8UPPLEMENTO AL VOLUME X X I I I , SERIE X N. 1, 1 9 6 Z

DiEL NUOVO CIMENTO 1o Trimestre

The Chemical Composition of the Primary Cosmic Radiation Above the Earth's Atmosphere.

~ . 1~. DANIEL ~md N. DU~GA:PR.XSAD

Tata Institute o] Eundame~tat Research - Bombay

(ricevuto il 6 Settembre 1961)

Summary. The chemical composition of nuclei heavier than beryllium in the primary cosmic radiation has been studied as a fmlction of atmos- pheric depth between 8 and 40 g/cm 2 by making observations on their tracks recorded in a vertical and a horizontal stack of nuclear emulsions flown from Texas, U.S.A., at an atmospheric depth of 6.6 g/era 2. I t is shown that it is useful and advantageous to divide the H-group of nuclei (which consists of all elements with charge Z ~ 10) into three subgroups: the H1, H 2 and Ha-nuclei comprising charge values 20+28, 16+19 and 10--15 respectively. This division is necessary because (a) of the rarity of the H2-mmlei in the primary radiation; (b) and also in that it helps to keep the mean mass number of all the charge groups (H1,112, Ha, M, L) almost constant with atmospheric depth. Very strong evidence is given to show that the ratio H / M of the number of H-nuclei to the M-nuclei, (C, N, O, F), slowly increases with atmospheric depth between 8 and 40 g/cm~-; the value at the top of the atmosphere is 0.30• The proportion of boron nuclei compared to the S-nuclei ( Z ~ 6) outside the earth's atmosphere has also been obtained; the value is (l 4 • 5)%. From this the ratio L(O)/S(O) is estimated to be 0.244-0.09. The absorption

!

mean free paths A/ of the H1, Ha, H and M-nuclei in air have been found to be 16.3• 54.94-16.2, 54.34-20.6 and 29.7• g/cm 2 respectively. While the absorption mean free path obtained for the M-nuclei agrees well with the values obtained by other workers, the values for the heavy groups are found to be much larger than those o~ other workers. I t is

!

shown that it is extremely likely that An > A~ for atmospheric depths less than 40 g/em 2. The flux of the II~, It3, H, M and boron nuclei at the top of the atmosphere is found to be 0.71• 1.42~-0.14, 2.07• 6.69• and 1.66~=0.58 particles/m2 s sr respectively; the flux of the H2-mlclei is estimated to be ~ 0.11 partieles/m 2 s sr.

TIlE CHEMICAL COMPOSITION OF THE I 'RIMARY COSMIC RADIATION ETC. 8 3

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

In an earlier investigation which was carried out in this labor~tory (1) (hereafter referred to as I), the relative proportion L/S of the number of Li,

Be, B nuclei (the L-group), to the number of nuclei with Z ~ 6 (the S-group)

in the cosmic radiation at balloon alti tude was determined as a funct ion of

the zenith angle using a stack of nuclear emulsions flown from Texas, U.S.A. ;

the ratio L(O)/S(O) corresponding to zero grams of overlying nlatter i.e. at the

top of the atmosphere was obtained by an extr~polation procedure. An at-

tempt was also made to extrapolate to the top of the atmosphere the ratio,

M/H, of the number of M-group nuclei (C, N, O, F nuclei) to the number

of H-group nuclei (with Z ~ 10). In I L(O)/S(O) was estimated to be

0.06 :~ 0.06 and M(O)/S(O) to be 3.45 • 0.65.

Other methods which have been employed to extrapolate these ratios to

the top of the atmosphere, make use of various constants such as interaction

nlean free paths and fragmentat ion parameters for the different groups of

~mclei in air; these constants are obtained in an indirect manner and are subject

to uncertainties. Uncertainties arising from the extrapolation procedures can,

in principle, be reduced to a minimunl by exposing the emulsions under very

little mat te r (~ 3 g/cm ~) in high flying balloons or in space vehicles. Indeed

such at tempts have already been undertaken (2;s). However, in all experi-

ments which have been reported thus far, on the flux of heavy nuclei of the

cosmic radiation except for the two experiments done ver} - recently (~.3) the

detectors have been flown under appreciable amounts of residual atmosphere

(~ 5 g/cm 2) which are not negligible compared to the interaction mean free

paths of the heavy nuclei in air (e.g. 2c~bo. ~ 25 g/cm s and 2~o. ~ 14 g/cm2). Since the earlier experiment reported here (1), a number of investi-

gations (2-~o) have been carried out to determine the ratios L(O)/S(O) and

(~) (~)

(7) V. (1958).

(1) M. V. K. APPA RAO, S. BISWAS, R. R. DANIEL, K. A. NEELAKANTAN a,nd [3. PETEI~S.: Phys. Rev., 110, 751 (1958).

(2) I. J. VAN IIEERDn~ ~ and B. JUDE~: Canad. Journ. Phys., 38, 887 (1960). (3) F. W. 0'DELL, hi. M. SIIAI'IIr ~nd B. STILLER: Prooceedit,gs o] rite Moscow

Cosndc Ray Con]erence, Vol. III , p. 118 (1960). (4) A. ENGLER, M. F. KAPLON and J. KLAI~MANN: Phys. Rev., 112, 597 (1958).

hi. KOSHIBA, G. SCIIULTZ &Ild M. SCHEIN: NUOYO Cimento, 9, 1 (1958). B. T, 0'BrclEN and T. H. NOON: ,u Cime~tto, 4, 1285 (1956).

BISI, R. CESTER, C. M. G.~RELLI and L. TALLONE: Xuovo Cimento, 10, 881

(s) K. KRISTIANSSON, 0. MATHJESEN and B. WALDnSKOG: Arkiv. for Fysik., 17, 455 (1960).

(9) B. WALDESKOG and 0. MATnIESEN: Arkiv. /or Fysit~., 17, 427 (1960). (10) O. MATHIESEN: Arkiv. /or Fysik., i7, 441 (1960). (11) K. KRISTIANSSON, O. h{ATHIESEN and B. WALDESKOG: Arkiv. /or Fysik,,

17, 485 (]960).

8 4 R. R. ] ) A N I E L ~nd N. D U R G A P R A S A D

tt(O)/M(O) at the top of the atmosphere. F rom these i~ is now thought tha t

the value of L(0)/S(0) is finite and less than 0.3; the exact value is still not

very well agreed upon, but the area of controversy regarding this r~tio has

been greatly narrowed down. As for the ratio H(O)/M(O), the value in I

was smaller than that generally thought. In ~n a t tempt to resolve this con- troversy, WADDINGTON (iv) determined the fragmentat ion parameters in emul-

sion for nuclei having 2 0 < . Z < 2 8 , and went on to deduce the corresponding

values in air. From these Ineasurements he infers tha t the r~tio H(O)/M(O)

is 0.38 which is much larger than that given in I.

In the present work an a t tempt h~s been made to estimate the , r a t io

H(O)/M(O) with an aceur~wy higher thma any reported hitherto. In I the

various ratios L/S, M/H, etc., were plotted as functions of atmospheric depth

x g/era '~ ~nd an extrapolation procedure employed to obtain the values ~t ~he

top of the ~tmosphere. The statistical weights a t tached to the values of the

ratios at depths x > 1 5 g/on? were very poor compared to those for depths

x = (8 +12) g/cmL thus introducing rather large errors in the final extra.pol~tions.

The observations reported in I were c~rried out using a vertical st~ek of

emulsions and with this stack it was difficult to get sufficient data on pa.rticles

entering at large zenith angles, i.e. for values of x > 15 g/('m 2. In order to

determine ratios at depths x > 15 g/('m 2, with statistical errors comparable to

those at lower ~tmospherie depths, we have made observations on ~ horizontal

stack flown in the same balloon flight ~s tha t which carried the vertical stack.

By combining the observations m~de on the verti('al and the horizontal st~eks,

uniformly good statistical weights have been obtained throughout the range

of depths investigated; further, since both st~cks were on the same flight,

the data ~re free from temporal variations and have the same ~scent eor- reetions. To account for geomagnetic effects at l~rge zenith ~mgles, ealcula-

tions have been used which take into account the quadrnpole and oetupole

term of the earth 's magnetic field in determining the cut-off energies.

In this investigation we have sub-divided the H-nuclei into three groups:

Hi-group comprising nu(.lei with 20<~Z~<28

H2-group comprising nuclei with 16~<Z< 19

and H,-group comprising nuclei with 10 < Z < 15.

(12) p. S. l"l~1E,t, 1'2. I'. N~;Y and C. ,[. \VaDmN(u Phy,s. Rer., 113, 921 (1959). (la) C. M. GAgI~LLI, B. QU.XSSIATTI and M. VI(;ONE: Nuovo Cime~do, 15, 121 (1960). (1~) O. B. YouN(; and t,'. E. HAJ~VEY: Phys. Rev., 109, 529 (1958). (la) R. E. DaNHgLSON and 1'. S. I,'REIm~: Phys. l?ev., 109, 151 (1958). (1,) C. J, \VA1)D~X,TON : The composition of primary cosmic radiatiott. Prog. in Nuclear

Phys., Vol. 8 (1960). (17) C. J. WADDIN(~TON: Phil. JIag., 5, 311 (1960). (is) R. R. HILLI~Zlt and V. Y. RAJOI'ADHY~;:,S'uppl. Nuovo Cimetdo, 8, 520 (1958). (19) W. P/dSCHEL: Zeits. Yatur., A 13, 80l (1958). (20) y . HIRASU~MA: Nuovo Cimento, 12, I (1959).

THE CI IEMICAL COMPOSITION OF T I l E P R I M A R Y COSMIC R A D I A T I O N ETC. 8 5

This is useful as will be seen later because: a) the H~-nuclei are comparatively

rare and b) by this classification it is possible to keep reasonably constant

the average mass number A for the different groups of nuclei for depths ranging

from 0 to 40 g/crab The results reported in this paper are based on measurements carried out

on a total of 1 202 tracks of particles with Z ) 3 found at atmospheric depths

mostly between 8 g/cm 2 and 40 g/era2; in this number are included the 613 trncks

used for the analysis in I. From these observations we have determined the

absorption mean free paths and primary flux values (and the relative abun-

dnnces) of the B(boron), M, Ui~ H2, Ha and H-nuclei. An a t tempt has been

made to deduce L(0)/S(0) from the values of B(0)/S(0).

Since in this field of work there are still uncertainties re~'arding the depen-

dence of the various parameters on energy, we have, for purposes of comparing

our datn with those of other workers, restricted ourselves to those investi-

g'~tions made ~t a geomagnetic lati tude ~ ~ 41 + o n l y . Earlier accounts of this work are contained in the proceedings of the Cosmic

Ray Symposia (Ahmedabad, March 1960 and Chandigarh~ March 1961).

2. - E x p e r i m e n t a l procedure.

2"1. ~b ' tacks u s e d . - The stacks used in tMs experiment were ttown from

Texas, U.S.A. on February 6th, 1956 and were exposed at a mean ~ltitude

corresponding to 6.6 g/cm 2 of residual atmosphere for a period of 6~ hours.

Two stacks were flown, one suspended vertically (as described in l) and

the second suspended horizontally. The horizontM stack consisted of a

celluloid sheet 3 mm thick of size 8 in. • in. sandwiched between two G-5 emulsion sheets of similar area, each 400 ~zm thick. These m~d the G-5 emul-

sions used in the vertical stack were taken all fronl a single batch and were

processed together; this ensured that the G-5 enmlsions from the two stacks

had the same sensitivity eharacteristics as determined by ionization meas-

urements.

Special care was taken to ensure that the horizontal stack would be truly

horizontal during the flight; the suspension was adjusted before launch such

that the stack was horizontM to all accuracy better than 1 ~ To determine

whether it had remained horizontal at ceiling altitude the direction of motion

of heavy primary particles entering the stack at large zenith nno'les (> 80 ~

u as determined. This was done either from interactions made l)y the heavy

nuclei or from fast ~-rays they produced when traversing the emulsion. All

particles used for this cheek, which had angles > 80 ~ with respect to the

direction perpendicular to the phme of the emulsion, were found to enter the

stack from the ~ top ~> surface and none from below. Using the azimuthal

8 6 R. t~. D A N I E L and N. I ) U R G A P R A S A D

redictions of all these t racks at large zenith angles, it was es t imated tha t the stack was horizontal at ceiling al t i tude to an accuracy be t te r than 5 ~ I t has not been possible to est imate the accuracy of suspension bet ter , because of the absence of t racks at zenith angles )~ 87% We have also studied the az imuthal angle distribution of about 600 heavy p r imary t racks and find no a s y m m e t r y

of significant value. We, therefore, assume tha t the stack was flown hori-

zontally. Ho~ever , in all of the analysis in this invest igation, only t racks

observed at zenith angles less than 80 ~ have been used.

2"2. ,~'electio~ oJ t r a c k s . - The central region of the top enmlsion of the

horizontal stack (>~ 1 cm from the processed edges) was scanned under a total

magnification of • for t racks satisfying the following conditions:

i) the projected length in the emulsion scanned should be ~900 ~zm;

this (.orresponds to ~ zenith angle ~66~

ii) the o'rain densi ty should be greater than tha t corresponding to a

relativistic Be nucleus;

iii) the t rack should be s t raight as determined by a hairline under a

to ta l magnification • (These emulsions had very little general distortion

of magni tude less than 50 covans.)

The t racks were then t raced to the lower emulsion. I t is impor t an t to separate out t racks due to slow particles which might otherwise be erroneously classified as due to heavy nuclei. Since the residual range of even a t r i ton

with ionization corresponding to a relativist ic carbon, (36 • I0), is only 0.5 m m in enmlsion, t racks due to slow singly charged particles will definitely not be included as due to relativist ic nuclei with Z ) 7 . However , for t racks identified

(see Section 2"4) as due to carbon or boron nuclei by 8-ray and gap length ineasurements the following conditions had also to be satisfied to el iminate

contaminat ion by slow singly charged part icles:

i) when it was found possible to t race the t rack to the second enml-

sion, (and this was the case for about 90 ~ of the t racks of boron and carbon

nuclei) the ionization measured in the two emulsions should bc the same within

exper imental errors;

ii) in ('ases where the t rack was not found in the second emulsion (ex-

cept for those events where there was definite evidence for an in teract ion in the celluloid), Coulomb scat tering measurements were made in the first emulsion

and t racks showing scat tering consistent with t ha t of slow singly charged

particles were rejected; only two such t racks due to slow particles which had an ionization corresponding to t ha t of a relativist ic carbon (within statistical

fluctuations) were found in the whole area scanned.

T I l E CHEMICAL COMPOSITION OF TII~'~ P R I M A R Y COSMIC t{,ADIATION ETC. 8 7

Tracks identified by ionization and multiple scattering measurements in

t, he first emulsion as due to boron nuclei and which were not found in the

second emulsion were not included in the analysis in view of the lack of cer-

ta inty of identification by measurements in one emulsion alone. This leads

~o an underest imation of the flux of boron nuclei by about 8 o/. the correction /o

for this is discussed in Section 2"6.

I t can easily be seen that the above selection criteria allow us to select

~racks of relativistic nuclei with Z > 5 without any admixture of slow singly

charged particles.

2'3. Ionization produced by the heavy nuclei at the detector level. - In this

investigation, as also in I, values of charge have been assigned to each selected

track on the basis of ionization measurements alone. Since the nuclei reaching

~he detector at large zenith angles have to traverse large amounts of air it

becomes impor tant to find out whether the ionization losses suffered in air

by nuclei of high charge are appreciable. The crucial thing is whether a nucleus

of the medium group could lose so much energy as to become non-relativistic

and have an ionization at the detector level corresponding to the ionization

of a relativistic nucleus of Z ~ 1 0 , thus resulting in the wrong classification

of ~ nucleus of the medimn group as a heavy nucleus. This has been inves-

tigated in the following two ways:

i) it is now known tha t the calculations given by ALPtIER (21) and

SCHlCE~'rP (~o.) for the geomagnetic cut-off energies as a function of azimuthM

angle for various zenith angles and for various geomagnetic latitudes need

substantial correction, l~ecent measurements of the flux of pr imary protons

as well as heavy nuclei as a function of azimuthal and zenith angles have con-

firmed this (4,~5,2s). SCI~W,~R~z (2~) has made some calculations for the geo-

magnetic lat i tude ~--~ 41 ~ using a dipole approximation for the earth 's mag-

netic field. Recently, however, KELLOGG (*)(~5) has modified these cMcula-

tions; by also taking into account the quadrupole and octupole terms he has

calculated the cut-off energies for g = 41 ~ as a funct ion of zenith angle for

various azimuthal angles. Using these calculations we have constructed the

expected ionization spread for nuclei of charge Z = 8, 9 and 10. The follow-

(21) R. A. AJ.Pnm~: Journ. Geophys. Research., 55, 437 (1950). (22) E. J. ScIIRE.~IP: Phys. Rev., 54, 158 (1938). (23) J. R. WINCKLER and K. A_~I)EI~SO~': Phys. 1~ev.,93, 596 (1954). (24) M. SCHWARTZ: Suppl. Nuovo Cimento, t l , 27 (1959). (*) We are very gratetul to Prof. P. J. KELLOGG of the University of Minnesota

who has kindly made for us these calculations. These calculated values are given in the appendix.

(25) p. j. KELLOGG" Private Communication (See Appendix).

8 8 R. R. D A N I E L a,nd N. D U R G A P R A S A D

ing quantities have been used to obtain this ionization spread: a) the relative

numbers of nuclei of charge 8, 9 and 10 are assumed to be in the ratio of 4 : 1 : 1,

b) the exponent of the integral energy spectrum used is 1.5, c) the entire range

of azimuthal angles has been averaged over, i.e. it is assulned tha t the stack

had no preferred azimuthal orientation in flight and d) the statistical error

involved in the measurement of S-ray density is 10%. The ionization spread

shown in Fig. 1 is for a typical zenith angle 0--70 ~ and ~,.=20 g/era 2. I t can

be seen from Fig. ] tha t if the number of fluorine nuclei is approximately equal

to the number of neon nuclei, as indicated by measurements made by various

workers, then the net change in the number of M and H-nuclei is expected

to be much smaller than the statistical errors involved in our experiment.

Calculations have also been carried out for zenith angles other than 70 ~ and

from these it is seen tha t the conclusions drawn on the basis of Fig. i will

O F 9.5 Ne

150

100 bined

7 _ a

50 ~ - L -,--~ ~:,-.

45 55 65 75 85 95 105 115 125 135 ionizotion Imln

Fig. 1. - C~lculated ioniza,tion distributions ~t detector level using Kellogg's (2~ ca.lculations ~t Z=41 ~ 0=70 ~ ~nd x=20 g/cin-% An ablmdance of ~V0:-/VF:2V~Ve=4: ]: 1

h~s been ~ssuined.

not be essentially altered if we consider tha t the particles hgve to traverse

a total of even 35 g/cm 2 of air corresponding to a zenith angle of 77 ~ (Tracks

observed at zenith angles > 80 ~ corresponding to an atnmspherie depth of

40 g/cm 2 have not been included in any par t of the analysis.)

if) We have also estimated this effect in another way. We selected tracks

of mult iply charged particles, with ionization less than or equal to tha t for

a relativistic li thium nucleus, which result from interactions in the celluloid

of heavy nuclei of Z ~ 8 arriving at zenith angles > 702 ~Ieasurements of

grain densities on all these tracks were made in the lower emulsion of the

horizontal stack. On each t rack about 500 grains were counted. The results

T I I E C I I E M I C A L C O M P O S I T I O N OF T H E P R I M A R Y COSMIC R A D I A T I O N lqYl'C, $9

~re given in Fig. 2. We have also shown in this figure the (~ restricted energy

loss ~> (in terms of its value at the minimum of ionization) estimated from grain

density measurements on stopping ~+-mesons and using the correspondence

between restricted ionization loss and range given by BARKAS and YouNG (26).

The curve shown in Fig. 2 includes only the statistical spread in the grain

's

~4 E

restricted energy loss Imin 3 4 5 6 7 8 9

60 7o groin density

8,0 lOO

Pig. 2. (}rain density distribution for tracks of multiply charged fragments (with ionization ~<9• from heavy nuclei with Z > 8 arriving at zenith angles > 70 ~

density distribution; it is assumed that all ~-partieles have the same mean

grain density value corresponding to 4Io. I t can be seen that the small excess

of tracks on the higher ionization side of the curve (if taken to be statistically

significant) is consistent with what is predicted by the calculations of I(ELLOGG

given in Fig. 1.

F rom these arguments we conclude that the effeet of the ionization energy

loss in the case of particles arriving even at very large zenith angles results

in an apparent increase in the number of H-nnelei by < 5 % and a decrease

in the number of M-nuclei by < 3 ~

2"4. Charge ident i] icat ion. - Three methods of charge determination have

been employed in this investigation:

i) Gap length measurements were used for tracks of particles with

Z ~ 6 . 5 as determined by ordinary 3-ray measurements. In this method the

total gap length per 100 ~m of all gaps > 0.6 Fm was measured. The variation

of gap length as a function of dip angle was studied using tracks from the

(,26) W. H. BARKAS and D. M. YOUN(;: UCRL-2579 (1954).

9 0 R . R . D A N I E L and X. D U R G A P R A S A D

vertical stack which had been assigned definite charges otherwise; suitable

corrections were then made in the case of tracks in the horizontal stack.

ii) Ordinary 8-ray measurements were employed for tracks of particles

with Z < 12; 8-rays with four or more grains were counted in this method.

iii) For tracks of particles with Z > 8 . 5 , as determined from ordinary

8-ray measurements, a ((long S-ray method ~) was employed. In this a reti-

cle with three parallel hairlines each spaced from the next by 2.5 ~m was

used. Under a total magnification • ] 500 the t rack was set along the central

hairline, and long 8-rays tha t were associated with the track, which reached

beyond the outside lines of the reticle were counted. A total of > 8 0 long

8-rays were counted on each track.

In all these methods a number of tracks well identified by ordinary S-ray

and grain densi ty measurements from I were used for charge calibration.

In method iii), the following additional calibration points were used: a) a favourable charge indicating collision of a nucleus breaking up into an oxygen

nucleus and three ~-particles (2V~, = 0 and n s = 0) gave a calibration point at

Z = 14: b) from measurements of long S-rays made on tracks considered in I,

we obtained five tracks at zenith angles < 45 ~ which gave the highest

values of S-ray density; these values were within experimental errors con-

sistent with a single mean value. This mean value was taken to correspond

to tha t of a relativistic iron nucleus. I t was then possible, within experimental

errors, to fit a straight line for long S-rays v s . Z 2 right from values of Z 2 ~ 60

to Z 2 ~ 600.

The procedure adopted, therefore, for charge identification in the hori-

zontal stack was to first make measurements of ordinary 3-rays in the two

emulsions on all t racks (except those due to the very heavy nuclei of Z > 15);

in cases where the t rack could not be traced to the second emulsion, meas-

urements were made only in the top emulsion. On tracks which had S-ray

densities corresponding to a charge value of Z < 6 . 5 , gap length measurements

were made and the particles assigned charge values as obtained therefrom;

for those which showed a value of Z > 8 . 5 , long S-ray measurements were

made.

In order to enable us to assign individual charge values, for the heavy

nuclei obtained in the vertical stack, we made measurements of long 8-r~ys

on all tracks which gave a charge value Z > 8 . 5 from the grain density meas-

urements. I t m ay be remarked tha t in I charges were not assigned to indi-

vidual particles belonging to the heavy group, since for tha t work all tha t was necessary was to classify tracks as being due to H-nuclei.

The observed numbers of nuclei which fall into the various categories al-

ready described arc given in Table I. I t can be seen from this table tha t the

T I l E C H E ~ I I C A L C O I ~ ' [ P O S I T I O N O F T I l E P R I _ ~ A . I ~ Y C O S M I C R A D I A T I O N E T C . 9 1

TABLE L -- Observed charge spectrum as a /unetioJt o/ atmospheric depth. . _ _ . - : = =

Atmospher ic l~Iethod of ! depth g/em 2 identificas B , C N 0 P i H3

i i

3 - r ~ y s 16 55 72 42

g~p length 19 52 77 ! 37

I -I 17.5 5{ean . . . . 53.5 74.5 ! 39.5

8-r~ys 33 41 74 37 l ! : : ] . . . . .

g~p length 32 ' 42 75 36 I

Mean 32.5 41.5 ] 74.5

17.4+20.0 (0=66 .0+69 .3 )

20 .1+25.0 (0~69.3 +73.5)

25.] +40.0 (0 73.5+79.8)

8-rays 16

gap length 27

~fean 21.5

i 36 5 6 32 lO

25 60 i-i--

30.5 .___58 _ _ ,

/ / : (*) H~ (*)

11 8

8_ Y

36.5

5

. . . . I

( * ) ! l [ , a n d I f , m l e h ' i h ! l v c bz~on i d : m t i i i c d b y t h e m e t h o d o f l o n g 8 - r a y s Oil |3-.

~ g r e e m c n t b e t w e e n t h e n u m b e r s o b t a i n e d b y d i f f e r e n t m e t h o d s for t h e s a m e

g r o u p of n u c l e i is q u i t e s a t i s f a c t o r y . T h e m e a n n u m b e r for each g r o u p of n u c l e i

used i n a l l ou r a n a l y s i s is also i n c l u d e d i n t h i s t ab l e . T h e c o m b i n e d c h a r g e

]~ABLE 11. The variation o/ the ratio o/ L-a~clei (Li, Be, B) to S-nuclei (Z~>6) with the sleepness o/ the track /or various zeuith angle intervals obtained in I.

I

Atmospheric depth i l = (1.0+1.5) m m

400 ~xm

(8 + ] 2) g/em 2 0.26 (45/170)

(12 +17) g/em ~ 0.39 (18/46)

> 17 g/cm 2 0.50 (16/32)

:> 8 g/era 2 0 .32•

L/S

l = (1.5 +3.0) mm

400 ~m

0.26 (29/110)

l > 3.0 mm

400 ~m

0.16 (2/12)

0 .53 0.21 (16/30) (5/24)

0 .69 0.60 (13/19) (9/15)

0.37 • 0 .31•

92 R.R. DANIEL and N. DURGAI'RASAD

spectrg obtained~ (using the p r o c e d u r e given in the previous paragrnph)~ for ~ different mean depths of a t m o s p h e r e are given in Fig. 3.

~ IVTJ vertical stack 20 ~ r-I horizontal stack

10 ~]~L (8-12) g/cm 2 (372 trocks)

o ]~.#'////////////////////Y/IWA ~ ~ ~ ~ ~ ~ .... ~ n n . . . . . . . .

I0 . 1 ~ (12-17) g/cm 2 (141 tracks J

~ 10 07.'-20) g/cm 2 (32*20z, tracks)

0 ' ~ " ,J:h.-, ~ ,.'rl n n

10 r ~ J ~ ~.,] (20~'25) g/cm 2 (23.197 tracks)

m . ~ . P ~ ,.It, r e . n.,-,-, n . . . . . . 0

10 d ] ~ (25+40)glcm a (34+155 trocksJ

0

10 >140 g/cm 2 (11+33 trac~s)

Ol 8 1'0 12 14 1~ 18 2'0 2'2 n 2,4 2'6 28 Fig. 3. - The observed charge spectrum o[ 1202 pai'ticles with Z > 3 as a function

of atmospheric depth.

WADDI]NGTON (16) has m~de ~ comparison of the plot of liux ratios against

the a tmospher ic depth which was repor ted in I, with those of other workers

and suggested t ha t in I there migh t have been a systema,tic underes t imat ion

of the M-nuclei at large a tmospher ic depths. This could presunmbly happen

if there is a sys temat ic error in charge es t imat ion which depended on the steepness of the tracks. In Tab le I I we have summar ized the values of the r~tio L/S for various a tmospher i c depths ~s "~ funct ion of the ~teepness of the

tracks. (The observed nmnbers of t racks are given within brackets . ) These

va lues 'were obtained in the earlier exper iment (1). As c~n be seen f rom this table, there is no detect~ble sy s t ema t i c error.

T H E CIIE?*[ICAL C O M P O S I T I O N OF T H E P R I M A R Y COSMIC R A D I A T I O N E T C . 93

2"5. Classi]ication oJ the heavy nuclei. - It is now common pract ice to group cosmic ray heavy nuclei as light nuclei (L-group, Z = 3, 4, 5), med ium nuclei (M-group, Z = 6, 7, 8, 9) and heavy nuclei (H-group, Z>~10). One then ascribes to a group, i, an interact ion mean free pa th }~, f ragmenta t ion paramete rs P~j (which describe the probabi l i ty tha t a nucleus in group i t ransforms into a

lighter nucleus in group j by f ragmenta t ion) and an absorpt ion mean free pa th A~; (A~=,),~/(1--P~)); these quant i t ies are always assumed to be con-

stants, independent of the a tmospher ic depth and are usually considered over

the range of depths x < 5 0 g/era ~ of air. Whils t this is sat isfactory in the

case of the L and M-nuclei (comprising of only few elements in each group),

it need not be so in the case of the H-group which covers elements f rom

Z = 1 0 up to Z = 2 8 . For this reason it appears appropr ia te to divide the H-group into subgroups each of which comprises of only few elements; then the average mass number _4 for each sub-group will not change appreciably

with a tmospher ic depth. Fur the r the respect ive mean free paths of the sub- groups will remain reasonably constant.

The following observat ions can be made regarding the H-nuclei : i) f rom our invest igat ion (see Section 6"3) as also f rom those of others (5,7,~G,~s) it is

found tha t nuclei with Z = 1 6 - - 1 9 are very rare at the top of the a tmos-

Phere; ii) f rom a s tudy of the change of the flux of nuclei with Z = 1 0 . 1 5 ,

Z = 1 6 - - 1 9 and Z>~20 as a hmct ion of x (see Section 5, Fig. 5) it is found

tha t these three groups of nuclei have quite different growth curves. For these reasons we thought it desirable to classify the H-group of nuclei into three

sub-groups H~, H~ and H3 including nuclei with charge values 2 0 . 2 8 ,

1 .6 .19 and 1 0 . 1 5 respectively. This classification of the H-nuclei can be justified f rom the point of view of not only keeping the various paramete rs constant with depth (which is purely an exper imenta l convenience), bu t also from considerations of cosmic ray abundance outside the ear th ' s a tmosphere.

2"6. Corrections.

a) C o r r e c t i o n f o r s c a n n i n g l o s s : As has been s ta ted earlier we

scanned the horizontal stack for particles which exhibi ted an ionization

> 15 t imes tha t of singly charged << m i n i m u m ionizing ~> particles. Since these

data, are to include nuclei with Z > 5 , it is necessary to es t imate the scanning

loss for the various groups of nuclei. In the horizontal s tack the t rack length of a particle in the emulsion is directly a measure of its zenith angle and,

therefore, of the am oun t of air t raversed b y the particle before detect ion;

this is in contras t with the s i tuat ion which applies to the vertical stack.

Since scanning loss depends to some exten t on the length per plate, i t is im- por t an t to determine it, for a given species of nuclei, as a funct ion of the zenith angle. For this purpose, the entire area of 135.1 cm 2 was rescanned

94 R. 1r DANI]~L and N. DURGAPRASAD

b y a second observer. The f inal vulues of s c a n n i n g effieiencies o b t a i n e d are

s u m m a r i z e d in Tab le I I I .

Atmospheric depth

TABLE III . Corrected charge s3oect~m as a /uqt(tivn o/ ai'qno,~lJhe~ic del~h.

-i H~ ~ Description B C ! N 0 F H 2 H~

Observed number 18.5 5 .5 74.5 , 11 8

(17.4+20.0) g/cm ~

(20.1 +25.0) g/em 2

(25.1 + 4 0 . 0 ) g/era ~-

Scanning efficiency %

Loss due to nuclear inter- action %

Corrected number of par- ticles entering the stack

Observed number

Scanning efficiency %

Loss dne to nuclear inter- action %

I

95 95 98.8

6.8 0.8

5 .8 7 .0

i

32.5 41.5 74.5

96 99.5 100

1.0

Corrected number of par- titles entering the stack

Observed number I 2].5

Scanning efficiency %

Loss due to nuclear inter- action %

Corrected number of par- ticles entering the stack

100

1.0

i

39.9 l

75.3 37.0

30.5 58.0 30.0

100 100 100

1 . 3 1 . 4 ] .6

i

30.9 58.8 30.5

100 100 E - - [ - -

1.1 1.3

1] .1 8.1

8 4 I

I r I i

[ 8.1

1~ L I 100 I 100

b) C o r r e c t i o n f o r l o s s b y i n t e r a c t i o n : Accord ing to the selec-

t ion cr i ter ia descr ibed in S e c t i o n 1"2 i t is r equ i red t h a t the bo r on nuc le i h a v e

t r ave r sed the two e m u l s i o n s a n d the cel luloid sheet w i t h o u t i n t e r ac t ing , whereas

all heav ie r nuc le i need h a v e t r ave r s ed only the top emuls ion w i t h o u t in te r -

act ing. The correct ions for t h e di f ferent groups which arise as a resu l t of these

cr i ter ia are also shown in T ab le H I as ~ f u n c t i o n of zen i th angle. These cor-

rec t ions were ca lcula ted u s i n g the i n t e r a c t i o n m e a n free pa ths g iven in Sec-

t i on 3.

TIIF CttEMICAL COMPOSITION OF THE PRIMARY COS_~IIC RADIATION ETC. 95

The corrections which have been employed in the case of the tracks con-

sidered in I are the same as given therein.

2"7. Results . - A total are~ of 135.1 em ~ was scanned in the horizontal

stack and 589 tracks due to p~rtieles with Z>~5 were obtained. The corrected

numbers of nuclei falling into the various groups are given in Table I I I

~s a function of zenith angle. We also included in the ensuing anMysis 613

trucks due to particles of Z>~3, obtained from an area of 170.0 em ~ in the

verticM stack. The charge speetr~ obtained by measurements on the total of

l 202 tracks are shown in Fig. 3 as a function of ~tmospheric depth. These

histograms clearly demonstrate the t ransformation in the charge spectrmn

which occurs as the radiation passes through the atmosphere.

3. - Calculated interaction mean free paths of heavy nuclei in air, emulsion and

celluloid.

I t h~s Mways been difficult to estimate the interaction mean free paths

for the various types of nuclei in uir. This is mainly because of insufficient

knowledge regarding the effective nuclear sizes of nuclei including that of

hydrogen. The radius of a nucleus of m~ss number A is usually written ~s

R = r o ' A ~ ; ro is given to be between 1.05.10 -13 cm and 1.25.10 -~'~ cm from

electron scattering experiments (27,~s), work on mesic X-rays (29) and from work

on nuclear interactions (30,3~). I t is also known that this kind of relation

does not strictly hold for very light nuclei (A < 10).

3"1. Heavy nucleus - heavy nucleus collisions. - In the very e~rly investigations

by BRADT ~nd PETERS (82) Oil the nuclear interactions of heuvy nuclei, when

the experimentM results indicated ~ value r o = ] . 4 5 . 1 0 -~8 cm, it was found

necessary to ~ssume a certain geometric overlap between the incoming and

target nuclei to explain the l~rge observed interaction mean free puths. Ac-

cording to these authors one c~n then write for the inelastic cross-section the

relation

(1) a = n ( R ~ + R j - - 2z lR) ~ ,

(27) R. HOFSTADTEI% B. HAHN, A. W. KNUDSEN and J. A. Me INTYRE: Phys. Rev., 95, 512 (1954).

(2s) R. HOFSTADTER: A~t~. Rev. o] Nucl. Science, Vol. 7 (1958). (29) V. L. FITCII and J. RAINWATER: Phys. Rev., 92, 789 (1955). (30) M. V. K . APPA RAO, R . R . DANIEL and K. A. NEELAKANTAN: Proc. Ind.

Acad. Sci., 43, 181 (1956). (a~) F. F. CI~EN, C. P. LEAVITT ~nd A. M. SlfAPIRO: Phys. Rev., 99, 857 (1955). ('~) H. L. BRADT and B. PETEaS: Phys. Rev., 77, 54 (1950).

96 1~. R. DANIFL and x. DURGAPRASAD

where R~ and Rj a rc t he rad i i of the two nuc le i o b t a i n e d f rom the r e l a t i o n

R = 1 . 4 5 . 1 0 - ~ a . A ~ a n d A R is a cons t an t . U s i n g the i r o b s e r v e d vMues of t h e

i n t e r a c t i o n m e a n free p a t h s (2) for t he va r i ous g roups of nuclei in b ra s s a n d

glass , t h e v a l u e of d R was e s t i m a t e d to be 0.85. I t shou ld be no t ed , howeve r ,

t h a t t he )~ va lue s in t he i r i n v e s t i g a t i o n were def ined as t hose c o r r e s p o n d i n g

to col l is ions i n v o l v i n g a loss of charge > 2. S u b s e q u e n t to th is w o r k b y BRADT

a n d PETEICS, t h e i r p r o c e d u r e has been w i d e l y used b y m a n y workers .

H o w e v e r , s ince i t is now k n o w n t h a t ro is a p p r e c i a b l y sma l l e r t h a n

1 .45 .10 -~a cm, i t wil l be more cor rec t to use a v a l u e of ro (cons i s ten t w i t h t h e

o t h e r a v a i l a b l e e x p e r i m e n t a l va lues) , which can p r e d i c t i n t e r a c t i o n m e a n free

p a t h s for h e a v y n u c l e u s - h e a v y nuc leus coll is ions, in good a g r e e m e n t w i t h t h e

o b s e r v e d values~ b u t w i t h o u t t he neces s i t y of us ing a n y over l ap . I t has been

f o u n d t h a t to fi t t he ca l cu l a t ed va lues to t h e o b s e r v e d va lue s of 2 w i t h o u t

us ing a n y o v e r l a p , t he v a l u e of r0 is 1 .17 .10 - l a c m ; th is va lue is c o n s i s t e n t

w i t h e x p e r i m e n t a l va lues o b t a i n e d for i t f r om e x p e r i m e n t s of e l ec t ron sca t -

t e r ing , music X - r a y s and nuc l ea r i n t e r a c t i o n s . The o b s e r v e d va lues of A as

also those c a l c u l a t e d us ing ro - - 1 . 1 7 . 1 0 - la cm, a n d b y us ing the ove r l a p m o d e l

a re g iven in T a b l e IV.

TABLE IV. Interaction rncat~ /rue patl, s ()~ in g/em 2) of heavy nuclei in air. emulsion and

1 0 . 8

14.1

Group

B

M

celluloid.

r o 1.17.10-1s cm

Air

26.0

23.9

I Overlap model Experimental va,1-

! in emulsion lies Emulsion Celluloid Air Emulsion

H a 24.0 19.8

!

54.2 24.2 I 30.4 I

50.0 21.9 27.1

41.8

H 2 ! 37.0 17.0 36.1

! H 1 51.0 14.9 ~ 31.5

17.9 21.2

15.0 17.6

]2.9 15.0

56.0

51.9• (aa) 50.9 51.6~3.8 (as)

!

41.3

34.5

30.0 32.0• (16) 33 .3 i2 .5 (a~)

3"2. Proton coll isions. - R e g a r d i n g t h e effect ive size of t he p r o t o n for t he se

i n t e r a c t i o n s t h e r e is also dif f icul ty . E l e c t r o n s c a t t e r i n g e x p e r i m e n t s i n d i c a t e a

v a l u e of ~- ,0 .8 .10 - la cm, whi le t he v a l u e of ( 2 5 + 3 0 ) m b for the p r o t o n - p r o t o n

i ne l a s t i c c ross - sec t ion i n d i c a t e s an ro,-- ( 0 . 4 + 0 . 5 ) - 1 0 - l a c m (if one uses a geo-

m e t r i c p i c t u r e as is t he case in h e a v y nuclei) . H o w e v e r , s ince in our exper i -

' ] ' I IF CI IEMICAL COMPOSITION 0I" T I l E PRI) , [ARY COSMIC R A D I A T I O N E T C . 9 7

m e n t we ( ,onsider on ly h e a v y n u c l e u s - p r o t o n col l is ions we h a v e m a d e use of

t h e m e a s u r e m e n t s of Chen et al. (3z) wh ich dea l w i th t he c ross -sec t ions for

p r o t o n s i n t e r a c t i n g w i th d i f fe ren t t a r g e t nuclei . A s m o o t h cu rve has been

d r awn , as has been done b y IIAJOrA])J~Y~ a n d WADmNGTO~ (3a).

W e h a v e d e d u c e d the i n t e r a c t i o n m e a n free p a t h s in d i f fe ren t m e d i a as

~ f u n c t i o n of t he m e a n mass n u m b e r .4 of t h e i n c o m i n g g r o u p of nuc le i (for

va lues of A > 1 0 ) us ing t h e p r o c e d u r e given above . These va lue s a re g iven for

ce l lu loid , a i r a n d emuls ion in Fi~'. 4. The curve o b t a i n e d for a i r us ing eq. (1)

5O

40

,~ "~ -~. ~ ~ ( 1 )

Fig. 4. t:he atomic number of the incident particle. Calculated mean free paths : - -

-- air; . - . celhfloid. (1) overlap model(a2); (2) our cMculations. mN(~'TON (]960); F CESTER et al. (1958).

~20 ~ . " - ~ " ~ .

~ . ~ . ~

" ~ . ~ ( 1 ) ~ . (2)

101 , r I J , I I 1 I 10 15 20 25 30 40 5'0 60 70 80 90 100

atomic number of incident particle l n l ;e rac t ion mea.n fl 'ee pa ths in emuls ion, a i r and ce l lu lo id as & f unc t i on of

emulsion ; @) WAD-

is also g iven in th is figm'e. I t can be seen t h a t t he v a l u e of 2 for m e d i u m

nucle i in a i r as d e d u c e d f rom our p r o c e d u r e is sma l l e r t h a n t h a t o b t a i n e d f rom

the rela4:ion due to BRADT and PETERS.

4 . - F r a g m e n t a t i o n p a r a m e t e r s .

The ce l lu lo id shee t s a n d w i c h e d be tween the two emuls ions in t he hor i -

zonta l s t a c k was 3 m m t h i c k and e q u i v M e n t to 0.49 g / e m ~. The c o m p o s i t i o n

(a3) V. Y. ]-{AJOPADHYE and C. J. ~VADDINGTON: Phil. Mag., 3, 19 (1958).

7 - S ' a p p l e m e r d o a l N u o v o ("r en fo .

9 ~ R . R . D A N I E L a l l d N . D U R ( L ~ . P R A S A D

No.

TABL[~ V. Fraqme . ta t io . of heavy nuclei ( Z ~ 6) in celluloid.

S e c o n d a r y Z ~ P r i m a - : Secondaxy Z I , P r i m a - i

r y Z H ! 11I

5 6 7 8 9

10 I I 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3O 31 32 33 34 35 36 37 38 39 4O 41 42 43 44 45 46 47

1 25 2 25 3 25 4 24

24 24 23 22 22 22 21 20 19 19 17 17 16 16 16 15 15 14 14 14 14 14 I4 13 13 t3 13 13 12 12 12 12 12 12 12 12 1] 11 1I l0

9 9 9

L l

16 i 1 12 6 - : 2 21 l 21 - - 18 6 - _ 22 - - 7 - - -

16 ]5 . . . . _ i 9

12 l l - - 4

1 3 i

- - 7

- - - 3

- - 3

- - 5

- - 7

6

- - - - - 3

10 - - 6

- - 7 - -

- - 6 - -

- - 7 - -

- - 7 - -

- - - 4

1 3 1 3 3

2"

2 l ]

1. 1 1 2 1 ]

2 2

1 3 2 2 1 1 1

2

3

1 1

1 4 1

I I x .~(*) ! No. r y Z

48 9 - 4 9 8

50 8 ] 51 8

52 8 2 53 S

--- 54 7 : 5 5 7

- - 5 6 7

57 7 - 5 8 7

- - 5 9 7

60 7 61 7 62 7 63 7

l 6 4 7

- - 6 5 7

66 7 - - 6 7 7

- 6 8 7

- 6 9 7

70 7 - 7 l 7

72 7 73 6 74 6 75 6

- - 76 6 1 7 7 6

78 6 79 6 80 6 81 6 82 6 83 6

3 84 6 5 85 6

86 6 2 87 6 2 88 6 l 8 9 6

- 9 0 6

91 6 - 9 2 6

- - 93 6 94 6

H , 11 L

. . . . . ]

- - - - i - - 2

- - 6

3 - - . . . . . . . 2

- - 1

- - 1

1 - - 5 1

. . . . ]

- - i - - 3

. . . . . 3

- 5 1

5 1

4 - - -

3 - - -

- 2

3

- - 5 3 3

- - - - 2

. . . . . 1

- - 2

- - 2

5 - - - - ]

- - - - - 2

- - - - - 2

- - ' - 2

(*) The efficiency for detection of singly charged satellite tracks is quite low.

n~(*)

3

3

T I I F C I I E M I C A L C O M P O S I T I O N O1' T I I E P R I M A R Y C O S M I C R A I ) I A T I O N E T C . 99

of eelhfloid (C60~N2Hs) is such tha t it resembles air except for tile addit ional hydrogen .atoms present . I t has been cus tomary in emulsion work to deduce

the f ragmenta t ion constants applicable to the collisions of heavy nuclei with air nuclei f rom those collisions made by heavy nuclei with nuclei of the emul- sion in which the num ber of heavy prongs N~,< 7. I t can be seen tha t in this

selection of interactions, produced by the average cosmic ray heavy nuclei,

the M-nuclei, the relat ive proport ion of ta rge t nuclei belonging to the heavy

emulsion elements, (Ag, Br, I), the med ium emulsion elements, (C, N, O),

and hydrogen are approx ima te ly 30%, 50(}/o and 20~ respect ively; in cel-

luloid the relat ive proport ions of interact ions in C, N, O nuclei and in hydrogen 0 / are about 90(}~o and 10/o respectively. Thus it can be seen that. the frag-

mentat ion parmneters deduced f rom interact ions in celluloid should apply to

the ease of collisions in air be t te r than those deduced f rom interact ions in

emulsion s. F rom our regular scan we obta ined a to ta l of 42 interact ions in celluloid

produced by nuclei with Z~>6. We, therefore, carried out an addit ional

scan, in areas not included in the regular scan, for t racks of particles with

Z ) 6 . All t racks found here which possessed directions such tha t they could

be followed in the lower emulsion were selected. Those e~ses in which there was evidence for f ragmenta t ion in the celluloid or a visible reduction in the

ionization in going from the upper to the lower emulsion were scrutinized care-

fully and necessary measurements made on the t racks of the p r imary and f ragment particles. Of the events which showed only a reduction in ionization in the lower emulsion wi thout any accompanyin~ �9 << satellite ~> t racks due t~o relat ivist ic singly charged or mul t ip ly char a'ed particles, only those which

showed a chantse of ionization equivalent to a loss of char~'e of three or more in the case of the H-group of nuclei and of two or more in the case of the M-group were accepted as events due to f ragmenta t ion . A to ta l of 94 ex-

amples of f ragmenta t ion of nuclei with Z > 6 in celluloid were obtained. A

List of these events is given in Table V. Since events in which the p r imary pa.rticle suffers a charge degradation

..~2 will be often missed, in this exper iment we have made an a t t e m p t to es t imate the num ber of such events. Using the interaet ion mean free pa ths calculated for celluloid in the previous section and the observed tota l t rack

length in celluloid for the various groups of nuclei, the nmnber of interact ions

expected in celluloid for each group was est imated. The observed ~nd expected aumbers of interact ions for the H~, H2, H3 and M-groups of nuclei are found

l~o be 12, 9, 23, 50 and 16, 9, 21 and 47 respectively. I t is thus found tha t

within exper imenta l uncertaint ies the observed numbers are equal to the

expected nmnbers . The difficulty here, as can be seen e~sily, is poor statis- l~ics. In Table VI, we have given the f ragmenta t ion paramete rs for the H, ,

H~, H3 and M-nuclei c~leulated from the observed interact ions in celluloid.

] 0 0 1 1 . R . D A N I E L and x . D U R G A P 1 " ~ A S A D

T h e n u m b e r s g iv en in b r a c k e t s a re t h e o b s e r v e d n u m b e r s of i n t e r a c t i o n s on

which the corresponding values of P~j are based.

As can be seen from Table VI the number of interactions obtained in eel-

hlloid is not sufficient to deduce accurate values of the fragmentqtion constants.

T A B I , E V ] .

.1: Fragmentation parameters i*t celluloid (lhe 'numbers show~ in hracl,:els re]er to the number o/ events observed).

see}h> : . . . . . - : : : - - - - - : - = dary

H 1 He Ha [[2 a H Jl L

l 'rimary

0.25 0.25 0.17 0.42 0.67 l i t

(3) (3) (3) (6) (9)

0.33 0.33 0.:)3 I[,, (3) (3) (3)

0.04 0.04 0.04 0.44 0.20 1.12 lfa

d) (1) (1) (10) (5) (28) i . . . . . . . . . . . . . . . . . . . , . . . . .

ii.2.a , 0.13 0.13 0.31 0.22 1.07 (4) (4) (10) (7) (34)

0.33 1.42 (4) (12)

0.11 0.29 0.86 d ) (2) (6)

I1 0.27 0.34 o.16 1.16 (i21 051 (7) (5~)

][ 0.04 0.26 0.78 (2) (13) (39)

i

B: Fragmentalion parameters derived by lVaddington ]rom those disb~tegratio~s observed in emulsion which have iYh ~ 7.

. . . . . . . . . . . . I - " I ' \ S e c o n - =

" dary i \

i P r i m a r y \ \

H,

H 1 H2, a H i

. . . . . . . . I . . . . . . . . !

0.26• i 0 .36• t

0.62•

M L i

. . . . . l - -

O.11• . 0 .16 •

0 .41• : 0 .20~0 .05 1

1 . 3 4 i 0 . 1 5

1.32~0.18i

i H2, 3 0.15:E0.04

i i H 0.28• 0 .31~0 .04 0 .33+0 .04 I 0.14_s 1 .30• ]

F -I M 0.21•

i

0.19• 0 , 9 3 •

THE CI IEMICAL COMPOSITION OF T I l E I 'RIMARJf CO83IIC :RADIATION ETC. 101

We h~ve included in the same table the values obta ined by WADDINGTOlX (16) by considering only those interact ions with enmlsion nuclei in which Nh~<7.

.X comparison of these two sets of values seems to indicate tha t , within experi-

menta l errors, there is not very much difference between them. However , t>rom observat ions oil the absorpt ion of H-nuclei (see Sections 5 and 6) we

haw~ strong evidence to say t ha t the ~ values shown in Table V I (A) are

very low. Exper iments are now being carried out in this l abora tory to deter- mine the f ragmenta t ion pa ramete r s in graphi te ~dth much be t te r s ta t is t icN weights.

5. - The absorption mean free path of heavy nuclei in air and their flux above the

earth's atmosphere.

In this section we h~ve made an a t t e m p t to es t imate the p r imary flux

w~lues Ji(0) and the absorption mean free pa ths A~ for the w~rious groups of

nuclei f rom the observed intensities a t the detector level. These intensities have been measured as a function of a tmospher ic depth using the angle of arrival of the individual particles. In using this procedure it is necessary to npply eorreetions for geomagnet ic effects at large zenith ~ngles. These cor-

rections haw~ been obta ined from the recent calculations of KELLOGG (2s). ] t is found tha t at zenith angles 50 ~ 70 ~ and 80 ~ the flux is reduced by 4:~o,

17 % and ~1 ~ o respect ively compared to the values one would obtain b y using

al~ all zenith angles the geomagnet ic cut-off values applicable to the ver t ical

direction. The a.bsolute values of J~(0) and A~ obtained here will, in addit ion

l.o statistical errors, be subjeet to any errors in the geomagnet ic corrections used. The absolute values of Ai for the different groups of nuclei are sensitive I o the corrections used a t large zenith angles. However the differences in the magnitudes of A~ for the different groups of nuclei will not be affected in sign liy these corrections.

I t is the usual pract ice of m a n y workers in this field to quote only llux values at the top of the a tmosphere obta ined b y ext rapola t ion procedure and not the observed flux a t flight a l t i tude; comparisons are then made, with flux

values obtained in a similar manner by other workers at near ly the sa.me geo-

magnet ic la t i tude ~ 41 ~ The stat is t ical errors usually a t t ached to the flux

vMues are those corresponding to the numbers of t racks observed. I t mus t

be remarked tha t in these eases the uncerta.inties due to t empora l var ia t ions

and in tile ext rapola t ion procedures adopted are very impor tan t . In addit ion

bhere are uncertaint ies even in the flux values a t the flight a l t i tude which arise

from: a) the zenith angle in terval used for es t imat ing the flux; b) the balloon t ra jec tory ; and c) the t rue thickness of the emulsions a t the t ime of exposure. While the impor tance of the uncer ta in ty arising from a) has been considered

by all workers, b) and e) have usually been ignored. F r o m a consideration

] ( )~ I~. 1~. I)ANIJ~I. bllid N. I ) I ' ICGAPI{ASAI)

of the change of cut-off energy with geomata'netie lat i tude, i t ean be seen tha t at ~ ~ 41 ~ a ehange of 1 ~ in ~, (about 70 miles of drift in the north-south

direction) corresponds to a chang'e of about 8 o~ in the flux of particles. Again

it is known tha t tile avera~'e thickness of a single large emulsion sheet can differ f rom the value indicated by the manufac ture rs by as much as 10%; this will correspond to a ehange of abou t 10% in the flux value. These con-

siderations emphasize the necessity of taking sufficient precaut ions in these

experiments , especially in those where Forbush decreases and t ime var ia t ion

with solar ac t iv i ty are studied.

I f one has a knowledge of the flux values for the different groups of nuclei

as a funct ion of a tmospher ic depth x it will, in principle, be possible to extra-

polate t hem to the top of tile a tmosphere . Whils t the flux of H~-nuclei, the heavies t group, has to decrease exponent ial ly with x, it can be shown

tha t in fact all groups, except H2-nuelei, do va ry almost e.xponentially in the region x = (10- -40)g /e ra 2. I t is, therefore, justifiable to make s t ra ight line fits to the exper imenta l ly observed values for these groups and ex t rapola te

them to the top of the a tmosphere . I t should be noticed t ha t the s t ra ight lines so fit ted will enable us to deduce directly the absorption mean free

pa th , as defined by the relation A ~ = 2 , / ( 1 - P,,), only for the heavies t

nuclei which in our case is the H~-group; for all other groups the quan-

tit ies deduced f rom their respect ive lines, denoted by A'~, are not the con-

vent ional absorpt ion mean free pa ths since there is a feed-in arising from f ragmenta t ions of heavier nuclei; in these cases A'~ will always be larger than A~.

No exper iment has so far been m~de to determine A, and A'~ for va~rious groups of nuclei in air b y making s imultaneous measurements of the vert ical flux under different thicknesses of the a tmosphere. However , a few ,~t- t empt s (~4,15,~.,) have been made by considering the ilux of particles as a function of zenith angle; the amoun t of a tmospher ic depth for any given zenith angle 0 will be given by h/cos 0 where h is the vert ical a tmospher ic depth

in g/em". This method had in the p~st the d isadvantage t ha t one did not

know sufficiently well wha t reduct ion there was in the average flux of par-

tMes arr iving a t zenith angles O > 45 ~ as a result of geomagnet ic effects.

R.ecently KELLOGG (25) has ealeulated the ~eomagnet ie cut-off values as a

funct ion of az imuthal and zenith angles at ~ ~ 41 ~ (San Angelo, Texas, U.S.A.).

These calculations, so far unpublished, are given in the Appendix. Since these calculations are avai lable and are dependable, we have made an a t t e m p t to

use the flux v,~.. depth (by zenith angle) method. We have assumed an integral energy spec t rum of the type N ( > E)~c 1 / (1 . .E ) ~, where E is the kinetic

energy per nucleon in GeV and y - - 1 . 5 . The calculations of KELLOGG have

been used to obtain the corrections for geomagnet ic effects at large zenith angles. The resultin~',~ corrections to the flux amom~t to 170~.o, 17 o/,.o and 30 %

for the angular intervals 66~ ~ , 69~ ~ and 73.50+80 ~ respectively.

THE CHEMICAL COMPOSITION OF TH/t; P R I M A R Y COSMIC R A D I A T I O N ETC, J 0 3

We have fitted s t raight lines to our points by the me thod of least squares

(Fig. 5). The values of A'~ obtained for the Ha, H~, H and M-nuclei with and

2.1:

1.C 0.8

0.6 0.5 0/.

0.3

0.2

2 8.c s "~ 6.C ~5.[ ~. a.C

N 3.C

1% 0.s

0.6 0.5 0Z 0.3

0.2

- - b e s t f i t l ine

10 4'0 20 30 atmospheric depth (g/cm 2 )

Pig. 5. The variation of the flux of H 1, H2, It3, H, M and boron nuclei (corrected for particles entering the stack during the time of ascent) as a function of atmospheric depth. The points at x = 18.6, 22.2 and 30.7 g/cm ~ have been corrected for geomagnetic

effects as stated in the text.

wi thout t i le above ment ioned geomagnet ic corrections are given in Table V I I ;

the corresponding values of the flux at the top of the a tmosphere have also been included in this table. The errors quoted correspond to s tandard de- viations.

t I t is found tha t the value of A~ is the mos t accurate one and is consistent

with the values obtained b y other workers. In spite of the large errors, the

value of A R is significantly larger than A~ and is in contradict ion to the

8

104 R.R. DANIEL and N. DURGAPRASAD

3 ~ A B L E V I I .

l A : Values o] absorption mean ]ree paths (Ai) o/ H1, Ha, H, ~i and boron, nuclei in air

and lheir flux values extrapolated to the top o] the atmosphere. . . . . . . . . . . . . . . . . . . . . . = : ,

Absorption mean h'ee Plux value Ji(0) Nuclei path in air (g/cm 2) I)articles/m" s sr

H1

H3

t6.34- 4.7 0.714-0.23 (~2.6) (0.86)

54.94-16.2 1.42• (27.9) (1.70)

H

3f

54.3i20.6 (27.6)

2.074-0.28 (2.49) i

. . . . . . I

29.74- 2.9 6.69• i (19.4) (8.08)

B

1/2

31.5_+_18.6 (20.3)

B: Derived ]hex values o] light nuclei Jrom the observed ratios.

1.66~=0.58 (2.oJ)

~<o.11

1

Nuclei Flux particles/m e ,~ sr

S = M + H i 8.76• B (from B/S) 1.274-0.56 L (from (Li+Be)/B) ' 2.12-*:0.98

ideas held b y the major i ty of workers in this field who believe, (on the basis

of f ragmenta t ion constants deduced for air f rom observat ion in emulsion),

t ha t A~ is much smaller than AI, ~. Our observat ion is independent of all pos- sible sys temat ic errors except i) wrong identification of particles of charge 8

and 9 as due to H-nuclei at large values of x, because of ionization losses in

air; and ii) the possibil i ty tha t the energy spec t rum of the H-nuclei is f lat ter t han t ha t of the M-nuclei. The effect due to i) has been invest igated in

Section 2"3 and shown to be very small. As for ii), there is so far no evidence

in its favour. We are, therefore, s t rongly of the view tha t A~ eanlmt be

larger than A~ and tha t A~ >~ A'~,. This, therefore, would mean tha t the rat io

H / M will ei ther increase with a tmospher ic depth or at the most remain more or less constant for values of r 4-50 g/era ~-.

TIIE CIIEMICAL CO~IPOSITION OF TIlE PRIMARY CO~51IC RADIATION ETC. 105

In the earlier work of ])ANIELSON et al. (a4) a vahle of : l a - - (41 ~_ 5) g/em" ?

and A~ = (26 _~- .')) g/era 2 was obtained at. a geomagnet ic la t i tude 2,=10% Though

these results are apparen t ly in good agreement with our values, i t cannot be (~onsidered to be meaningful because their method of charge identification involves measurements on steeply dipping t racks and is therefore less reliable.

The measurements based on flat t racks in a more re( 'cnt paper by DANIELSO~N

and t~REIER (~5) seem to favour a value of A~r ~ 22 g/cm 2. However , these

~'esults are based on two different flights, one with a horizontal stack and the

other with a ver t ical stack. ] t is interest ing to note t h a t in this exper iment the rat io H / M , (which is p resumably independent of tempora l wtriations),

is a constant and has a value of about 0.25 for values of x = ( 1 0 + 5 0 ) g/cm:; t

this indicates t ha t A~ ~ A~.

6. - T h e r a t i o s of f l u x v a l u e s .

The absolute llux values a.t the top of the a tmosphere as they are normal ly obtained are subject to a large num ber of uncertaint ies arising f rom extra-

polation procedure, t empora l variat ions, geomagnet ic effects, differences in

flight t rajectories and differences between the t rue and assumed thicknesses of emulsions. Therefore, the flux values obtained by various authors are not direct ly comparable . However , i t is reasonable to expect t ha t for flights made [rom places a t about the same geomagnet ic la t i tude (]~ = 41 ~ in our case) the

ratios of any two groups of nuclei at a given pressure level should be inde- pendent of the uncertaint ies ment ioned above. I t has been shown tha t the growth curves of all groups of nuclei, except the H2-group show an almost exponent ia l decrease wi th depth; the depar ture of l inear i ty in the ]og J~(x)

vs. x plot is smaller t han the exper imenta l errors involved. I t would appear

therefore justifiable to ex t rapola te l inearly to x----0 the s t ra ight lines which

give the dependence of the flux ratios on a tmospher ic depth over the range . c= ( 1 0 + 4 0 ) g / e m 2. Even in the absence of absolute flux va lues~the ratios of the flux values of the different groups of nuclei outside the ear th ' s a tmosphere

have a useful significance for theories of the origin and acceleration of cosmic

radiation.

6'1. The ratio H / M . - F r o m nleasurements made in 1 there was good

indication t lmt the value of H / M increases with x from x---- 0 to x ~ 20 g/cm ~.

(:34) 1~. E . I)ANIEI,~ON, l ' . S. ]~'RIER, J . E. N.~U(;LE a n d E . P. XEY: Phys. l?er., 103, 1075 (1956).

]O(J l~. 1/. D A N I E l , a n d N. DUIIGAPII , ASAI~

I t was then suggested in a qua l i t n t i ve r ammer t h a t beyond x ~ 20 g /cm ~,

this ra t io will s t a r t decreasing'. This su~z~z'estion was made f rom generM con-

s idera t ions t h a t A , , (because of the lar~'e i n t e rva l of cha.rge covered in the

H-group) , will be larger t han A',, for x < 20 g/era ~ a.nd the rea f te r become

0.22

0.18

0.14

0.10

0.4 i

o.21

0.[

0.4

0.2

a/S

I l

H, /H2,H3

H~/H3

o.oc H/M

_ _ _

0.20 - - - - 10 20 30 40

atmospheric depth (g/cm 2)

Fig. 6. - The ratios of H/: l l , I t2 /H a, II1/H2, a and B / S as a function of atmospheric depth. The solid lines are that of least squares fit for our values only. The dashed line (for H / M ) is the diffusion growth curve obtained by "~VADDINGTON (16). • present work; ~ JUDEK et al. (1960); ~ 0~DELL et al. (1960); v \~TADDINGTON (1957); A CEST~R et al. (1957); | KOSttlBA et al. (1958); C, I~'REIt~ el ~l. (1959); [] (~ARELLI

et al. (1959).

T]tE CIIE311CAI. COMPOSITION O1" TIlls; PRIMARY COSMIC RADIATION ETC. 107

smaller than A'.,,. However, other workers in this field believe, (from consi-

derations of f ragmentat ion parameters deduced for air from observations in

emulsion), tha t HIM should decrease with x for all values of x. This aspect

of tile problem has thus far remained controversial. With more data now

~vailable we have made another a t tempt to s tudy the ratio It/M as a func-

tion of x.

We have plotted in Fig. 6 the values of H/M obtained by us as a function

of x and fitted a straight line to these values by the method of least squares.

We have also shown in this figure the values obtained by other authors who

measured this ratio at geomagnetic latitude ~ ~ 41 ~ or dose to it and whose

results are based on 50 or more tracks of M• nuclei. I t is found that these

values based on reasonable statistics agree extremely well with the line fitted

I~o our points. I t is now possible to draw the folloudng conclusions from Fig. 6.

i) There is strong evidence tha t the ratio HIM increases slowly with x;

it is still possible on the present evidenee tha t the ratio H/M is constant with x.

However, it seems extremely unlikely that H/M decreases as fast {~s indicated

by the line due to WaDDI~GTON (17).

ii) There is no indication of the value of H/M decreasing significantly for values of x > 20 g/era ~.

iii) The value of the ratio H/M at the top of the atmosphere is 0.30 •

this is obtained from the extrapolation of the best line fitted to our points.

However, if all the other points shown in the figure are taken into aeeount

then the value at x = 0 g/era 2 will be smaller than 0.3.

I t has been pointed out in the beginning of this paper, tha t any experi-

ment done outside the earth 's atmosphere or very close to the top of it

(< 3 g/cm ~ of atmosphere), involves much less extrapolation to obtain H(O)/M(O) a.nd thus be subject to small systematic errors. The only experiment in this

~:ategory is tha t of VA.X I-IEERDE.N and JUDEK ("), who got their emulsions ex-

posed under 3.2 g/era 2 of air at ~ - -41 ~ . The value obtained by them is

H(O)/M(O) = 0.31 • 0.03 in excellent agreement with our values of 0.30 • 0.02.

These may be compared with the values of 0.38 • 0.51 • 0.39 •

and 0.48 • obtained by WADDINGT0~N (17)~ CESTER et al. (a~), ENGLER

~'t (*l. (4) and KOSHII~:~ et al. (~) respectively using emulsions exposed under

larger amounts of atmosphere and which involve eonsiderab]e extrapolation

t,o the top of the atmosphere using' diffusion equations. We believe that the

significantly large values obtained by the latter authors arise from systematic

errors in the constants used in the diffusion equations.

(35) R . CESTEI'[, A. DI~'BENEDETTI, (:. ~i. (~AblELLI, B. QUASSIATTI, la. TALLONE

and M. Vmo~-Ja: Nuovo Cimeuto, 7, 371 (1958).

r~

[0,S II. R. D A N I E L a n d .',. I )UI / ( ;APRASA1)

6"2. The ratio LImb'. - In I the ratio L/;5' was obtailmd as a function of

~ttmosphcric depth and was then extrapolated to the top of the atmosphere.

A value of 0.06 • wa~ obtained for L(O)/S(O) :ts eolnpared to 0.2--0.3

obtained by the majori ty of other workers. I t may be mentioned here tha t

the individual values of L(x)/N(x) obtained in i for values of x > 1 5 g/era ~

were based on rather poor statistics. Since in the present investigation we

have in addition ~ large sample of tracks of boron nuclei for values of

x - : (17- -40)g /cm ~, we thoug'ht it would be useful to obtain the value of

B(0)/S(0) using' the method of straight line extrapolation and then to deduce

the value of L(O)/S(O) from the knowledge we have of the relative proportion

of Li, Be and B-nuclei at balloon altitudes.

In Fig. 6, we have plotted the experimentally determined ratios B(x)/N(x)

as a function of x. The stra.ight line drawn in this figure represents the best

lit line obtained hy the method of least squares. F rom this we lmve obtained

value of B(0)/N(0)= 0.14 • after makinR' an ascent correction according

to the procedure described in I. We also have shown in Fig. 6 the available

values of B(x)/S(x) obtained by other workers; these agree very well with

tim line corresponding to our observations.

In order to deduce the value of L(O)/S(O) one should know the numbers

of Li and Be nuclei as compared to the J3-nuclei close to the top of the atmos-

phere. For this purpose we made use of the recent im'estigations (~,a,~2) made

with stacks exposed at ~----41 ~ and very closc to the top of the atmosphere

and obtained the ratio (L i • as 83/12~----0.67. From this we estimated

the value of L(O)/S(O) as 0.23 • 0.09. It~ therefore, seems tha t the earlier

w~lue of L(O)/S(O) is rather low and tha t the true w~lue lies proba,bly between

l0 and 30~ the precise value in still to be determined. I t may be emphasized

here tha t these values of L(0)/S(0) refer to ~ = ~fl ~ and do not give us any

information regarding their possible dependence on energy.

6'3. The ratios H.2/H3 a~d H,/(HT+Ha). - We have also a t tempted to esti-

mate the value tt2(0)/H3(0) by the method of linear extrapolation. This is

not strictly correct since we know that the growth cm've for H,,-nuclei deviates

quite appreciably from a straight line. The value of H~(O)/H3(O) thus obta ined

will, therefore, be only an upper limit.

In Fig. 6 the values of H~(x)/Ha(x) are shown as a function of x and from

this we get H~(O)/Hs(O).<.O.08 • This strongly b~clicates that nuclei with Z =~16--19 are absent or almost absent in the primary cosmic radiation.

From a similar procedure we have Mso obtained the extrapolated value

of the ratio H~/(H~+H.~) at the top of the atmosphere and obtain a value of

0.31 • 0.02. I t may be stated that the value obtained by WADDINGTON (17) for this ratio at ]2 g/era 2 is 0.24 in good agreement with the value of 0.23

obtained by us at a corresponding depth.

TI lE CIIEMI( 'AI , COMPOSITION OF T I l E PRIMARY OOSMTO R A D I A T I O N ET('. ]0 ,0

7 . - C o n c l u s i o n s .

Tht, impor tan t (.on('lusions which follow from this h/vesli~'ation are:

1) The H-group as conventhmal]y defined covers too ~'reat a range of charge from Z = 1 0 io 28. ] t is shown tha t it is advantageous to sub-divide I.his into sturdier sub-~'roul)S. We have divided it into H~, H~ am1 H3-nuclei which cover the range of charges Z = 2 0 - - 28, Z = ] 6 - 119 and Z = 1 0 --'. 15

~'espeetively. This procedure is justified because it is found tha t nuclei with

Z - - 1 6 +;19 are ex t remely rare in the p r imary radiation~ it also helps to keep

t~he various paramete rs associated with ea.ch group (such as mean mass m~m-

her A, interact ion mean free pa th )~ 'rod f ragmenta t ion constanis P~) con-

s tant with a tmospher ic depih.

2) The absorpt ion mean free paths A I asso(.iated with the different groups of nuclei have been deduced from the intensities observed at various a tmos- pherie depths (corresponding to different zenith angle intervals) af ter making

(.orreetions for the decreas~ of flux at large zenith angles due to geomagnet ic effects. These corrections were made using some recent calculations of KEL- LOGO (-%) in which quadrupole and octupole te rms of the ear th ' s magneti(t Iield h~ve been taken into account. The values of A'~ obta ined for the H~,

lIa~ H and M-nuclei are 16.3• 54.9-~16.2, 54.3~20.6 and 29 .7~2.9 g/cm ~,

respectively. The valne of .4' for the M-nuclei has the smallest error and is

consistent with the values obtained by other workers. In spite of the large

errors associated with the value of A n it seems ex t remely likely tha t A~z > A'~r. This conclusion will not be al tered by any errors in the geomagnet ic corre(,- tions applied to our observations.

3) We have obl, aincd the pr imary flux for the various groups of nuclei using a s t ra ight line extrapolat ion procedure. The values obtained at the top of the a tmosphere are 0.71 • 0.23~ 1.42 -~ 0.14~ 2.07 • 0.28~ 6.69 • 0.39 and

1.66 • 0.58 par t ic le /m ~ s sr~ for the HI~ Ha, -/~ M and boron nuclei respectively.

(These values have been corrected for particles entering the s tack during ascent

l~inle.) On the basis of the ex t rapola ted value of the rat io H2(O)/Ha(O) it in

es t imated tha t the flux of H2-nuclei at the top of the a tmosphere is ~- 0.11 par-

t icles/m ~ s st.

4) The rat io H/M has been determined as a function of atmospheri(~ depth. These values arc ahnost independent of sys temat ic errors which arise

l'rom geomagnet ic corrections~ temporal variations~ flight trajectories and dif-

ferences between the apparen t and true thicknesses of emulsions. These values �9 ire therefore direct ly comparable with the values obta ined b y other workers.

The various other observed values of the rat io H/M over a range of a tmos-

1 I0 ir 1r 1),',,NIEI, ~lll(I N-. IH3ICGAPICA,qAI)

pher ie d e p t h f rom 3 to 20 t~/('m ~ a~'ree ex( ' e l len t ly with the l ine f i t ted to our

va lues (FIE. 6). W e the re fo re ( 'onelude t h a t t he ra t io H I M s lowly inc reases

with a t m o s p h e r i c d e p t h f rom 0 to 40 tz/em ~. W e o b t a i n for the r a t i o H(O)/M(O)

a va lue 0.30 ~ 0.02 whi( 'h is smal l ( ,ompared with th'~t o b t a i n e d b y o thers .

5) W e have also d e t e r m i n e d t i le r a t i o B(0)/,~'(0) ~l(1 o b t a i n e d a va lue

0..14 ~ 0.05. Us ing then the mean v a l u e of t i le r a l i o (Li ~ Be) /B o b t a i n e d by

FREIER et al. (~2)~ V,~5" HEER])EN ~nd JU])EK (") a n d O'])ELL et al. (a) f rom

s t acks exposed v e r y (.lose to the t op of t he a t m o s p h e r e , the r a t i o L(0) /S(0)

has been e s t i m a t e d to be 0.23-~: 0.09. The r a t i o L(0)/,s'(0) d e d u o e d here is

l a rge r t h a n t h a t o b t a i n e d in i n v e s t i g a t i o n 1. The v~due deduoed in th is p a p e r

is ba sed (m b e t t e r s t a t i s t i c s a t large a t m o s p h e r i c dep ths .

W e would l ike to express our t h a n k s to l)rof. M. G. K. ME.~()~- for go ing

t h r o u g h the m a n u s c r i p t in g r e a t de t a i l and m a k i n g useful sugt~estions. W e

wou ld also l ike to r eco rd our ' t pp r ec i a t i on to l ) r . ( ' . J . ~VADDI~(;TON of Br i s to l

U n i v e r s i t y , for useful d i scuss ions and or i t ic i sms. W e a c k n o w l e d g e wi th t h a n k s

t he t ed ious t a s k of s cann ing and reseanning~' the emuls ions b y Miss F. F. BITE-

SARA, Miss ~. JOSHI and Mrs. T. M. ITPADIIYAY.

AI~ , I ,END FX

Professor P. J . t(ELI,O(~G of the U n i v e r s i t y of M i u , e s o t a , U.S.A. , has k ind ly m a d e for us ca l cu l a t i ons of t he ('ut-of/' r ig id i t i e s for eosmi(, r a y p~r t i c l es in the e a r t h ' s m a g n e t i e field a t a g e o m a g n e t i c l a t i t u d e of ~ = 41~ These ca lcu la - t ions ] lave been m a d e , s i n g the m e t h o d desc r ibed in :l p a p e r b y KELLOe,(~

Azimuthal angle ~/,

0

30 90

150 210 270 300 330

(*) No cu t -of f f o u n d .

Cut-off r igidity in GV

0 = 5 0 ~ 0=70 ~ 0=80 ~ i

- - 6.65 4.05 4.35 5.98 4.05 4.25 (4.21) (*) 4.37 4.25 - - 5.53 6.3.q (7.00) (') 6.06 7.05 20.6

- - I [ . 3 9

5.08 10.20 1.7.5

T H E CIIEMI( 'A[ , ( ' O M P O S I T I O N OF T I l E P R I M A R Y (!()SMIO RADI.XTION ETC. i l l

t~nd SO'HWARTZ (3~) in w h i c h ~ll m o m e n t s of t h e e a r t h ' s m % g n e t i c f ie ld i n c l u d i n g t h e o c t u p o l e t e r m s h a v e b e e n t a k e n i n t o a c c o m l t . T h e s e c a l c u l a t i o n s a r e un- p u b l i s h e d u n d nre g i v e n b e l o w w i t h P ro f . KELLOGC,~8 k i n d p e r m i s s i o n .

C a l e u l ~ t e d c u t - o f f r i g i d i t i e s fo r v a r i o u s z e n i t h ~ngles 0 as a f u n c t i o n of t h e ~ z i m u t h a ] t ingle y, m e a s u r e d w e s t of g e o g r a p h i c N o r t h . Vertie,~] ( 'n t -off ri- g i d i t y : 4.62 GV.

(:~") P. J. KELLOG(; all(I M. SC/I~VARTZ: N?T, OlY~ ('ime~lto, 13. 76] (1959).

I { J A S S I I N T ( ) (;~)

Si 6 st.udia~a la conq)osizione chimica della, radiazione eosmica prima ria ill nuclei pifi pesanti del beri]lio in funzione della profondit,5 a.tmosferic~ fra 8 e 40 g/era'-', osser- vando le tra.cce regis l ra le su una pila. di emulsioni vertieali ed orizzontali f a t t a innal- za.re da.1 Texas, U.S.A., ad una profondit'~, a tmosfer ica di 6.6 g/era 2. Si dimostr~ ehe ~'. vantaggioso dividere il gruppo I t dei mlelei (ehe eonsiste di (ut t i gli elementi con ~'~rica Z ~ 10) in tre so t togruppi : i nuclei Ha, 1t2 ed H3 che eomprendono i valori della eariea 20--28, 1 6 - 1 9 e 10--15, r i spe t t ivamente . Questa divisione b. neeessaria: a) per la rarith, dei nuclei H~ nel]a radiazione pr imar ia ; b) ed a.nehe pereh6 a iuta a ma.ntenere quasi eos tante il numer<) di massa medio (li tu t t i i gruppi di earica (H~, H2, Ita, M, L) al var iare della profondi th a trnosferica. Si danno prove sostan- ziali per d imos t ra re ehe il ral)l)orto H / M fra. il numero di nuclei 1[ ed M (C, N, O, F), ('resce l en tamen te al crescere della profondi t5 atmosferica, h'a 8 e 40 g/<;m2; il valore al sommo del l ' a tmosfera b 0.30d:0.02. Si b a, nche ot tenu~a la. percentuale di nuclei di boro sui nuclei N ( Z ; , 6) fuori de l l ' a tmosfera ter res t re ; questo valore b (14~:5)%. I)a questo si s t ima (.lie il rappor to L(0)/N(0) valga, 0.24:k0.09. Si 6 t rova to ehe i (:ammini liberi medi di assorbimento Ai (lei nuclei H1, H a , H ed M hel l 'ar ia son<) (16.3:k4.7), (54 .9• (54.3:k20.6) e (29.7=[=2.9)g/cm 2, r i spe t t ivamente . Mentre i valori o t tenut i dei cammini l iberi medi di a ssorbimento dei nuclei M concorda, abba- stanza, bene con i valori o t t enu t i da altri autori , si r iscontra che i valori per i gruppi pesanti sono molto maggiori di quelli degli altri autori . Si d imost ra che 6 molto

t probabile che A~ > A i per profondi lh a tmosfer iche inferiori a 40 g/cmL Si 6 t rova to (~he il fiusso di nuclei Hj , H:~, H, M e di boro a.1 sommo del l ' a tmosfera b (0.71• (1.42• (2.07~0.28), (6.69:k0.39) e (1.66-k0.58) par t ice l le /m2.s . s r , r i spet t iva- men te ; si va lu ta ehe il flusso di nuclei H e sin G 0 . l l part ice l le /m: .s . sr .

(*) Traduzione a cara della Redazione.