SUPPLE,mNTO AL VOLUME VIII, SERlE X

DEL ~UOVO CnmNTO

On the Origin of the Charge Spectrumof the Primary Cosmic Radiation ("),

S. F. SINGER

University of Maryland - Oollege Park, Maryland

1. - Introduction.

N. 2, 19582° 'I'rimestre

A fundamental question to ask is the following. Is the charge spectrum ofthe primary cosmic radiation (i.e., at the top of the atmosphere) the sameas the charge spectrum of the original cosmic radiation (i.e., at the point oforigin), or have modifications taken place in the travel between the origin andthe earth.

It is presently most widely held that no modifications, or at any rate veryminor ones, have taken place and that the primary charge spectrum representsessentially the original charge spectrum and also resembles the general abun­dance of elements in the universe [1J. A consequence of this hypothesis isthat the cosmic radiation during its existence cannot have made many eol­lisions with interstellar hydrogen. This means that the lifetime of cosmicrays in the galaxy must have been very short, corresponding to a maximumpath length of 2 g!em2 [2]. The lifetime must be less than 4 million years [3].As a consequence of this hypothesis, therefore, the cosmic rays must escaperapidly from the galaxy, that is, the trapping field cannot be a very efficientone and, as a further consequence, the rate of acceleration of cosmic rays mustbe very rapid to replenish the cosmic rays which escape [2, 3J.

Now this point of view hinges very crucially on the resemblance betweenthe primary charge spectrum and the abundance of elements, but this re­semblance, as we shall show, is quite superficial and can be achieved throughnuclear fragmentations. In order to state the matter quantitatively, we sum-

(*) This work has been supported in part by the Air Force Office of ScientificResearch under Contract AF 18(600)-1038.

:3() - S U}J plemento al ~VllUr() (1 ime 1/to,

550 S. F. SINGER

marize in Table I the present data on cosmic abundances and on the chargespectrum of the primaries above the atmosphere.

TABLE 1. - Data on cosmic abundances, including the primary cosmic radiation(beyond Z = 10, only the most abundant species are listed).

Z

. I

234567

89

1014182026

a bI

C--_._----- ···_·----1

H 4 .1010 12.00

1

1

620He 3 .109 11.06 90Li 100 0.68

L-nucleiBe 20 2.43 ItB 24 [5.0]

3

C 3.5 .106 8.56 I 3 (4)N 6.6 .106 7.98 ~ 2 (I)0 2.15.107 9.00 J 2 (I)F 1600Ne 8.6 .106 8.81 1Si I .106 7.60 I H-nucleiA 1.5 .105 7.7

1 tCa 4.9 .104 6.382.5

Fe 6 .105 6.76 IJ

(a) H. E. Sm;ss and H. C. UREY: lie». Mod. Phys., 28, 53 (1956). (These values are referredto silicon = I' J06).

(b) log N for thc sun, except that for Hc and No wc give their ratios to H for stars(after ALLER).

(c) Vertical cosmic ray flux (in particles per m' sr s) at A= 41 0 [8].

A crucial point in this comparison is the question of the presence or absenceof lithium, beryllium and boron (L-nuclei) in the primary radiation, becausethere the discrepancy is most severe. On the other hand, if the L-nuclei areabsent, then the discrepancy will be less severe. In other words, if the L-nucleiare present, the hypothesis of fragmentation will be greatly enhanced, sinceit is not easy to conceive of a mechanism whereby Li, Be and B exist at thesurface of stars or wherever cosmic rays are initially injected and accelerated.

Now the importance of Li, Be and B was first pointed out and discussedin great detail by BRADT and PETERS in their outstanding series of papersconnected with the discovery of the heavy primaries. However, they inter­preted the data to signify an absence of L-nuclei and therefore adopted thehypothesis of no fragmentations of cosmic rays [1]. The Bristol workers, onthe other hand, who deduced evidence for the presence of Li, Be and B, adoptedan opposite interpretation and were the first to suggest that even a substantialfraction of the protons and alphas could be produced by fragmentation [4.].This line was further developed on the basis of empirical data on productionof various nuclear fragments in collisions between hydrogen and iron; thesedata were taken from the inverse process which occurs when iron meteorites

('p ,)(, 0( »

Li, Be, BFe

ON THE ORIGIN OF THE CHAR'lE SPECTRU~1 OF THE PRDIARY COSMIC RADIATION 551

are bombarded by relativistic hydrogen nuclei. This work led to a calculationand a discussion of the significance of the production of tritium and 3Re infragmentations of heavy primaries in interstellar space. An attempt was alsomade to calculate the charge spectrum which would result from an originalcosmic radiation consisting only of iron [5] (*).

This charge spectrum is shown in Table II.

TABLE II. - Charge spectrum of cosmic rays calculated as a function of pathlength.An initial radiation is assumed composed only of Fe; fragmentation probabilities for« protons » (this includes neutrons and deuterons) and for « alphas ,) (including 3Hand 3He) are obtained empirically from meteorite data; for Li, Be, B from data ofNOON and KAPLON. The mean-free-path for primary iron nuclei in hydrogen is 1.9 gjcm2•

In this calculation we have neglected fragmentations of lighter nuclei since their mfpis considerably longer than 1.9 gjcm2 •

I !Path length 0 }. i 2}' 3). 4}'

-~--~- - ~- -~- 1---:1

- - - - - . ------

o I 400 I I 900 I 2 100 2 160o 276. 378 I 415 430o 63 I 86 95 98

100 37 13 5 2

The agreement with the actually observed charge spectrum is not toogood, but, as was pointed out, it depends very much on what one takes for thefragmentation probabilities for the L-nuclei (Table III).

TABLE III. - Comparison of observed and calculated charge distribution of primaries.

Calculated charge distribution(normalized from Table II)

for path length

Observed primarycharge distribution

(normalized from Table I)at Lat. = 41° 2}. 3}'

H 1000 1000He 145 200

Li, Be, B 5 4510-15 (a) 22-15 (a)

Z;;;.lO 4 6.8

1000200

4522-15 (a)

2.4

(a) Those values were calculated usiug the fragmentation probabilities of Ref, [9].

Since, then, a number of new proposals and data have come into the foreground.

(*) Another way of phrasing the question is: if all of the Li, Be and B is due tofragmentation of heavies, what fraction of the protons and 0( arise in the same frag­mentations?

5ii2 S. F. SINGER

1) Prompted by the apparent success of the explanation of the syn­chrotron radiation from the Crab Nebula [6], HAYAKAWA [7] has again sug­gested a supernova origin for cosmic rays and pointed to the fact that theinjected nuclei would be mostly heavies, since a supernova is thought tocontain a high abundance of heavy nuclei (*).

:2) ::\lany more experiments have now been performed on the primaryradiation in order to measure the energy spectrum and charge spectrum. Thisexperimental evidenee has been analyzed [8] and the flux values for Lat. = 410

are shown in Table III. These data indicate an appreciable abundance ofprimary L-nuelei.

3) Finally, the Bristol group has presented new data on fragmentationprobabilities [9]. While these are based on relatively few stars and have notbeen critically discussed, we shall go ahead and use them, if only to illustratethe great dependenee of our detailed conclusions on such experimental data.It is to be hoped that efforts will be made to check these results and makethem more precise.

2. - Importance of fragmentation probability.

The results of the Bristol workers are given in Table IV and comparedwith results of fragmentation probabilities by other workers. The main im­mediate conclusion is that the fragmentation probabilities are less by a factorof two to three, as compared, for example, with Noox and KAPLON [10] (**).

This result has two immediate consequences: 1) The number of Lvnueleiproduced in fragmentations in interstellars spaee will be reduced by a factorof two to three compared to iX-partieles, and 2) The primary flux of L-nuelei,which is derived normally from extrapolation of balloon data, can now bere-evaluated.

Using the smaller fragmentation probabilities, the primary flux will onlybe slightly less than the flux measured at ba1100n altitudes (which includes

(*) Another method for obtaining a preferential injection of heavy nuclei dependson the acceleration mechanism. If injection takes place from a stream moving witha velocity v, such as a beam of gas shot out from the sun, then those partieles havinga large enough radius of curvature to diffuse into the adjacent turbulent transitionregion mav become accelerated there. Heavy primaries which are not vet fully ionizedwill ha ve a larger radius of curvature than the main gas, which consists of protons.

(**) It is to be notcd that the Bristol results do not refer as ye1 to collisions withhydrogen nuclei. However, there is little difference found in the fragmentation pro­babilities between emulsion nuclei in general, and the light nuclei in the emulsion orperipheral collisions; we will therefore assume that the fragmentation prohahilitv forhydrogen is similarly decreased by a factor of t.wo to three.

ON THE ORW!:'! OF THE CHARGE SPECTRUM OF TilE PRIMARY COS\lIC RADIATION 55:3

a number of Lvnuclei created in fragmentations of heavies in the atmosphereabove the balloon). The result of this correction, as shown in Table III,is a rather good agreement between calculation of a primary spectrum on thebasis of original iron plus fragmentation, and the observed primary spectrum.

TABLE IV. - Data used in calculat-ing primary charge spectrum.

Fragmentation probabilities for L-Nuclei in light nuclei of emulsion(or in air)

(a)(b)

(a)(b)

PFe,L

0.:3:3 ± 0.160.00

PFe",

3.12 ± 0.722.08 ± 0.68

P H . L

0.52 ± 0.080.17 ± 0.07

r«,2.00 ± 0.20

L__~~:3 "".__

(a) 4(b) 8

Fragmentation probabilities for sin~ly and doubly charged nuclei with primary ironOIl hydrogen. Values are derived from nuclear evaporation theory (I') using' adistribution of excitation energies in accord with empirical results from highaltitude emulsion stars (checked by meteorite data) (d). Values shown arerelative; in the calculation they are normalized to the Pve,ex, and P II . , values.

OIl15

1116.2

2I11.1

311.75

311e1.2

(u) Ref. [10].(b) Ref. [9].(c) K. J. LE COUTEUR: Proc. Phys. so«, A 63, 259 (1950).(d) Refs. [6] and [12J.

The relative numbers of neutrons, protons, 2H, 3H, 3He and 4He producedin these fragmentations (*) were obtained by considering the inverse process,namely, the evaporation of a stationary iron nucleus which is struck by acosmic ray proton. We have calculated the frequency of emission of thesefragments, using evaporation theory and checking the applicability of thetheory from experimental results on iron meteorites. It is not safe to useresults from accelerators, as can be seen from the fact that the tritium cross­sections reported [11] are an order of magnitude smaller than those directlyobserved in meteorite samples which have been taken from reeently fallenmeteorites [12]. On the other hand, the fragmentation probabilities for light

(*) It should be noted that the first four species all become primary" protons »

while 3He and 4He will be counted as primary" alphas ».

5.54 S. F. Se,GER

nuclei have been normalized to the proton and ~ values by using the experi­mentally determined ratio in photographic emulsions. In this way it is hopedthat a consistent calculation is produced which is based entirely on empiricalcosmic ray data. Our deuteron-proton ratio, for example, agrees very closelywith that obtained from cosmic ray stars in emulsions [13J, but the triton­deuteron ratio does not agree too well.

3. - Conclusion.

We find that we can account quite well for the observed primary chargedistribution by assuming (quite artificially) a model in which the originalradiation consists only of iron (*). After about three mean free paths (6 gjcm 2

)

a charge distribution is obtained which resembles very much the observedvalues. The good agreement is possible only if one uses results on « p ) and« rx) fragments obtained from meteorite measurements, and if one uses thesmaller fragmentation probabilities obtained by the Bristol group for Li,Be and B.

It is seen that the charge distribution so calculated is much closer to theobserved values than are the cosmic abundance values. In particular, wecan reproduce very much better the large ratio of heavy to medium nuclei,which is of the order of h as compared to the cosmic abundance value of 10-1

•

The existence of an iron peak in the primary cosmic radiation can be explainedmore naturally as the remains of an initial large iron peak than in any otherway. Certain features, such as the C: N: 0 ratio, are more in accord withfragmentation than with natural abundances, but here the evidence is not asconclusive.

Certain crucial tests of the fragmentation hypothesis are necessary andshould be made. They consist principally in a measurement of the Li, Beand B flux above the atmosphere. The definitive absence of the L-nuclei wouldspeak against the fragmentation hypothesis; the presence of the L-nuclei wouldbe in accord with the fragmentation hypothesis, but would only be a neces­sary condition. More subtle measurements would help establish the fragmen­tation hypothesis: these consist of the measurement of the primary deuteronflux and primary 3He and perhaps tritium fluxes. From the results of meteo­rite measurements some numerical values can be given for the fluxes to beexpected, provided they originate from fragmentations (see Table V).

(*) On the other hand GINZBUR(; and FRADKIN [14] consider that they can explainthe primarv charge spectrum without an original enhancement of the heavies; howeverthey use N L :N)I « 0.1 and large values for the relevant fragmentation probabilities.Therefore their conclusion is not surprising.

O~ TIlE ORIGIN OF THE CHARGE SPECTRUM OF THE PRIMARY COSMIC RADIATION 555

TABLE V. - Primaru flux values (at A = 41°) for deuterons, tritons and heliurn-3.Calculated from the data of Table IV under the assumption that all of the (, protons ,)

and « alphas » come from fragmentation of original iron primaries._______==-..7_-_-__ -_._- ._- ..-------_--_-==_:-~:_===~

( 1.1 )2H flux = 15 +6.2+ i.i ·650 = 32 peters,

3H flux = 5·lO-3e peters (*),

3He flux =(_ 0.75 + 1.2_)'90 =41 peters.0.75 + 1.2 + 2.3

(0) Ref. [,i]; because of the short halflife of 'H (~ 12 yrs when nonrelativistie) the nux dependson the gas density in whieh the cosmic rays have spent the preceding few deeades. For an averageinterplanetary gas density of 200 protons/em' the flux would be 1 peter.

REFERENCES

(1] B. PETERS in Progress in Cosmic Ray Physics, vol. 1 (Amsterdam, 1952).(2] P. ;\IORRISON, S. OLBERT and B. ROSSI: Phys. Rev., 94, 440 (1954).[3] B. ROSSI: Suppl. Nuovo Cirnento, 2, 275 (1955).[4] A. D. DAINTON, P. H. FOWLER and D. W. KENT: Phil. Mag., 43, 317 (1952).[5] S. F. SINGER: Proc, of Duke Univ. Cosmic Ray Conf. (Nov. 1953), ed. by

L. Nordheim (1954); S. F. SINGER: Phys. Rev., 98, 1163 (1955) (A).[6] V. L. GINZBURG: Usp. Phys. Nauk, 51,343 (1953); V. L. GINZBURG, S. B. PIKEL'·

~ER and J. S. SKLOVSKI.I: Astron. z«. FlSRR, 32. 503 (1955).