On the possibility of neutrons producing secondary interactions in high energy showers

IL NUOVO CIMENT0 VOL. XI, N. 6 16 Marzo 1959

On the Possibility of Neutrons Producing Secondary Interactions in High Energy Showers.

P. K. ADITYA (*)

Physics Honours School, Panjab University - Chandigarh Institute ]or Theoretical Physics, University o] Copenhagen

(ricevuto il 14 Gennaio 1959)

For nuclear disintegrations ini t ia ted by cosmic ray part icles of great energy (E per nucleon ~ 1012 eV), there exists a t present no sat isfactory method of estimating the relat ive proport ion of n- mesons, K-mesons, hyperons, and nucleon-antinucleon pairs produced amongst shower particles. Since direct mass meas- urements of secondary part icles are im- possible at such high energies, several a t tempts by indirect methods have been m a d e .

A method due to BRISBOUT et al (~), and la ter used by other workers (~), of determining the proport ion of neutral ra ther than charged K-mesons, hyperons, and nucleon-antinucleon pairs (here- af ter called x-particles) amongst shower particles, involves the following assump- t ions:

a) because of their very short life- t ime, ~°-mesons cannot contribute to nuclear interactions;

(*) Fo rmer ly known as P. KUMAR. (~) F. -~. BRISBOUT, C. :DAIIANAYAKE,

A. ENGLER, Y. FUJIMOTO a nd D. t I . PERKINS: Phil. Mag., 1, 605 (1956).

(2) ]~. EDWARDS, J . LOSTY, D. H. _PERKINS, K. PINKAU and J . REYNOLDS: t~hil. Mag., 3, 237 (1958).

b) secondary interactions produced by neutra l particles are due to x°-particles or ejected nucleons;

c) the mean free pa th of x-particles, nucleons, and =-mesons is the s a m e ;

d) nucleons and (or) heavy mesons (K :~, 0 °, =6°) with isotopic spin, I = ½-, are produced in a charge-inde- pendent way, so tha t if one assumes tha t i t is true also for the hyperons, then un- like pions for which n~_+ = 2n,~o, nx± ~ n~,.

Using N °, the number of secondary interactions produced by neutral particles and N ±, the corresponding number of interactions produced by charged particles all observed within the same angular interval (defined by a strip of width 720 ~m and length ~ 10 cm) within the narrow cone of high-energy showers ini- t ia ted by singly and doubly charged particles of energy ~ 101~eV, BRItBOUT et al. (1) obtained the rat io N°/N +- as Q = 0.25. Because of assumption (c) above, Q = n+/n~± or ~ , + / ( n ~ + n ~ ) , where nr,, nx and n~ refer to the numbers of ::-mesons, x-particles, and the to ta l number of charged shower particles,

O N T H E P O S S I B I L I T Y OF N E U 2 R O N S P R O D U C I N G S E C O N D A R Y I N T E R A C T I O N S E T C . 873

respectively. While considering the possibility tha t the large proportion of observed non-pions could be due to nucleon contamination, they (~) discussed the pro- babili ty that nucleons produced from the target nucleus as a result of multiple collisions within it, would be found in the region of the narrow forward cone, bu t in view of the high muttiplicit.y in- volved at such high energies, estimated tha t such a contribution from the nucleons would be negligible. No account seems to have been taken of the nucleons of the primary, which as we shall see would continue undeviated or only slightly affected in a collision even with a single nucleon of the target. I t is our aim to consider presently f, he processes by which high-energy neutrons of the projectile enter the forward cone and to see whether such considerations affect the result. Since charged secondary interactions are produced by both =+- and x± while the neutral interactions are due only to the x°-particles (=°-niesons being excluded because of assumption a) above) the relative proportion of x-particles is much more sensitive to the presence of a few neutrons than it would be if an equal number of protons were present.

There are two ways by which neutrons can enter the forward cone of high- energy interactions. These are:

i) If the primary is a complex nucleus, an a-part.iele or a heavy singly charged particle (deuteron or triton), only a part of the constituent nucleons may part icipate in the first interaction and the remainder proceed in the shower with the same energy per nucleon as ~hat of the primary.

ii) The primary nucleon may par- t ieipate in the collision and emerge from it with an energy still higher than that of any of the nucleons from the target.

We are at present not particularly interested in heavy primary interactions for which it follows naturally that during

collisions with nuclei only a fraction of the incident nucleons take part in the interaction. For a-particle interactions within a w i d e range of primary energies (3-5), it is known that, during collisions with emulsion nuclei, on the average only half of the incident nucleons contribute to meson production, in collisions with lighter elements oi" peripheral collisions with heavy targets (i.e., events of smaller number of heavy prongs), one would expect a still smaller fraction to take part in the collision. I t is reasonable to assume tha t all such nucleons which do not take part in the first interaction would appear within an angle e to the primary direction where a~(1)½pdpo (p~ is the internal momentum of the nucleons witlfin tim nucleus and P0 is the external momentum per nucleon of the primary). For Pi corresponding to the average binding energy per nucleon (~ S MeV) and Po corresponding to the energy per nucleon of the incident ~-par- title, E (in eV), the angle ~ (in radians) is given by the relation ~z,-lOS/E. For a-particles of energy from 3(}0 MeV to ~> 10 GeV per nucleon, several workers (3-5) have experimentally obtained the angular distribution of singly charged particles. From these data it is possible to find the energy dependence of the maximum angle within which are fmmd most of the nucleons of an c~-partiele which presumably do not take part in the first event. We find this energy dependence to be in agreement with the relation for ~ derived above. Consequently, this relation may be used also for the energy region we are interested in at present, and one concludes that the nucleons of the projectile, which do not take part in the primary event, would be able to eontri-

(8) ~[. CEUCARELLI, G. QUARENI a n d G. T . ZORn,': Nuovo Cimento, 1, 669 (1955).

(4) G. QUARENI a n d G. T . ZORN: Nuo~to Ciroento, 1, 1282 (1955).

(5) M. V. K . APPA I1AO, R . I~. DANIEL

a m t K . A. NEJ,;LAKANTAN: Prom Ind. Aead. Sci. , 43, 181 (1956).

56 • ]l Nuovo Cimcnto.

874 P. :K. ADITYA

b a t e to secondary neu t ra l in terac t ions in the region under inves t iga t ion . On account of the secondary Pr0eesses oc- curr ing in the uppe rmos t layers of the a tmosphere , i t seems reasonable to as- sunle t h a t some fract ion of the high- energy in te rac t ions in i t i a ted by singly charged par t ic les in the s t ra tosphere m a y in fact be due to deuterons or t r i tons (*). Similar ly as for mu l t i p ly charged pri- m a r y events , the nucleon whieh does n o t pa r t i c ipa t e in the p r i m a r y coll ision is l ikely to produce secondary interactions. The caleula t ion of this eontr i- bu t ion is no t s t ra igh t forward and so we shall no t enter into more detai l here.

As to process ii), the nucleons t h a t have pa r t i c ipa ted in the p r imary collision can produce secondary in terac t ions only if they appear in the angular in- t e r v a l defined by the scanned volume. A n u m b e r of factors, such as the na tu re of the pr in lary and t a rge t nuclei invo lved in t he collision, inelas t ic i ty of the interact ion, and pr imary energy de te rmine this probabi l i ty . In the first approxi- mat ion , le t us consider for example an elast ic nue leon-nueleon collision. At re- la t iv is t ic velocities, t he angle between the two depar t ing nucleons is given by 2y~/(~ - - 1) < tg 0 < oo, where ),~ is re- l a ted to t he ve loc i ty fi~ of the e.m. sys tem by the re la t ion 7,.--[1--fl~] -~-. (I t m a y be seen t h a t t he fac tor 2yd(y~-- 1) reduces in the non-re la t iv is t ic ease to ~ 4/W, where W is the kinet ie energy of the nucleon in t e rms of its rest mass, so t h a t the angle 0 is a lways about 90 ~, as is well known). The m i n i m u m angle be tween the two nucleons is ~ 2/7 ~, so t h a t b o t h

(*) I n s u c h a e a s e t h e s t r i p p e d off n u c l e o n

w o u l d p r o c e e d ~ i_ thout d e v i g t i o n or loss of e n e r g y , so t h a t i f i t i n t e r a c t e d , t h e s e c o n d i n t e r - a c t i o n w o u l d h a v e s i m i l a r c h a r a c t e r i s t i c s as t h e f i r s t e v e n t . A n e v e n t of t h i s t y p e o b s e r v e d i n a n e a r l i e r w o r k (~) l e d u s t o s o m e i n t e r e s t i n g c o n s ! u s i o n s , w h i c h we sha l l d e s c r i b e s e p a r a t e l y w h i l e c o n s i d e r i n g t h e p r o b a b i l i t y of t h e p r e s e n c e of d e u t e r o n s a n d t r i t o n s in t h e s t r a t o s p h e r e .

the nucleons will only rare ly appear to- ge ther wi th in the nar row core. I t also means tha t , if one of the nueleons makes an angle be tween 1/yc and zero, the o ther nucleon will appear correspondingly between angles f rom 1/7 c and 90 ° • In ac tual Draetiee, the collisions are no lon- ger elastic, bu t sinee at ve ry high energies the p r imary par t ie le does no t lose more than a small f rac t ion of its energy in meson product ion, t he l ikel ihood of t he p r imary nucleon appear ing in the nar row cone of half-angle 1/y c is ve ry high. Oil the same grounds, the s t ruek nucleon of the t a rge t is not l ikely to appear in the scanned vo lume unless there are mul t ip l e collisions. If one makes fu r the r the reasonable assump- t ion t h a t in half of the cases t he interact ing nucleon would suffer a, charge exchange, then both , pro tons undergoing charge exchange and neut rons which leave the in terac t ion af ter suffering only energy loss, would con t r ibu te to secondary neu t ra l interact ions.

Concluding t h a t t he nucleons f rom the pro jec t i le (whether or not they have par t ic ipa ted in the p r imary collision) can cont r ibu te to secondary interact ions, let us look at t he da t a of BmSBOUT et al. O) for which some exper imen ta l details are avai lable. 9 neut ra l int.eractions were observed while fol lowing 166.2em of axial l eng th along showers produced by singly charged par t ic les and 82.1 cm of the shower axis for ~-particle stars. In the same region, 36 charged in teract ions were also observed. If i t is assumed a) t h a t one neu t ron is present, for a f ract ion F of the length 166.2 era, b) t h a t two neut rons are present along 82.1 era, and c) t h a t the in terac t ion mean free p a t h of the neu t ron is the same as t h a t of the proton, i.e., 2~= 34 era, one finds t h a t even for / ~ = 0.5 (which corre- sponds to the presence of an exehange neu t ron in half of the cases and takes no account of the possible cont r ibut ion of neut rons resul t ing f rom heav ie r singly charged primaries) 7.3 in terac t ions out

ON ' I H E P O S S I B I L I T Y OF N E U T R O N S P R O D U C I N G S E C O N D A R Y I N T E R A C T I O N S E T C . ~ 7 5

of the 9 can be at tr ibuted to neutrons, thereby reducing the proportion of x-particles to about 5 °/o of the shower particles. This value may further be modified if account is taken of the possibility of deuteron and triton primaries. In view of the linfited statistics such detailed considerations may not be meaningful, but it appears that the proportion of x-particles determined from the ratio of neutral to charged secondary interactions is highly sensitive to the presence of nucleons amongst the shower particles.

Some of the arguments presented here are based upon an earlier work (6) done at the Panjab University, Chandigarh, India.

Thanks are due Professor B. M. ANAND for encouragement and to the Government of India, Department of Atomic Energy, for financial assistance.

(6) p . KUMAR: Proc. 454h Ind. Sci. Cong., I I I - 3 , A b s . n . 9, Jan. 1958.

The author is indebted to Professor B. PETERS for the facilities afforded at the Tara Inst i tute of Fundamental Research, Bombay, and for many stimulating dis- cussions at the Insti tute for Theoretical Physics in Copenhagen. I t is a pleasure to thank Professor NIELS BOHR for the hospitality of this Insti tute.

Note added in proof.

Since this paper was written, the results of an investigation by LOHRMANN and TECCUE~ (Pl*ys. Rev., 112, 587 (1958)) have come to our attention. Amongst secondary particles produced at all average energy of ~ l01'~ eV, they obtained the ratio of interactions produced by neutral to charged particles as (16~6)% . Their procedure of cor- recting for the presence of nucleons has been different from ours, and has yielded

~9 +s~°/ for the proportion of a value of ~,-6//o strange particles and anti-particles among charged secondary products. This result is in agreement with our present considerations.

On the possibility of neutrons producing secondary interactions in high energy showers

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