The absorption of high energy cosmic ray photons

Bruin,

M.

Physica XIX 719-728

Clay, J. 1953

THE

ABSORPTION OF HIGH ENERGY COSMIC RAY PHOTONS by M. BRUIN and J. CLAY

Natuurkundig

Lnboratorium

der Universiteit

van Amsterdam,

Nederland

Synopsis Measurements are reported which were performed in order to obtain a value of the absorption coefficient of high energy photons in cosmic radiation. Results are given for photons belonging to the continuous radiation as well as for those found in extensive air showers. The absorbers consisted of paraffin, carbon, aluminium, iron, tin and lead.

Intro&&on. During the last years many measurements have been performed on the absorption in matter of photons having an energy below about 10 MeV. An extensive survey of this work up to 1952 was given by Davisson and Evans(Dl).Thegamma ray sources used to measure absorption coefficients were radium, thorium C”, and artificial radioactive materials. Also photons from nuclear reactions and X-rays have been used. Especially for the low energy range the agreement between theory and experiment proves to be very good. It is well known that when gamma rays pass through matter three effects are important, namely the photoelectric effect, the Compton effect and pair production. Each of these three effects predominates in a particular energy range. When a number N of mono-energetic photons passes through a thin slice dn- of material the change in number dN due to the effects mentioned may be represented by the formulae (AN),,=-

ap,N Ax,

(AN),,=-

a,,N Ax,

(AN),,=-

apnN Ax,

(1)

in which ap,,, ace, and apn are absorption coefficients. The three processes being independent one obtains for the total decrease of the number of photons due to the three effects together (AN) fofal= -

tap,, + a,, + ap,) N Ax. -

719 -

(2);

720 Therefore

M. BRUIN

AND

J. CLAY

it is possible to define a total absorption

coefficient

a = aph + a,, + ap..

(3)

The relation between the number N(o) of incoming N(x) of transmitted photons can thus be written

and the number

N(x) = N(o) e+‘.

(4 As the quantity ax is dimensionless the dimension of a changes according to the units in which x is expressed. Mostly the thickness x is given in cm or gcme2, a thus having the dimension cm-’ or g -’ cm2 respectively. The absorption coefficients for photoelectric effect, Compton effect and pair production are approximately proportional to 24.5, 2 and Z2 (D 1)) 2 being the atomic number. For a few elements the energy range where the absorption through one of the effects predominates is given in table I. Also the energy where the minimum absorption coefficient approximately occurs is mentioned. The minimum occurring in the total absorption coefficient as a function of energy is displaced to lower energies for higher atomic numbers. The energies are expressed in MeV. TABLE

I

Energy range (in MeV) where absorption of photons is mainly due to one of the three absorDtion DrOCeSSeS

carbon aluminium iron tin lead

6 15 26 50 a2

< .03 < .05 < .1 < .2 -=c .5

.03-25 .os-20 .l -10 .2 - a .5 - 6

>25 >20 >I0

>a >6

20 15 7 5 4

In the energy range above 20 MeV only few absorption measurements have been made with gamma rays from accelerated particles produced in the laboratory; e.g. by L a w s o n (Ll) and by D e W i r e et al (D2). In the cosmic radiation many high energy photons are present, in the continuous radiation as well as in extensive air showers. For both cases the photon density has been measured (B 1, B2, B3, C 1, D3, J 1, M 1, M2). However a precise measurement of the number of photons in cosmic radiation is rather difficult due to the fact that these photons are not mono-energetic. Their energy spectrum may

THE

ABSORPTION

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ENERGY

COSMIC

RAY

PHOTONS

721

in good approximation be written as a power-law spectrum, both for the photons in the continuous radiation and for the extensive air shower photon component (B3, C2, Ml). In order to detect gamma quanta one has to make use of their transition effect in some material. The apparatus imposes a low energy cut-off, as particles one counts must have an energy of at least 5 MeV in order to be able to penetrate the walls of ordinarily used glass or metal Geiger counters. This implies that electrons produced through photoelectric effect will not be observable in cosmic radiation measurements. Gamma rays with an energy above 5 MeV are very abundant. At sea-level photons with an energy higher than 1O4MeV will be rare, so the energy range one deals with is roughly between 10 and lo4 MeV. For this range a power-low spectrum appears to hold, i.e. the number of photons with an energy between E and E + dE is proportional to some power of E: N(E) dE = C E-k dE.

(5)

The exponent of this spectrum experimentally proves to have a value of about 1.3 for the photon component of the continuous radiation (C2), whereas it is about 2 for photons in extensive air showers (B2, B3, M 1, M2). Early measurements on the absorption of the photon component of the continuous cosmic radiation at sea-level were performed by J 6 n o s s y and R o s s i (J 1). They used a counter coincidence arrangement in order to separate charged and non-ionizing particles and determined the total absorption coefficient of cosmic ray photons in aluminium, iron and lead. Measurements on this subject were also performed by C 1 a y and L e v e r t (Cl) and later on by C 1 a y and K 1 e i n (C3) who distinguished experimentally between absorption due to Compton effect and pair production. Their absorbers consisted of paraffin, carbon, aluminium, iron, tin and lead. In the present investigation we report the absorption of extensive air shower Photons in the same materials. Experimental arrangement and results. In fig. 1(A) an anticoincidence arrangement is shown which is only slightly different from the one first used by Janossy and Rossi(J1). Clay and K 1 e i n (C3) also used a set-up of this type. The counters in row A are connected in parallel, as well as those Physica

SIX

46

722

M. BRUIN AND J. CLAY

the rows B and C. We assume that coincidences ABC and A-BC are registered (A- denoting the fact that a discharge of B and C is not accompanied by a discharge of A). A coincidence ABC may be interpreted as a charged particle crossing the counters A, B and C, whereas a coincidence A-BC means that a neutral.particle after having passed A produces at least one charged secondary which strikes B and C. When a material is placed in space 2 of fig. 1(A) the rate ABC will decrease due to absorption of charged primaries in this layer. On the other hand, as photons may produce ionizing secondaries, the rate A-BC will rise when only a thin layer of material is placed in space 2. Due to absorption of the charged secondaries in this material this will be followed by a decrease when we increase the layer thickness. The set-up should be shielded at the in

i’

c

Fig. 1. Arrangements for counting cosmic ray photons, (A) of the continuous radiation, (B) in extensive air showers.

sides in order to prevent spurious photon coincidences caused by a charged particle coming in from a slanting direction and missing the anticoincidence counters: The rate A-BC will be too low due to photons accompanied by parent electrons which discharge A. However in measurements on the continuous radiation this will not cause a serious error. If one wants to measure photons belonging to extensive air showers it is necessary to add at least one extension tray at a distance of over 1.5 m in order to select only events due to these showers. However if one would use the set-up of fig. 1(A), one would hardly count any photons at all. The reason for this is, that even for intermediate shower densities the probability will be small that a photon crosses the surface A without being accompanied by an electron which discharges one of the counters A. Therefore if one wants to measure any photons at all one should use a small surface

THE ABSORPTION

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ENERGY

COSMIC RAY PHOTONS

723

of anticoincidence counters. Adisadvantage of this is that the counting rates will be low. A small advantage of extensive air showers is that the particles will only come in from the vertical direction, thus simplifying the discharge probability considerations concerning the geometry of the set-up. It is still desirable to shield the set-up at the sides to prevent B and C being discharged by particles from a direction not purely vertical. In order to detect photons in extensive air showers we used an arrangement which is schematically drawn in fig. 1(B). The surface of the anticoincidence counters A was 250 cm’. Therefore this set-up was roughly speaking sensitive to a photon not accompanied by an electron in an area of 250 cm2. It follows that very dense showers are excluded from registration. The extension tray should be large in order to include as many showers of lower mean density as possible, these events providing the larger contribution to the photon coincidence rate. Events where a photon produces an electron in space 2 which is scattered backward may also discharge the anticoincidence counters A and are excluded from being registered. One may determine the absorption of photons by varying the thickness of a layer of material in space 1. We neglect the effect of an electron producing a photon in the absorber in space 1, which might travel unaccompanied through the anticoincidence counters. Furthermore we ignore the probability of more than one photon striking the absorber simultaneously. Indeed in very dense showers several photons may hit the lead, but the probability is small that these photons would not be accompanied by at least one electron which discharges one of the counters A. When placing a material in space 1 photons may give rise to an electron pair or produce a Compton electron in that material and this electron will discharge the anticoincidence counters A *). Thus the number of coincidences A-BCD will decrease when we increase the layer thickness in space 1. The absorption we then measure may be called ‘real’ absorption, as the photon is no longer detected as soon as it has produced a secondary. For all measurements we used a layer of lead in space 2 having a thickness of .5 cm. We assume that the energy spectrum of the incoming photons may be characterized by a power-law spectrum according to for-*) The influence of the fact that for Compton effect the energy of a photon is not completely lost to an electron in one such process is discussed elsewhere (B3).

M. BRUIN AND J. CLAY

724

mula (5). In its most general form the number of coincidences to be expected per unit time as a function of the thickness of the layer of material in space 1 is R = R, &y P (.5 cm Pb, E) e-@)* E-k dE,

Fig. 2. Absorption Fig. 3. Absorption

(6)

of cosmic ray air shower photons in paraffin, carbon and aluminium. of cosmic ray air shower photons in aluminium, iron, tin and lead.

in which R,is a normalization constant dependent on the time unit chosen, E, is the lower energy cut-off imposed by the apparatus, Pt.5 cm Pb, E) is the probability of a photon producing at least one ionizing secondary in space 2 emerging from the .5 cm thick lead layer, a(E) is the total absorption coefficient for photons of energy E and x is the thickness of the layer of material in space 1. According to Arley (Al) the mean probability of a photon producing at least one ionizing secondary which emerges from .5 cm of lead does not depend greatly on the energy of the photons hitting the lead, and we will assume this value to be constant for the energy range we are dealing with here.

THE ABSORPTION

OF HIGH

ENERGY

725

COSMIC RAY PHOTONS

The values of the coincidence rates A-BCD per hour measured as a function of the layer thickness of different materials in space 1 are given in table II. The probability is very small that a photon traverses 5 cm of lead without undergoing any interaction. We therefore consider this value to be the zero-rate caused by spurious effects. We subtracted the value of the number of coincidences per hour with 5 cm of lead in space 1 from all coincidence rates thus obtaining the corrected coincidence rates per hour. In order to see whether one may derive some kind of absorption coefficient from these figures one may then plot the corrected figures on a logarithmic scale. TABLE Ahsorotion

1

of cosmic rav air shower ohotons in different

material carbon.

.

paraffin

I

.

.

2 6

. . . .

I

thickness (cd

iron.

tin . .

lead

.

. .

. . . .

.

. .

. . . . . .

13

26

50

a2

rate per hour

materials corrected rate per hour

14 28

4.0 f .4 4.2 i .3

4.5 * .2 4.7 * .4 4.1 f .3

4 12 lb

4.5 f .4 4.5 + .2 3.8 * .3 4.2 rt .5

4.4 4.4 3.7 4.3

& * f *

.4 .2 .3 .5

2 5 10 15

3.9 3.3 1.5 1.8

f * * f

3.8 3.2 1.4 1.7

& & j, *

.3 .4 .2 .l

.5 1 2 3 4 5

3.4 2.1 2.0 1.0

f + f *

3.3 2.0 1.9 .9 .46 .32

f

.b

1 2 3 4

2.2

* .3

2.1 .a2 .51 .24

f + k f

.3 .09 .Ob .04

.5 1.0 1.5 2.0 2.5 5.0

2.4 1.3 .a5 .36 .31 .I4

2.3 1.2 .44 .22 .I7 -

& * * * 5 &

.6 .2 .13 .12 .I0 .Ol

0

a

aluminium

II

4.6

& .2

.3 .4 .2 .l

.b .2 .2 .I .bO & .lO .46 i .08

.9b 6 .08 .b5 i .05

.3a j, .03 & .b

f * & * 5

.2 .12 .ll .09 .Ol

* .2 * .2 k.1 * .ll & .09

726

M. BRUIN

AND

J. CLAY

This has been done for the different absorbing materials in the fig. 2 and 3. The errors indicated are standard errors. We see that one may represent the absorption by a straight line. However it is not directly to be seen from formula (6) that the absorption can be approximated by an exponential absorption, and furthermore it goes not without saying that if this would be the case, the value of the slope of the straight lines may directly be interpreted as a sort of mean absorption coefficient. Theoretically the dependence of the absorption coefficient on energy for the energy range we are considering here may in first approximation be described (Rl) by the relation u=aInE+b. (7) Then by integration of the integral on the right hand side of formula (6) it is easily shown for constant P that R = R, P [E,‘k-“,‘{ax

+ (K -

l)}] c?‘(~o)~.

(8)

In our case k - 1 will be about 1 whereas u is about .2 forea lead absorber.’ For an absorber with a lower atomic number the latter value is even smaller.The factor before the exponential will thus have the effeet that especially at larger values of x the tail of the exponential is somewhat too low. If one still represents the absorption plotted on a logarithmic scale by a straight line, the slope of this line will be larger than would be the one due to an exponential absorption with a = a(&). This is equivalent to saying that the effective absorption coefficient thus obtained corresponds to a mean photon energy higher than E,. TABLE

III

Values of the total absorption coefficients for high energy photons. The dimension of (I is cm-l. authors Adams (A2) Lawson (Ll) D e W i r e et al

source 22 bIeV betatron 100 MeV betatron 300 MeVsynchrotron

energy I ( MeV) 19 88

paraf- I car/“‘,“,I / iron / tin / lead ! bon ,063 .26 .6 .068 .49 1.0

i fin

283

-

-

lo*--103

-

-

.076

.57

-

1.2

02) J a n o s s y and Rossi (Jl) C 1 a y and K 1 e i n (C3) B r u i n and Clay

continuous cosmic radiation spectrum continuous cosmic radiation spectrum extensive air shower spectrum

.085

* .Ol IO’-toa lo*-103 f

-

-

.53 5.01 *.08&.09i ,088 .53 ,006 ,005 .oos & ,005 & ,017 f .07 f .03

.02

.54

& .07

.I0

1.0

* .92

.o 1.8

.7b

.2 1.4

.lO *

.2

THE

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727

The values of the effective absorption coefficients derived from the lines of the fig. 2 and 3 are collected in table III. For comparison we have also given values obtained in the high energy range by other authors. The values quoted from nuclear physics experiments have statistical fluctuations smaller than 1.5%. The values quoted from experiments by C 1 a y and K 1 e i n have been obtained by adding their values of the separate absorption coefficients for Compton effect and pair production. Con&&on. We described an experiment to measure the absorption coefficient a of the photon component of cosmic ray extensive air showers. The values found in the energy range of about lo*-IO3 MeV prove to be .006 f .005 for paraffin, .005 & .005 for carbon, .088 h .009 for aluminium, .53 -J=.07 for iron, .76 f .lO for tin and 1.4 & .2 for lead. These values agree with those obtained with photons in the high energy range provided by accelerators. The results from the latter experiments appear to be somewhat lower than predicted by theory (D2, Ll). As in the present measurements we have an energy spectrum instead of one single energy it would be difficult to deduce a meaningful conclusion in this respect. The values are in agreement with those obtained for photons belonging to the continuous cosmic radiation. The values found by C 1 a y and K 1 e i n (C3) appear to be somewhat larger. The authors wish to acknowledge Prof. G. W. R a t h e n a u’s interest in this investigation. This work represents part of the research program of the foundation for fundamental research of matter (F.O.M.) made possible by the financial aid of the Netherlands organization for pure research (Z.W.O.). Received

9-7-53.

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OF HIGH

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PHOTONS

REFERENCES Al A2 Bl B2 B3 Cl c2 c3 Dl D2 D3

Jl Ll Ml M2 Rl

A r 1 e y, N., Thesis, Gads Forlag Copenhagen (1943). A d a m s, G. D., Phys. Rev. 74 (1948) 1707. B a s s i, P. et al., Nuovo Cimento 8 (1951) 735. B a s s i, P. et al., Nuovo Cimento 0 (1952) 358. B r u i n, M., Thesis, Amsterdam (1952). C 1 a y, J. and L e v e r t, C., Physica 12 (1946) 321. C 1 a y, J., Physica I4 (1949) 569. C 1 a y, J. and K 1 e i n, G., Physica 17 (1951) 858. D a v i s s o n, C. M. and E Y a n s, R. D., Rev. Mod. Phys. 24 (1952) 79. De W i r e et al., Phys. Rev. 89 (1951) 477. D a u d i n, J., Thesis, Paris (1942). J d n o s s y, L. and R o s s i, B., Proc. roy. Sot. London A 175 (1940) 88. L a w s o n, J. L., Phys. Rev. 75 (1949) 433. Millar, D.D.,NuovoCimento8(1951)279. M i I o n e, C., Nuovo Cimento 8 (1952) 549. Rossi, B. and Greisen, K., Rev. mod. Phys. 13 (1941) 240.