Primary cosmic radiation and extensive air showers

IL NUOVO CIMENT0 VoL XXI I , N. 4 16 Novembre 1961

Primary Cosmic Radiation and Extensive Air Showers.

B. PETE]~S

Institute /or Theoretical Physics, University oJ Cope~d~age~ - Cope~t, hage~t.

(ricevuto il 19 Agosto 1961)

Summary. - - The hypothesis, that separate sources of cosmic ray partieles of widely differing strength predominate in different energy regions, has been examined. In particular the following questions are discussed: Can such separate sources dominate neighbouring energy intervals of the primary particle spectrum without introducing appreciable changes in slope or discontinuities in the size-frequency distribution of air showers ? Can such separate eontributions, if they exist, nevertheless be distin- guished experimentally with existing techniques? Do available data on extensive air showers provide evidence for or against the hypothesis? It appears that , if such separate sources existed and even if they differed in strength b.y factors as large as thousa~nd, no significant departure from smoothness in the size-frequency relation of air showers would occur, provided only that all chemical components in the primary radiation have identical spectra when expressed in terms of the m~gnetic rigidity of the particles or energy per nucleon, and provided further that the chemical composition of the accelerated particle beam does not deviate too radically from its composition at lower energies. While under these conditions even an infinitly sharp cut-off in rigidity of the particles supplied by the stronger of the contributing sources will not produce a significant disturbance in the size frequency spectrum of air showers, it will nevertheless produce discontinuities and irregularities in the dependence of certain other shower parameters on shower size.--Irreg- ulm~ities which so far have found no adequate plauMble explanation have been reported by various investigators at a shower size corresponding to a primary energy of about 10 ~5 eV. Each of these observations seems to support the hypothesis that a rather sharp rigidity cut-off occurs in the source which supplies most cosmic ray particles below this energy. Additional measurable irregularities can he predicted which have, however, not yet been diseovered.--The considerations leading to this hypothesis emphasize the important role which the complexity of the chemical composition of primary cosmic radiation must play~ in the interpretation of air shower phenomena. In view of the resulting complexity in the origin of showers of a given size, it is suggested that a classification of

P R I M A R Y COSMIC R A D I A T I O N ANt) E X T E N S I V E AIR SftOVCERS ~ 0 ]

~ir showers according to the maximum energy of the nuelea,r-active par- tides in the axis may be more relevant to an understanding of the various underlying nuclear and electromagnetic processes than the customary classification on which is based the totaI number of shower particles.

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

One of the most remarkable features of cosmic radiat ion is presented by the apparent ly smooth and uniform variat ion of particle number with energy

over a very large energy range. This fact is usually expressed by the state- ment tha t a power law with an almost constant exponent represents the energy distribution adequately over nine or even ten orders of magnitude.

This is not easy to understand. I f it were strictly true. it would seem to

lead to either of the following conclusions about the sources which contr ibute cosmic ray particles observed in our neighbourhood:

a) One single source dominates all others and gives rise to particles whose energy follows a power spectrum over the entire energy range.

b) Several or m a n y sources contribute comparable amounts over the major port ion of this energy range. I n tha t case the sources mus t have pre- cisely the same energy spectra for their contributions to be comparable bo th at the high and at the low energy end.

e) The bulk of the particles in different and restricted energy intervals

is contr ibuted by different sets of sources. I n tha t case the aggregate s t rength of the various sets mus t be very accurately adjusted in order to insure tha t the number of cosmic ray particles decreases smoothly with a power of the energy over m a n y orders of magnitude.

A theory of the origin of cosmic radiat ion like tha t proposed by FEa~I , in which particles are accelerated th roughout galactic space, corresponds essen-

tially to ease a) and smoothness and uniformity in the energy spectrmn could be expected, t Iowever, this part icular featm'e of Ferrules theory, namely acce-

leration throughout the galactic volmne, has generally been abandoned after

the composition of the pr imary radiat ion and the physical conditions in the interstellar space had become bet ter known.

If one accepts instead the hypothesis tha t a substantial fraction o~ cosmic rays originate in or near some specific stellar objeeL as Li. Novae or Super-

novae, then one approaches case b) or c). I t would be surprising if these various sources contr ibuted nuclei with the same energy spectra, the more so since historic supernovae which have been identified~ like the Crab and Cassiopeia~ A,

8 0 2 B. PETERS

have different radio spectra and therefore are known to contain relat ivist ic electrons whose energy distr ibut ions are quite different f rom each other.

I n the th i rd case, e), a near ly perfec t correlat ion m u s t exist over a very wide range be tween the n u m b e r and s t rength of accelerators and the part icle

energy a t which their ma in ou tpu t occurs. I t is difficult to believe t h a t ei ther condit ion b) or e) could be satisfied wi th

grea t accuracy over the entire range of observable cosmic r a y energies. Thus, if careful examina t ion of the in tens i ty of the cosmic radia t ion as a func t ion of energy should reveal no significant localized depar tures f rom a power law, it would seem difficult to avoid the conclusion t h a t case a) prevails , n a m e l y t ha t a single source of particles dominates the cosmic r a y flux in our tinge

and our region of space. Bu t before such a conclusion can be accepted, i t is of g rea t impor t ance to

establ ish whether or not there is any indicat ion in the p r i m a r y spec t rum which points towards contr ibut ions f rom several different sources. I t has general ly been argued t h a t the absence of m a r k e d discontinuit ies in the par t ic le flux in the la t i tude-sensi t ive energy region and in the air shower region provides strong evidence against the presence of distinct, recognizable p r i m a r y cosmic ray sources domina t ing different pa r t s of the spec t rum. This a rgumen t would be val id if cosmic rad ia t ion consisted of one k ind of particles only, f.i. of p ro tons only. I f a complex radia t ion like t h a t which arr ives a t the ear th were subject to a cut-off, and another , much weaker source cont r ibu ted the bulk of part icles above this cut-off, the differential s ize-frequency spec t rum of Mr showers f.i. would not show any gap; for the cut-off would occur a t a critical magnetic rigidity; the energy a t which the cut-off takes place will then be higher, the higher the a tomic weight of the p r i m a r y nuclei. Thus a cut-off in a complex spec t rum can never be sharp as long as the quant i t ies observed are funct ions of p r i m a r y energy. The energy region in the p r i m a r y spec t rum which is affected b y such a cut-off in r ig idi ty will ex tend over a t least a f ac to r th i r ty , i.e. the energy ra t io be tween iron nuclei and protons which h a v e equal radii of curva tu re in inters tel lar magne t i c fields. A fac tor t h i r t y in energy corresponds to a fac tor of order 5000 in intensi ty . Another , m u c h weaker source could therefore cut in, in such a way t h a t the differential s ize-frequency spec t rum for air showers does not exhibi t a break, bu t only a d iscont inui ty in slope, while the in tegral s ize-frequency spec t rum remains a lmost smooth .

Nevertheless, one predicts ve ry m a r k e d observable effects, when the pri- m a r y radiat ion, coming f rom a source which dominates observat ions a t lower energy, approaches such a critical magne t ic r igidity. Such observable effects are discussed in this paper . There seems to be considerable, though not ye t conclusive, exper imenta l evidence in f avour of a t least one b reak in the p r i m a r y spect rum, name ly a t a magne t ic r igidi ty corresponding to t h a t of protons

wi th abou t 10 ~5 eV.

PRI)IARY COSMIC RADIATION AND EXTENSIVE AIR SHOWERS 803

2. - Observable effects produced by a primary rigidity cut-off.

I n order to exhibi t clearly the par t icu lar effects which a sharp cut-off in m~gnet ic r igidi ty of p r i m a r y part icles will have on observable quant i t ies in the air shower region~ we app rox ima te the charge composi t ion of the p r i m a r y rad ia t ion b y a somewhat smoothed-ou t dependence of flux on a power of the a tomic weight A in the range AH~<~A <~ AFo. (A represen ta t ion of the charge spect rum, which th roughou t varies inversely as the cube of the mass n u m b e r A~ gives a good approx ima t ion to the ac tua l composi t ion in the emntsion region (which extends up to abou t 10 ~ eV)~ as long as one is not in teres ted in the finer details of the dis t r ibut ion of e lements bu t only in the relat ive in tens i ty

of groups of elements.) (*) The differential n u m b e r spec t rum of p r i m a r y part icles n(e, A ) d s d A can

be wr i t t en

n ( s , A ) - Ao+3e~.I ~ for A n < ~ A - < . A r ~ and e<e~, (1)

= 0 , for s > s ~ ,

where No is some constant . A more accura te representa t ion m u s t t ake into account t h a t p resumably

deu te r ium and atte, just as Li, Be, and B are rare in the p r i m a r y rad ia t ion and also t h a t the cut-off energy per nucleon is twice as high for p ro tons as for the other elements. Wi th these refinements,

F0 (1') n(e, A) = s-:~

r . r . o

r~~ -~d c3a.1 , A~

0

W for e < e~,~

AG+I

f o r g c < g < 2 e c ,

for s > 2s~.

Here ~ is the Kronecker symbol, and

1 , for A c < ~ A < ~ A F o ,

W = 0, otherwise.

r . and r~o have the numerical values 0.t-7 and 0.45, respect ively, and are re la ted to the f ract ion of protons and s-part ic les in the p r i m a r y b e a m at cons tan t energy per nueleon~ b y

= A-~ __ A-~ 15 ~r~ A~ ~ H ~e ~ 1~

r A . o = . o - - c ~ - - 18"

(*) See Appendix.

804 B. PETERS

In order to t r ans form the p r i m a r y spec t rum into a size-frequency spec t rum for ah' showers, one usual ly expresses the to ta l n u m b e r 32 of shower particles on the ea r th ' s surface in te rms of the energy and mass of the p r i m a r y b y

(2) A t= v A e ~ ,

where v, ~ are constants . The size-frequency spec t rum is ob ta ined b y insert ing the va lue of e f rom

eq. (2) into eq. (1) or (1') and in tegra t ing over the allowed range in mass numbers A. One obtains

(3) n ~ , ~ ( N ) = x - ~ . . . . . . . . . P ~ y

where 2g M = A_r._IV 1 = vAroe~.

Depending on whether one uses the p r i m a r y spect ra of eq. (1) or (1') one obtains (using the symbol p = g - - ( y / e ) )

(3a) P~,:, =

Or

(3b) Po, v =

[A~ - - 1] , 1 I< ' ; l P N- - - 1 ,

for N < N a ,

for N~ <~ N <~ ST~,

A~.~\~;/ ,AZ, j ~- 1 for ~v< yo,

A,e ~a-\~FJF~ / _] @ ~ \ m e / 1 , for Nc~Sr<JAHe)F1,

1 [(AFo~ ~ 1[ for AI~eAVI<2V<AogVI,

k[ere N ~ = v ( 2 s ~ ) ~' represents the cut-off shower size for protons. The average value (F (N)} of an observable quant i ty , xv, which depends

on the energy per nucleon e and the n u m b e r A of nucleons composing the

p r i m a r y particle, as

is given b y

~'=Ai(e)

PIglMAF.Y COSh~IC R A D I A T I O N AND E X T E N S I V E AIR SHOW2]RS 8 0 5

If one approximates /~ by

(4) F = Aer

one finds

(5)

Observables of the type F which, for a given energy per nucleon, depend l inear ly on the number of nucleons composing the p r imary particle, are for instance:

the number of secondary particles of a given type, at a given al t i tude, in a given energy interval, a t a given distance f rom the shower axis, or making' given angles with the shower axis.

The average value (G(N)} of an observable G, which is i ndependen t of the number of nucleons composing the pr imary part icle and which can be up- proximated by

(6)

is given by

(7)

G = ef ~

Observables of type G are f.i.:

shower age, lateral distribution, energy spectra of secondary particles, in tensi ty ratios between various types of secondary particles in different

parts of the shower, etc.

The observables quantit ies represented by expressions of the type illus- t r a t e d by eqs. (3), (5) or (7) exhibit a change in slope at the shower sizes corresponding to the cut-off value for protons ( N = N ~ ) and /or e-particles ( N = 4N1). The absence or ra r i ty of deuter ium and 3tte, und of Li, Be, and B, which is implicit in the assumed pr imary spectrum of eq. (1'), gives fur thermore rise to small discontinuities at these values of shower size.

The differential shower-size spectrum based on a sharp cut-off in magnetic r igidi ty is shown in Fig. 1. The curve is drawn for an assumed exponent , 7, of the pr imary energy spectrum 7 - 1.65. The exponent ~, which charac-

5 t - II Nuovo Cimento.

8 0 6 B. PETERS

t e r izes t he c h e m i c a l d i s t r i b u t i o n s of e l e m e n t s in t h e p r i m a r y cosmic r a d i a -

t ion , ha s been t a k e n as a = 2, i.e. t h e v a l u e a p p r o p r i a t e for energ ies u p t o

10 3

10 2

10

~ 10 -2

~ 10-3

~ 10 -5 k.

"~ lO-S t,. ca

~ 1co ~

10""

10 -g i

10" 10 7 10 s

'nuiiis due to cut-off Fe

10 s 10 6 Number of shower perticles N Fig. 1. - The curve represents the differential size distribution of air showers a t mountain al t i tude in a rb i t ra ry units. This distr ibution results from a pr imary radiation which has: 1) the same chemical composition as tha t observed in nuclear emulsions; 2) an energy spectrum proport ional to E-r with y = 1.65; 3) a sharp cut-off at a magnetic rigidity corresponding to proton s with about 10 ~5 eV. The discontinuities in the curve correspond to an assumed deficiency of 21~[, 3He, Li, Be and B in the pr imary beam.

~-~101~ eV. T h e p a r a m e t e r ~ w h i c h c h a r a c t e r i z e s t h e d e p e n d e n c e of a i r - show e r

size on p r i m a r y e n e r g y (eq. (2)) is u s u a l l y a s s u m e d to l ie b e t w e e n 1.0 a n d 1.2.

I n d r a w i n g F ig . 1, we h a v e chosen ~ = 1 . 1 .

F ig . 2 shows t h e i n t e g r a l shower - s i ze s p e c t r u m u s i n g t h e s ame p a r a m e t e r s .

I t i l l u s t r a t e s t h e f a c t t h a t a quite s m o o t h s p e c t r u m is o b t a i n e d e v e n in t h e

e x t r e m e case w h e n on ly two sources , d i f fer ing b y a f a c t o r 1000 in i n t e n s i t y ,

c o n t r i b u t e to t h e p a r t i c l e f lux a n d w h e n t h e s t r o n g e r of t h e t w o sources h a s

a n i n f i n i t e l y s h a r p cut -off a t a p a r t i c u l a r m a g n e t i c r i g i d i t y .

P R I M A R Y (~OSMIC I~ADIATION AND EXT~iNS]VE A I R S H O W E R S ~ 0 7

F i g . 3 shows t h e b e h a v i o u r of o b s e r v a b l e s of t y p e ( /~) a n d ( G ) as a f u n c t i o n

of shower size in t h e c r i t i c a l reg ion . T h e cu rves are d r a w n for v a r i o u s v a l u e s

of t h e p a r a m e t e r fi w h i c h c h a r a c t e r i z e s t h e d e p e n d e n c e of t h e o b s e r v a b l e s

on t h e e n e r g y of t h e i n c i d e n t nuc l eons a n d a re b a s e d on t h e s i m p l e r of t h e

t w o ve r s ions of t h e p r i m a r y s p e c t r u m (eq. (1)).

10 J

102} - ! Discontinuities due to cut-off

1 P He Fe

s

&

s

- . , , \ u ~ 10 -5 ~ ~ ~

", 10-s

10 -7

E 10-8

10 -~ ' ' 'o 10 ~ I0 S 10 6 1 7 i0 b

Number of shower particles N

Fig. 2. - Curve I represents the integral size-frequency distr ibution of a.ir showers, corresponding to the differential distr ibution of Fig. 1. Curve I I i 'eprescnts the distri- but ion contr ibuted by a hypothet ical and different source with the following prop- erties: 1) an energy spectrum proport ional to E-Y with y = 1 . 5 ; 2) an energy ou tpu t which is one thousand times smaller than tha t of source no. 1; 3) a cut-off which lies much higher than tha t of source no. 1. The solid line represents the combined effect

of the two sources.

The m o s t i m p o r t a n t conc lus ions w h i c h can be d r a w n f rom t h e cu rves a n d

u n d e r l y i n g c o n s i d e r a t i o n s a r e t h e fo l lowing :

a) D i s c o n t i n u i t i e s in s lope occur in t h e f r e q u e n c y of a i r showers a n d

in t h e d e p e n d e n c e on shower size of a l l o b s e r v a b l e s of t y p e s F a n d G a t t h e

808 B. PETERS

same critical values of shower size. I n the case of the logar i thmic size-h'equency shower curve the slope changes f rom (?/~)d-1 ~ 2 . 5 , which depends on the p r i m a r y energy spec t rum to sd -1 ~ 3 which is character is t ic of the p r i m a r y charge speet rmn. The change in slope, therefore, is not ve ry large.

/ F F end 6 independent of ~ . I

J . ~ J / F

I- y . . . . o / / r Fend 5 proporEono/ to ~fE /

/ /

__< . . . . . . - / s . . . . <F> ~ / / (G>

/ / ....G / F and O proporttbnalto~Atz - . . . . . . . . . " l

J Protons , Iron 10 -z 10 -) 10 o 10 ) 10 2

N/Nc

iFig. 3. - T h e v a r i a t i o n of o b s e r v a b l e q u a n t i t i e s of t y p e tv a n d G is s h o w n as ~ f u n c t i o n

of the number of shower particles for various assumed dependences of these functions on the energy s of primary nucleons. The curves show a break at the shower size at which a sharp magnetic rigidity cut-off in the primary spectrum begins to influence the nature of the showers. Dashed and dotted portions refer to variables of types F

and G, respectively.

b) The behaviour of observables of types F and G above the critical region is well defined for a given dependence on shower size below the cri- t ical region.

e) Beyond the critical shower size, observables of t y p e s / ~ and G behave quite differently f rom each other ; differently f rom wha t one would pred ic t if one assumed t h a t bo th types of observables were s imply funct ions of p r i m a r y par t ic le energy, wi thout taking' into account t h a t t hey Mso depend in specific and dist inct ways on the m a s s of the p r i m a r y part icle. Thus observables of type G decrease in thei r dependence on shower size and become essential ly independent of shower size beyond the crit ical region~ irrespect ive of whe the r they arc slow or fas t va ry ing funct ions of the p r i m a r y nucleon energy~ while ob-

PIr COSMIC R A D I A T I O N AND E X T ~ N S I V ~ A:[I~ 8/JOWElZS 8 0 9

servables of t ype /e increase in thei r dependence on shower size and tend to increase l inearly or somewhat slowlier above the critical va lue (*).

d) I r regular i t ies are in t roduced in the size dependence of shower propert ies b y the gaps in the p r i m a r y charge spec t rum (i.e. the gap due to the p r e sumab ly low abundance of deu te r ium and SHe and the p robab ly equal ly pronounced gap due to the low abundance of elements represented b y the mass numbers 5 < A < l l ) . Fo r instance, the pr imaries responsible for showers with a part icle num ber N > N , should, on the average, have a lower energy per nucleon t h a n those responsible for showers of size N~< N, ; the corresponding air showers should, therefore; show ar a ther ab rup t change in thei r absorpt ion coefficient, zenith ~ angle dependence, and ba romet r i c coefficient.

3. - Evidence for the existence of a rigidity cut-off in the primary spectrum.

The question arises now, whether exper imenta l da ta suppor t or cont rad ic t the existence of a critical air shower size beyond which

a) observables of t ype F become essential ly propor t iona l to shower size, b) observables of type G become independent of shower size, c) the absorpt ion coefficient of the part icles in the shower core shows

a sudden increase, d) the logar i thmic differential s ize-frequency s p e c t r u m of showers suffers

a (probably slight) change of slope.

I f such discontinuities are observed and if t hey occur a t the same shower size, they const i tu te a s t rong a rgumen t in favour of a sharp drop in the p r imary spec t rum at the corresponding magne t ic rigidity.

(*) The m~in features of this behaviour are easily derived if one simplifies eqs. (3), (5) and (7) with the help of the approximation AF,= 56 >> 1. One obta,ins

and

am[ (if fi./~ >-~)

n(N) ~ X -((v'~)+~)

~l (N) ~ N -'+~)

(G} ~ eonstan'

when N <N~

when N > N .

8]0 B. PETERS

D e t a i l e d m e a s u r e m e n t s of t h e v a r i a t i o n of q u a n t i t i e s of t y p e s / ~ a n d G w i t h

s h o w e r size h a v e b e e n cu r r i ed ou t on ly d u r i n g t h e l a s t f ew years~ m o s t l y w i t h

t h e l a rge a i r shower a r r a y in t h e P a m i r m o u n t a i n s a t ~ r e s i d u a l p r e s s u r e

of 650 g / c m ~.

3"1. Observables o] t ype ]~. - T h e n u m b e r of F -mesons wi th energ ies u b o v e

1 GeV w~s f o u n d (~) to d e p e n d on shower size hr as

, t ~C > 1 GeV) ~-- 27 ~176 for i V < 4.105 e l ec t rons

a n d

n ~ ( > 1 GeV) ~ N ~176176 for ~r > ~. 105 e l ec t rons .

The n u m b e r of n u c l e a r - a c t i v e p a r t i c l e s w i t h energ ies a b o v e i GeV was

f o u n d (~) to d e p e n d on shower size N as

n~,.~.(> 1 GeV) ~ N ~

n~.a . (> X GeV) ~ N .

H e r e also t h e d i s c o n t i n u i t y was p l a c e d a t N = 4.105 e lec t rons . (See F ig . 4).

B o t h of t h e s e q u a n t i t i e s a r e of course v a r i n b l e s of Cype F , i.e., for a g i v e n

10 4

.~ 10 ~ ~d {3

-G

10" 10

/2 10 '~ 10 's

Eo (eV)

e n e r g y p e r n u c l e o n of

t h e p r i m a r y , t h e y m u s t

v a r y s t r i c t l y p r o p o r t i o n a l

to t h e n u m b e r of n u c l e o n s

w h i c h c o n s t i t u t e t h e p r i -

Fig. 4. - The number of nuclear-active particles, as given by •IKOLSKIJ et aI, (~), as a function of shower size. The numbers on the abscissa represent pr imary energy in eV, obtained by mult iplying the observed number of shower particles

by 3.109 .

(1) K. N. VAVlLOV, F. ESTIG~EEV and S. I, NIKOLSKiJ: ~UT?~. J~kS 2. Teor. ~'iz., 32, 1319 (1957).

(2) S, I. NIKOLSKIJ, U. N. VAVILOV and V. V. RATOV: Dokl. Akad. Nau~ S S S I L 111, 71 (1956).

PRIMARY COSMIC RADIATION AND EXTENSIVE AIR SHOWERS 811

m a r y part icle. They should, according to our model, become near ly propor- t ional to iV above the critical shower size 27~.

A special case of an observable of t ype F (when fi = 0 in eq. (4)) is the a tomic weight of primaries. The average a tomic weight <A} of the pr imaries , responsible for air showers larger t han N~, should increase with 27. If, as now seems likely, high energy nucleons lose only a minor fract ion of thei r energy in meson producing collisions and a lways emerge as b y far the mos t energetic p roduc t of the interact ion, i t follows t h a t the n u m b e r of ve ry high energy nucleons in the shower core (at moun ta in a l t i tude the energies should lie be tween 10 '2 and 10 ~ eV) const i tu te a measure of the a tomic weight of the p r i m a r y part icle. F r o m the t ransverse m o m e n t a which such nucleons t ransfer to ~-mesons, one can es t imate the scat ter ing angles in inelastic collisions; one concludes t ha t when the p r i m a r y nucleons reach ground they should fall wi thin a few square meters , if their energy s0 a t the top of the a tmosphere exceeded 10 ~ eV. I n an appa ra tus of the type used b y G ~ m o ~ o v et al. (8) and b y NIJ<OLSKIJ and others (4), such p r i m a ry nucleons shouldmani lest them- selves as so-cMled (( cores exhibi t ing s t ruc ture ~. Since, according to our hypothesis, the average a tomic weight of pr imaries , (A>, m u s t increase propor t ional to 27 for 3 / > 27~, we expect a s t rong increase in the p robab i l i ty of observing such , s t ruc ture cores )) when the shower size passes the critical value. Such

behaviour is for instance indicated b y Table I , t aken f rom a pape r b y NI~OLSKtJ et al. (%

TABLE I.

i Shower size

N nuc leon in t h e sho- I i i . . . . . . . . . . . . .

1 . 5 " 10 4 i 2 . 9 - 1 0 r 10 i i 5 - 1 0 ~ 8 i

8 �9 104 6 1 . 5 �9 1 0 5 5

N u m b e r of o b s e r v a t i o n s of a t l eas t one h igh ene rgy

shower axis

N u m b e r of eases whe re two or more nuc leons

axe obse rved

7 2

3.5- 105 6 5 5.8- 105 1 1

/

[ ~30~

J /

(a) N. L. GRmOROV, V. IA. SHESTOPER0V, V. A. SOBLNIA~COV and A. V. PODOUR- S~AIA: ~urn. Eksp. Teor. Fiz., 33, 1099 (1957).

(4) S. I. NIKOLSRIJ a n d A. A. PO~[ANSKIJ: Zurn. ~,ksp. Teo,'. Fiz., 35, 618 (1958); ~ n d ~ l so 0 . D O V Z K E N K O , W . ZATSEPI1% E . ~ [URZINA, S. N I K O L S K I J , I . R O K O B O L S K A Y A

and E. TURKISH: DokI. Akad. Nauk SSSR, 118, 899 (1958).

812 B. e~TEaS

The top curve for the observable of t ype F in Fig. 3 can be in te rpre ted as represent ing <A}, i.e. the average a tomic weight of pr imaries responsible for an ~ir shower, as a funct ion of shower size. ]~elow the cri t ical region, for an air shower spec t rum whose exponent y/~----1.5, i t has the value

P~.v - - 7 . 5 or 9.4

depending on whether one uses eq. (3a) or (3b). For larger showers, i t increases

towards the value <A} = Ave = 56. The cont r ibut ion of var ious groups of e lements below the critical region

can be easily calculated on the basis of the p r i m a r y composi t ion given in the Appendix , val id in the emulsion region which borders on, and even sl ight ly overlaps, the air shower region. Assuming a value y/~ ~-1.5 the re la t ive con- t r ibut ions are

H --~ 49~o

He ---- 24 ~o

C,)7, O , F , = 1 3 %

~e , ~g~ Si = 7~o

F e = 7 %

3"2. Observables of type G. - We now turn to observables of type G, which according to this model should be independent of shower size in the in te rva l N ~ < N < 5 6 N 1 ~ 30iVo, wha teve r thei r behav iour below N----2V~. There are m a n y well-known exper imenta l results which have a bear ing on this question. Especially, the la tera l dis t r ibut ion funct ion and the shower age (var ia t ion of electron n u m b e r wi th al t i tude) are known to be independent of shower size. Also the energy spec t rum of ~-mesons is a quan t i t y of t ype G and is inde- penden t of shower size (5).

However , more refined measuremen t s are expected to show a somewhat more complicated behaviour of the average value of observables beyond N~ because of the large gaps in the chemical abundances be tween A ~ 1 und A ~ 4 and between A = 4 and A ~ 1 2 . As we go to larger showers and pass the critical size 5T~, where the p ro ton contr ibut ion vanishes and the hel ium contr ibut ion becomes dominant , the energy per nucleon suddenly drops b y a factor four f rom 2e~ to �89 B y the t ime we reach s it will h a v e

(5) O. I. DOVZ]IENKO, B. A, •ELOPO and S. I. N1KOLSKIJ: Zurn. J~ksp. Teor. Fiz., 32, 463 (195~).

PRIMARY COSMIC RADIATION AND F~XTENSIVR AIR SHO~ERS ~13

part ial ly recovered and have reached s = e~. I t will then drop again to e~/3-

Once more it will recover and reach a value s=a~ at 2r etc.

On this picture, we expect that the high energy nucleons in the shower

core should be harder, though less munerous, below Nc than they ~re above

JV~ and that therefore the absorption coefficient of particles in a shower core,

when measured with thick absorbers, should show a sudden increase at the

critical shower size ~V~ and then recover partially at N----122(i ~ 6N~.

Fig. 5 shows the result of measurements by IqIKOLSKIJ ~nd P0~A~SK~J (~)

on the absorption of air shower cores by 230 g cm 2 of aluminium and carbon

absorber. The da ta have been interpreted by the authors as showing a significant increase in the absorption coefficient at N ~ 2.105 followed by a part ial

recovery. The discontinuity in abs orp-

tion of shower cores as a function of air shower size should ~lso reveal itself as a discontin- u i ty in the barometr ic coeffi-

cient and the zenith angle distribution. Until those mutua l ly related discontinuities have

been detected, the observations of N I K O L S K I J and I~

which const i tute perhaps the strongest evidence to date for the existence of a magnet ic

r i ~ d i t y cut-off, cannot yet be

considered conclusive.

0.6:

0.~

00.4

0.3

0'2 t

I0':

0.7

Ittt

2 5 10 s 2 5 10 r~ log %

Fig. 5. - Results of NIKOLSKIJ et el. (~) showing the absorption of shower particles by 230 g/cm 2 of carbon plus aluminium as a function of shower size. The ordinate gives the ratio of particles

below a.nd above the absorber.

I t seems, however, worth-while to point out that , if the interpretat ion given

here is correct, such measurements, with only slightly bet ter resolution, could lead to a determination of the relative abundance of elements among primaries in the energy range close to 10 ~ eV nucleon, i .e. an order of magni tude greater

than obtainable with photographic emulsions. One other effect which a hypothet ical magnet ic r igidity cut-off must pro-

duce on an observable of type G should be ment ioned here. A shower size between 2 and 4.10 ~ at mounta in altitude, where all these

discontinuities seem to appear, corresponds approximately to a p r imary proton

energy of E 0 = 2 s c ~ 1 0 1 5 eV. Nucleons of such energy should arrive at 650 g/cm 2 with reduced energy E of order E 0 ( 1 - ~)65o~ where ~ is the frac-

tion of energy transferred to mesons in each collision and 2 the interact ion

814 B. PETERS

mean free path. If one uses A =- 60 g/em ~ and a---- 0.3, one finds E ~ 2-10 x~ eV.

One should then expect that , a l though the size of accompanying air showers keeps on increasing, the energy of nucleons in the shower core does not con-

t inue to increase when this value is reached. The flux of nuclei of energy larger than some value E, when plot ted against the energy E, should show a decrease

in the neighbourhood of 2 .10 ~8 eV, whose sharpness will however be reduced by statistical fluctuations in the average number of inelastic a tmospheric

collisions. Such a. drop has been observed by 1Vfc~zIN+= et aI. (~) who measured the

arrival rate of high energy nuclear-active particles (more than 80 % of which occurred in air showers) as a funct ion of energy. The drop seems to occur a t E~- ].5.1013 eV.

3"3. The size-]reffucucy spectrum o] air showers. - Altogether, the experi-

mental evidence regarding observables of types /~ and G seems to support the existence of a critical magnet ic rigidity in the dominant par t of the pr imary

spectrum at a value which corresponds to a proton of energy 1015 eV and

therefore to a value e~----5.10 ~4 eV. I t is now necessary to discuss whether the observed size-frequency spectrum of air showers is in conflict with such a hypothesis.

At sea level the critical shower size corresponding to the assumed value of ~ is about iV]----7.10 ~ electrons. The same peculiarities which have been observed at mounta in alt i tude should have their counterpar t at sea level at

a somewhat smaller critical shower size. However, experimental data of suf- ficient accuracy are apparent ly not available.

I f there was only one source of pr imary cosmic rays, then the sea level

shower size spectrum should, for all practical purposes, terminate at a size

N~,, = AF~ ~ 1.8' :[ 0 6 electrons.

Evident ly this is not the ease. (See f.i. CLAI~K et al. (7)).

Let us, therefore, suppose tha t a second source exists which has the same or a slightly flatter energy spectrum than the first, .characterized by an exponent Y', and which has a cut-off at a higher magnetic rigidity. Then, as

illustrated in Fig. 2, no break in the differential shower size-frequency spectrum t

needs to occur, unless F. , which is a measure of the intensi ty of this second

source, is smaller than ]a o by a factor of the order of one thousand.

(6) E. M.URZINA, ~. I. NIKOLSKIJ and V. I. JAKOLEV: Z~rn. /~:8~. Teor. Fiz. , 35, 1298 (1958).

(~) G. CLARK, g. EARL, W. KRAUSIIAAR, J . LINSLEY, B. ROSS~ t~n(]_ ~. SCHERB: Suppl. Nuovo Cimento, 8, 623 (1958).

I~RIMAI~Y COSMIC R A D I A T I O N AND E X T E N S I V E AIR S H O W E R S 8 1 5

Thus the differential shower size spec t rum m a y well be continuous and on ly show a change of slope when there are different p r ima ry cosmic r ay sources contr ibut ing to air showers in different size intervals . At the points corresponding to a cut-off, changes in the slope of the integral shower size spec t rum could be quite small. The curves in Fig. 2 i l lustrate su(th a hypo-

thetical si tuation. KULIKOV and KtIRISTIA~NSEN {s) have drawn a t ten t ion to an appa ren t dis-

cont inui ty in the slope of the integral s ize-frequency spec t rum at sea level, which they place a t iV = 8-105 electrons. I t is, however, no t clear as ye t how this is connected with the various discontinuities observed a t moun ta in al t i tude. Apa r t f rom the changes in slope of the size f requency dis tr ibut ion which should occur where the p ro ton componen t of the dominan t source cuts off and again in the region where the p ro ton componen t of a new source becomes dominant , our hypothesis suggests t h a t there should be a general t endency for the size f requency distr ibution of air showers to become f lat ter r a the r than steeper as the shower size increases. For , as long as we re ta in the existence of power laws as a character is t ic fea ture of cosmic r a y accelerators, the source which is un impor t an t a t low energy bu t becomes dominan t a t high energy m u s t have a f lat ter part icle spec t rum than the source which dominates a t lower p r i m a r y energy. Exis t ing measurements on the air shower f requency spec t rum do not contradict this conclusion; ra ther they seem to suppor t it, a l though, within the as ye t considerable s tat is t ical uncertainty~ the observed

f la t tening could well be spurious.

4. - Conc luding remarks .

The hypothesis presented in this pape r emphasizes the i m p o r t a n t role which the complexi ty of the p r i m a r y cosmic radia t ion plays in the in te rpre ta t ion

of air shower data . Observat ions with nuclear emulsions show tha t a t least those pr imaries

which give rise to the smaller air showers (N </105 particles) mus t be com- posed of comparable numbers of nuclei whose a tomic weights (and therefore whose energy per nucleon) differ f rom each other b y large factors. Since the average a tomic weight of pr imaries cont r ibut ing to the smaller showers ought to be close to ( A ) = 9.5, i t is clear t ha t the t radi t ional classification of air showers according to the to ta l num be r of charged particles m a y not be the best suited one for comprehending the under ly ing basic nuclear and electro- magnet ic processes. The (( normal )) shower of size iV is only in abou t half the cases produced b y a nucleon of energy e, and in abou t 7 % of the cases b y 50 nucleons of energy s/50. Thus one should expect , especially near the

(s) G. V. KUHKOV and G. B. KfiRIs'rIA~SEN: ~urm l~ksp. Teor. Fiz., 35, 441 (1958).

816 m e~TERS

core, large differences in the proper t ies of showers of equal , size ,. The inter- p re ta t ion of f luctuat ions of observables in showers of a given size in te rms of f luctuat ions in fundumenta l processes seems ha rd ly possible wi thou t taking this basic cause of f luctuat ions into account .

I n order to arr ive a t a more na tu ra l classification of air showers one could s t a r t f rom the current p ic ture t h a t p r i m a r y nucleons survive the meson producing collisions in the a tmosphere and appea r as the mos t energetic nuclear- act ive part icles in the central area of the shower core. I f this p ic ture is correct , the nuclear-act ive part icles within one me te r f rom the shower axis could serve as a basis for classification. The events could then be classified accord ing to the energy of the mos t energetic of these nuclear-act ive purtieles. Th i s energy is p r e sumab ly re la ted to the energy per nucleon of the incident p r i m a r y and determines all shower proper t ies as well as the dis t r ibut ion of shower part icles except for a scale factor. The number of nuclear-ac t ive part icles of compurable energy close to the axis is p re sumab ly re la ted to the a tomic n u m b e r of the incident p r i m a r y and m a y furnish the scale factor.

Above energies of order 10 ~ to 10 ~5 eV, nuclear emulsion da ta provide no guidance as to the na tu re of primaries. Certain measu remen t s a t m o u n t M n a l t i tude show var ia t ions of shower propert ies with shower size which indicate an increasingly i m p o r t a n t role of h e a v y pr imaries in the energy region be tween 10 ~s and a few t imes 10 ~~ eV. Such a p reponderance of h e a v y nuclei could be in te rpre ted gs a magne t i c r igidi ty cut-off in the source which con t r ibu tes the bu lk of pr imaries below 10 is eV. While exper imentu l evidence in f avour

of this hypothes is is not ye t conclusive, it appears to be fair ly strong. There also seems to exist no difficulty in reconciling the hypothes is wi th all o the r observat ions on extensive air showers which have been repor ted so far.

An abbrev ia t ed version of this coork has been publ ished in the Proceedings ~ o] the Moscow Cosmic Ray Con]erenee, Vo]. V I I I , 157 ( Ju ly 1960). [Consider- at ions of a similar na tu re can also be found in the work of UEDA, Progr. Theor. Phys., 24, 1231 (1960)]. The complete art icle was no t sent for publ icat ion, because m a n y of the quoted exper imenta l results were still controversial a t t h a t t ime: The au thor wants to express his g ra t i t ude to the members of the Air Shower Group of the Tara Ins t i t u t e of Funda - men ta l Research, in par t icular to Dr. B. V. S~EEKA1NTA~, Dr. S. ~%t~.~A~ and Mr. A. S~;B~A~A~IA~ who have pointed out to h im t h a t the sal ient features of the curly exper iments discussed in this p~per are s t rongly suppor ted by more recent and par t ia l ly unpubl ished investigations. Publ i - cation of the manuscr ip t seems, therefore, now appropr ia te . The au thor also would like to express his g ra t i tude to Prof. I t . J . B]~ABEA and Prof. M. G. K. MENON for the hospi ta l i ty ex tended to h im during his recent s tay in Bombay~

P R I M A R Y C O S N [ I C R A D I A T I O N A N D E X T E N S I V E AI I~ S I I O W E R S 817

A P P E N D I X

T h e c o m p o s i t i o n a n d t h e e n e r g y d i s t r i b u t i o n of t h e p r i m a r y cosmi( , r ad i - a t i o n in t h e m a s s i n t e r v a l

1~<A~<56 ,

gr id i n t h e e n e r g y in i n t e r v g l f r o m ~ b o u t 1 .5A G e V to a b o u t 4 5 0 0 G e V , is r e p r e s e n t e d f a i r l y a c c u r a t e l y b y

t70 n(s, A ) ds d A = Ao+le,+l de d A ,

a n d t h e c o r r e s p o n d i n g i n t e g r a l s p e c t r u m

F o (8) JV~.~ . (> s) = yas~ [ A ; ~ - - A ~ ] '

I 'Am.E I I .

[

Energy per Group of nucleon (GeV) [ e lements

I I

H Texas e l l= 4.9 He )~=41 ~ c a = 2 . 6

C, N, 0 , F Z / > I O

Par t i e les /m 2 s sr

calc. obs.

610 57O • 88.5 90 • 9

Referene es

MCDONALD (9}

7.1 7.5 ~ 0.65 APPA RAO et at.(1~ 3.45 2.2 t 0.35

tt 116 115 :c12 ~'[c DONALD (9) He 17.3 18 ~: 2

Guam eu = 16.1

)~=3 ~ s~--8 .3 C, N, O, F 1.38 0.93 ~ .08 JAIN et al. (11) ! Z ~ 1 0 0.68 0.36 :c .06 l ]

s i i=1600 H 0.19 0.29 i 0.07 LAL (1.~) s a = 1600 ' He 0.01 0 .035• 0.025

s i~=4500 H 0.045 0.04 -L 0.015 KA~LOX and s A = 4 500 He 0.002 6 ~ 0.002_: RITSON (la}

(9) F. B. McDONALD: Phys. Rev., 109, 1367 (1958). (10) M. ~r K. APPA RAO, S. BISWAS, R. R. DANIEL, K. A. NJo3ELAKANTAN and

B. PET~nS: Phys. ttev., 110, 751 (1958). (11) p. L. JAIN, E. LO~R~A~'N and M. W. TJ~ucuEg: Phys. I~ev. i15, 654 (1959). (19) D. L~L: P~'oc. Ind. Acad. Sci., 38, 93 (1953). (la) M. F. KA]'LOX and D. 1K. RITSOi, r: Phys. Rev., 88, 386 (1952).

8 1 8 B. P E T E R S

where F0 is a constant, and s is the energy per nucleon including rest mass. This formula does not actually reproduce the detailed chemical compo-

sition but gives a smoothed-out distribution of elements. However, it does represent the various mass groups correctly, provided one uses the following values for the constants:

F 0 : 1 . 7 ' 1 0 ~,

-- 2.0 ,

7 - : 1.40 ,

and expresses s in GeV and X in partieles/m~-s sr. In Table I I , flux values calculated with the help of eq. (8), are compared

with measured values. (<~ H ~> in the Table stands for all elements with mass number 1 < A < 3 ; <~ He >> stands for all elements with mass numbers 4 < A < 11 and includes therefore the elements Li, Be, and B. But hydrogen and helium are without doubt by far the dominant elements in their respective groups.)

The formula representing the spectrum must be slightly modified in the energy range which corresponds to air showers. The size frequency spect rum of air showers has an exponent which varies slowly with size. For showers of N ~ 105 electrons the exponent is y/~ ~ 1.5, which probably corresponds to an exponent for the pr imary spectrum, y ~ 1.65.

A very slowly increasing exponent of the form suggested by C o e c o ~ (~4) could probably represent the pr imary spectrum over the entire range of cosmic ray energies above ~ 1 . 5 A GeV adequately within the existing errors of measurement. This small dependence of exponent on energy has been neg- lected in this paper, since it does not affect the validi ty of the arguments .

The only data on chemical composition which are available in the energy range 10~< E <1015 eV come from the observation of very large meson showers in nuclear emulsions. No accurate tabulat ion has been made; but roughly 50 % of the observed events are due to protons, and among the largest of the observed meson showers the very heavy primaries seem to be dominant.

(14) G. C0CCONI: Suppl. Nuovo Cimento, 8, 560 (1958).

R I A S S U N T 0 (*}

Si esamina l'ipotesi che sorgenti separate di particelle dei raggi eosmici di energie fortemente differenti predominino in differenti regioni di energia. In parbicolare si discutono ]e seguen~i questioni: possono tall sorgenti separate essere predominanti in intervalli di energie dello spettro primario delle particelle adiacenti senza produrre variazioni apprezzabili della pendenza o diseontinuit~ nella distribuzione grandezza- frequenza degli sciami atmosferici? Possono, tuttavia, tall contributi separati, se esistono, essere distil~ti sperimentalmente con le tecniche esistenti ? I dati disponibili sugli sciami

(*) T r a d u z i o n e a e u r a de l la R e d a z i o n e .

P R I M A R Y COSMIC R A D I A T I O N A N D E X T E N S I V E A I R S H O W E E S 819

estesi dell 'aria forniscono prove a favore o contro tale ipotesi? Sembra ehe se tali sorgenti separate esistessero ed anche se differissero in energia per fattori fino a mille, non si dovrebbero avere seostamenti significativi dalla eontinuit~ della relazione grandezza- frequenza degli sciami dell 'aria, purch6 tut t i gli elementi ehimici componenti la radiazione primaria abbiano spettri identiei se espressi in termini della rigidit~ magnetica delle particelle o di energia per nucleone, e pnreh6, inoltre, la eomposizione ehimica del ~aseio di partieelle aeeelerato non si scosti troppo radicalmente dalla sua eomposizione ad energie inferiori. Mentre in tall condizioni anehe un taglio infinitamente netto della iigidit~ delle particelle derivanti dalla pifi forte delle sorgenti agenti non produrr~ un'alterazione signifieativa nello spettro grandezza-frequenza degli seiami atmosferiei, produrr~, tut tavia, diseontinuit~ e irregolarit~ nella dipendenza di alcuni altri parametri dalla grandezza dello seiame. Da vari osservatori sono state riferite irregolaritk per grandezze degli seiami eorlispondenti a un'energia primaria di circa l0 la eV, ehe finora non hanno trovato una spiegazione adeguata. Ognuna di tali osser- vazioni sembr~ sostenere l ' ipotesi ehe un taglio abbastanza netto avvenga nella sorgente ehe fornisce il massimo numero di particelle al disotto di tale energia. Si possono predire ulteriori irregolarit~ misurabili ehe, tut tavia, non sono aneora state osservate. Le eonsiderazioni the conducono a questa ipotesi mettono in evidenza l ' importanza e h e l a eomplessit~ della composizione ehimiea della radiazione eosmica primaria deve avere nell ' interpretazione dei fenomeni degli sciami atmosferici. In vista della com- plessit~ risultante dell 'origine degli scia.mi di una data grandezza si pensa the una elassifieazione degli seiami dell 'aria seeondo la massima energia delle partieelle nuclear- mente att ive giaeenti nell'asse sia pih significativa per la eomprensione dei vari processi nucleari ed elettromagnetiei in atto, della eonsueta elassificazione basata snl numero totale delle particelle dello sei~me.

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Primary cosmic radiation and extensive air showers