on the inclusion of the t r ident t)rocess

into cascade theory are not readily awdlable, it might not be very nlu(.h wroug

to say t h a t tile contr ibut ion of t r ident I)roccss in the general deve lopment of

showers ( though it may not be completely iusignifieant) is not appreci:~ble,

especially because of the very strong ener~o'y dependence of the t r ident cross-

section.

A p a r t f rom t r ident product ion, whi(.h is the s t rongest r ival to the con- vent ional processes, it might al)l)ear useful to think of mult iple processes such as a) I)rodu(.tion of more than two photons at e+-e - annihilat ion a t very high energies; b) mult iple b remss t rah lung by an electron; c) mult iple pair pro-

duc.tiou "~t, the materia.lization of a single photon and d) direct produ(,lion of

more than one pair by an electron. Some ~/sl)ects of process a) have been con- sidered before (Section 2"1, a), iii)). For mult iple processes one might expect

according to HEITLEn (~2) t ha t the cross-section of these processes falls r:q)idly

with n, being prol)ort ional to (~/n) ~', where ~ is the, fine str t teture eoustnut,

= 1/137. The mul t ip le processes are therefore not l ikely to make significant

contr ibut ion unless such a thing occurs accidental ly in the most initial stage of de~velopment. Fo r process b), G~PTA (1:~) has es t imated the (,ross-section to be negligibly sm'fil even a t ex t remely high energies. I t m a y be ment ioned tha t such a process cannot be direct ly observed under the conditions of our exper iments . I so la ted examples of mul t ip le pair product ion by a single pho- ton (~) and of the direct p roduct ion of two pairs by an ele(,troll (~) ha.re been exper imenta l ly observed. I t is however, not safe to draw conclusions abou t

the f requency of such events, since only these few events (~.~5) should not

exhaus t the whole mater ia l (~6). Such processes though direct ly obserw~ble

(lo) J . W . GARDNER: .:¥UOVO Cimenlo, 7, 10 (1958). (11) S. K. CHAKitABA~T~': Proceedings o] the Cosmic Ray Symposium (Bombay,

February 1958), unpublished. (~2) W. t t~ITL~: 1OC. cir., p. 228. (aa) S. N. GUPTA: Phys. Rev., 99, 1015 (1955). (a4) j . E. HooP~lt and ]). T. KING: Phil. Mag., 41, 1194 (1950). (15) C. (~ASTAGNOLI and A. MANFREDINI: 2V~tOVO Cimcnto, 8, 778 (1958). (16) A. A. VARFOLO_MEEV, R. I. GnI~ASlMOVA ~nd V. A. TVMANYUN: 2U. Eksper.

Teor. l"iz., 32, 969 (1957).

1020 P.K. ADITYA

are difficult to be identified wi thout doubt if occurring in already developed

eas(~a(les, because al ternative assumptions such as ~eeidental coincidence ace

more probable. In view of the large fluctuations permit ted in the e~scade

tlwory, a separation of the small contr ibution due to multiple processes is not

possible in normal cases.

2'4. - Fluctuations: The theoretical formulation of the fluctuation problem

in the case of cascades has been known to be hopelessly complex. Since the

product ion of successive electrons is not a typically random process i.e., in whi(:h subsequent events are independent of those occurring prior to any one

of them, the fluctuations from the average have been expected to be mu(.h

more than those for a Poisson distribution. Among many theoretical a t tempts ,

good quali tat ive and quant i ta t ive arguments are found in the books by

HEITLER (17) and RossI (~s). AI~LEY (~9) has worked out in detail the natur~

of the stochastic processes, and in the model proposed by him, under certain

cir(~umstanees the fluctuations may be as high as the average itself. For our

purpose~ we have preferred to derive the tluctm~tions from the little experi-

ment:ll data awdl~ble to us (for details, see the following section).

3. - Observed a n o m a l o u s s h o w e r s .

Experiment:~l data on some of the anomalous cvents known to us (3.20-24)

have been presently used to derive the fluctuations. Irrespective of all other

considerations (see Appendix), the only criterion adhered to while collecting

the events has been to include those showers whi¢.b originate with a pair mate-

rialized within the emulsion or with a closely collimated pair of tracks entering

the stack. The development of the <( mean cascade )) derived from these showers

has beell plot ted in Fig. 1, curve (a). The horizontal lines have been drawn

to indicate the root meal! square deviation of the (( dist:mce fluctuation ~) for

the respective pairs. For comparison, plotted in the same figure are the eor-

(17) W. KEITL~R: 1OC. cit., p. 394. (~S) B. RossI: High E~ergy Particles (New York, 1952), p. 288. (19) N. ARLEY: Stochastic Processes (Copenhagen, 1943). (20) A. DEBENEDETTI, C. ~ . CTARELLI, L. TALLONE and M. V~GONE: Nuovo Cimento,

(a) 2, 220 (1955); (b) 4, 1151 (1956). (21) L. BARBANTI-SILVA, C. BONACINI, C. DE PIETRI, I. IORi, G. LOVEICA, R. PERILLI-

FEDELI and A. ROVERI: Nuovo Cimento, 3, 1465 (1956). (22) M. MIi~SowIcz, 0. STANICZ and W. WOLTER: NUOVO Cimento, 5, 513 (1957). (23) M. KOSHIBA and M. F. KAPLON: Phys. Rev., 100, 327 (1956), (Shower. (P.-I.).) (24) 0. B. YOUNG and T. S. YOON: Phys. Rev., 108, 908 (1957).

k H ~ E ( J T R ( ) M A ( ; N E T I C P R O C E S S E S A T H I G I t E N E R G I E S - I 1021

responding da ta f rom FAY (~5) and ADITYA (1) as curves (b) and (c) respectively.

Apar t f rom the p robabi l i ty of there being in some cases (see Appendix) more

t h a n one p h o t o n a t t he s t age (~ cons ide red as t he or igin ~> of t h e cascade , t h e

i n d i v i d u a l f l u c t u a t i o n s in cu rve (a) do n o t seem to be a p p r e c i a b l y d i f fe ren t f r o m

t h o s e in cu rves (b) a n d (e). W h i l e j u d g i n g th is , i t has to be r e m e m b e r e d t h a t

15

10

" ~ 0 o" ~ - - . o -

o - - . - . - . - o - --4c.--

Z 3

e) b) c) - - - - - o o - o - - - - o - - - -

I I i I I I i

0 0.4 1.0 1.4

OtshJnce f rom origin (cascede units) =

t . . . . I , , t , , , I ' d ' 0 0.4 1.0 1.6 0 6 1.2

Fig. 1. - Distribution of the distances at which each of the first fourteen pairs mate- rializes, plot ted against the number of the pairs. Distances are measured from the otis'in of the primary pair or from the point of entry into the stack (3). Curves (a), (b) and (c) refer respectively to the anomMous showers (3,2o-24) and to the cascades due to Fay (2~) and Aditya (~), The horizontal lines denote the root mean square

deviation of the distances.

for curve (a), since the energy of the secondary pa.irs has not been precisely

defined in relat ion to the ener~'y of the pr imary, a par t icular value of the

p a r a m e t e r y -- In (Eo/Em) cannot be prescribed, whereas in the ease of curve (b)

and (c) it is known. This unce r t a in ty is l ikely to change the slope of the

~, mean cascade ~> as well as to allow for larger deviat ions in the case of anomalous

events. Lack of reliable knowledge of the pair energies, does not permit at.

this s tage a consideration of the energy spectra.

In order to be able to find the f luctuat ions in the number of electrons ob- served a t a certain distance f rom the origin, da ta are avai lable f rom FAY (2~)

(e~) H . FAR: NUOVO Cimento, 5, 293 (1957).

1022 P.K. ADITYA

and ADITYA (1), Ill order to find the number of electrons present at a (.ertain

depth for the anomalous events, it is necessary to take into ae(.ount the dif-

ference in the number of electrons from twice the number of pairs materi~-

lizing in tha t distance. This is due to scattering away of the low energy

electrons, and we have used our data to obtain the (:orresI)onding approximate

vahws for the anomalous events. The root, mean sqm~re of the ~ number fluc-

tua t ion ~) has been obtained from the aven~ge number observed at various

depths and <(percentage fluctuation ~) computed. We have taken in the ease

of the observed d~m~ and for Monte Carlo calculations (:6):

Percentage Flucituation, (P.F.) = ~Vme,: ~ ,

and in the ease of the Poisson distribution,

(P.F.) = 100 ( N - - 1)½, N

where X is the total number of electrons at a (.crtain depth, (or N - - 1 is

the number of secondary electrons) and n is the number of events used in

70 4-

6O I

50 j ~ . . . . ~ . , . ~ a + 0 " 40 !~ X ~ + °0 0

+ Foy-Montecorlo (26) 30

x Fay- experimental (25)

20 ~ * Anomolous (3,20-24) x x

~. o Ads'lye (I) I0

Pol~son ¢~tribution Number of electrons

Fig. 2. - Percentage fluetiuation (for definition see text), ploited ao'ainst the total nulnber of electrons observed at a certain depth. The Poisson fluctuation based upon

lhe number of secondary electrons is included for comparison.

a part icular samp]e of (.ascades. Since P.F., is based Ul)On the s tandard d(,-

vintion, one might expect to find one third the number of ea.s(.~tdcs of a par-

t ieuhlr s'lmple having fllletuations greater than those given hereafter. We

(26) H. FAY: Nuovo Cimento, 6, 1516 (1957).

E L E C T R O : ' * [ A G N E T I C P R O C E S S E S A T l I l ( I I ! E N E R G I E S - i 1023

h a v e inc luded in this eompih~tion the results of the Monte Carlo calcula t ions

d o n e b y F ~ ¥ (~6) and the resul ts are p resen ted in the f o r m of Fig. 2. I n this

fo rm these m~ty be c o m p a r e d with some of the theore t ica l computa t ions . I t

m i g h t ~ppear (~onvenient to p lo t P .F . , agains t the d is tance f rom the origin n t the r

t h a n the lmnlber of electrons, b u t since a t a ( 'ertain depth the avera,ge n u m b e r

of e lect rons is :t fun(. t ion of the (( m i n i m u m a(.(.eptable energy )) and of the

theore t i ca l results emi)loyed for ( ,omparison (see below), we lmve preferred

to p lo t P.F. , aga ins t the n u m b e r of ele(.trons. The (( n u m b e r f luc tua t ions )> for

Lhe :l, IlOlllti~h)llS even ts do llot see!ql to 1)e signifie:intly different f r o m those for

two o ther samples of (.as('ades (~,~), nor are these ve ry mut 'h hlrger t h a n those

for :~ Poiss(m dis t r ibut ion , as appears to be the general belief. Fo r example~

a, ceord ing to ARLEY (~'~), P.F. , ( 'ould be ~ S0°o for the region of Fig. 2.

F ron l these ( 'onsiderat ions we s treng 'hten our po in t ing ou t in the begining,

t lmt the de(,ision on an indiv idual even t being anomalous is ha rd to m a k e be-

(.ause the flu( 'tm~|ions intrinsic in the process m a y be large indeed for an indi-

v idmd event .

Before we end this dis( 'ussion it appears useful to say ~ word a b o u t the

, average mmfl)er of l )ar t i ( ' les , expe( ' ted at. a cer ta in depth , as pred ic ted theo-

ret ical ly. Var ious au thor s lmve (,omF.ared their exper imenta l findings wi th

some of the m a n y cas(,ad(, t heo ry (.ah.ulations, su('h as of ARI.EY (ev)~ BHABHA

~md (~}]AKRAI{AIITY (2s), I{IIABII.~, and lIEm'Lnl~ (~-'~), Jh.xossY (~o), tl(>ssI a n d

GmESF~N (:~1) and with the Monte t ' : ,rlo (.ah.ulati(ms of FAY (~6) and of KA:t']~ON

aud W n . s o x (~:~). T h o u g h the general f ea tu re of :~.ll these results are simil:~r,

in the region of our in teres t , i.~,., inilial s takes of :1 ('as(.ade~ the average mlml)er

of (~lectrons is no t the same, the (lil'[erel~('e going u t) to a f',a'ior of ~ 1.5. This

f~wtor in t roduces a cer ta in a n m u n l of m~cert~dnty in the theoret i( ' :d in terpre-

l:~tion of the ext)er imental da la . At this 1)l:we, il is ne i lher possible nor (.on-

venient for us to dis(ross the various a t t e m p t s in detail.

4. - Conc lus ions .

F r o m the foregoing' cons idera t ions the fol lowing conclusions ma,y be sum-

ina, rized :

1) in order to classify all evetl t as anonla ious it is essential to m a k e

sure of the mltl lre ~lnd Ilunlh(~r of the p r i m a r y l)articles. E v e n t s or ig inat ing

(~7) N. AIILEY: i)roc, l~'oy. See., A 168, 519 (1938). (2s) H. J. BHABIIA and S. It. CIIAKRABARTY: Phys. 17~e~,., 74, 1352 (1948). (e,) H. J. BHAm~A and W. HEITI~EI~: t)roc. Roy. See., A 159, 1432 (1937). (30) L. J,L~ossY: Cosmic Rays (Oxford, 1950). (3~) B. RossI and K. GlCIESEN: RCV. Mod. Phys.. 13, 240 (1941).

1{)24 P . K . A 1 ) I T Y A

with a single pair are far superior than those ini t ia ted by one or more electrons. In order to avoid the observat ional bias it is useful to select events having smMler angles to the plane of the emulsion;

2) enet'gy es t imat ion should be done by taking iuto ~ccomlt the mul-

t iple Coulomb scat ter ing and the t rue opening angle der ived f rom the observed

aper tu re ;

3) the contr ibut ion of dire(.t pair product ion and of the mul t ip le pro-

cesses is insignificant in the generM deve lopment of a shower. In a particubLr

event in which such a I)rocess o(.curs in the very initial stages, it should 1)e

possible to ident ify i t ;

4) the f luctuations of the so-called anomalous showers arc no nn)re them

those for the normal cascades. In mos t of the cases the fluorinations are not very much larger than those for a Poisson distr ibution. I,l a.ny par t icu lar easc,

however, the deviat ions may be as large ~ts the average itself;

5) the average number of electrons expected a t "t certain dep th is not

known very precisely, as various theoret ical results a.re not identical. Before

the electronic computers can be used for this purpose, it is ra ther hard to pre-

dict accura te ly bo th the num ber distr ibution and the number f luctuat ion.

The exper imentM work on which this art icle is based, was done while the au thor was a t tim Pan jab Universi ty , Hosh ia rpur (at present a t Chandigarh) and pa r t l y during a short leave to the Tara Ins t i t u t e of F u n d a m e n t a l Research, Bombay . Thanks are due to Professor B. M. A~:t~D for his keen interes~ during the course of the work and to Professor B. PETERS for providing excellent

facilities "~t the T a t a In s t i t u t e and for the loan of some emulsions. The work

was suppor ted financiMly by the Governmen t of India , ] ) c p a r t m e n t of Atomic Energy, to which thanks are due. This article has been wr i t ten during the aut-

hors s tay a t the Ins t i t u t e for Theoret ical Physics, Univers i ty of Copcnh~gen,

Denmark . I t is :~ pleasure to thank Professor NIELS Bo}m for the hospi ta l i ty

extended a t this Ins t i tu te .

A P P E N D I X

The following comments on some of the anomalous events m a y be made .

Schein et al. (3) event: I f one of the first two t racks is the paren t electron and the other is due to an electron f rom a high energy high dispar i ty pair

E L E C T I t ( ) ' ~ [ A ~ ; N E T I C P R O C E S S E S A T t t l ( ; l l E N E R ( I [ E S - I 1025

crew, ted outsi4e the se~tsitive volume of the stack, then the origin of the cascade cannot~ be defined. In tha t case both the longitudimd d_evelol~metlt an(1 the l~teral spre{~([ coul4 be in ~tee<)rdatwe with a normal cascade, llut for the lateral spread, the lon/itudinal development is not 1)eyon(t the flue- tu~tions for a cottven~ional ease:tde.

,Shower t ' - I (e:,): As pointed, out by the authors, the anom~lies would_ 4isappear provide4 the i>rimary e~n~r~y has been underestimated. Since energies were obtained from t lw openillg ant~le without taking into a('eount the ('on- tr ibution due to multiple relative scattering, the fe~rs :~re likely to })e true, especially since Borsellino's relatiol~ was used. (Th(, energies in the ,.:tse of Borsellino's relation are smallel: by a fact()r of ~ 5 as compared to th,>se obtailied from the rei:~tion due to Stearns (:~2)). The ])ossibility of mult~i- photon ()r'igi~ may not be (,x(.hldcd i~t s.iew of the l)resenee of another pair similar to the, primary l)air, at :~ r:tdial dist:m(.e of 5.3 ram.

Firs t event (~0a): l a view (~f the steeI)m'ss of the event ( ~ 1 mm per emulsion), it is not improbabh, tha t it has been impossible to detect the t):t- rent electron, espe('ially if in a r~tdiation l)roe('ss it had been sc~tt, tered through a large angle. In tha t ease since the origin of lhe shower would most I~robat)ly be the point ,)f e~lrauee of the (, im~tgimtry ele[.tron )) into the stack, it might not 1)e 4iliicult to explain both the fas~ lonKitu4inal growth and the u~usual lateral spread.

Second erent (2oa): The presence of the low ener /y pair prior to th(, high energy one suggests definitely tha t the high e~erg~ ~ photon was not alotw at the point (( considere4 as the origin of the cascade ~). As the latter paiL's all arise after about one cascade u~fit (whi(.h may be nothing else but fluc- tuation) from the first two pairs, it is improbabh~ thai more tha~r two photons were present. The steepness of the event again allows the possibility of the i)arent electron having passed undetected. FAY (~) has carried out 5[onto Carlo cah~ulations on fifteen showers of high energy and obtained the resem- t)lanc(~ of one of the eoml)utcd showers wil h this event under referent( ~.

(32) .~l. STI";ARNS: Phy,~. Re~,., 76. 836 (1!)4(.)).

R I A S S I ~ N T I ) (*}

l'; stato discuss(> it t)roblema degli sciami am>malt all(> sc(>po di melt;ere a r~ff- front() le ttuttuazioni degli sciami stessi con quelle di due altri tipi di cascate elcttro- magnetiche. Si conchlde ehe le discxepanze osscrv:~te sono dovute aiit+ individualiih deffli even(i, e ehe le fluttuazi<)ni son(> simili a quelle deltc normali ('ascale. Si trova che, iu linea ~enerale, le fluttuazioni sono m(>lio pih ample di quelle dovute a um~ distribuziolm di l'oisson.

( ' ) Trad~,~io~c a ct~ra del la R e d a z i o l w .