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Decrease of hard primary cosmic rays in matter
Physica
IV, no 7
Juli
DECREASE
OF HARD PRIMARY RAYS IN MATTER
by J. CLAY, J. T. WIERSMA Natuurkundig
Laboratorium
1937
COSMIC
and E. M. BRUINS Amsterdam
Summary The decrease of hard cosmic primaries is determined in mercury, lead, iron, tin, sulphur and water under layers up to 1300 gr/cm*. We were able to establish that the decrease depends on the mass and not on the electron density or the dimension of the nucleus. The coefficient of decrease is decreasing with the thickness of the layers. On account of these two facts and the constancy found of the number of coincidences between 230 and 330 m. water equivalent, it is suggested that the protons are partly replaced by neutrons and partly lost by energy-loss in ionisation, showers and radiation.
In a former publication 1) we gave the coefficient of decrease of the hard primary cosmic rays in lead and in iron under layers up to 700 gram/cm2. We came to the conclusion that the coefficients of lead, iron and water were proportional to the- density of the layer. This relation was found first by A 1 o c c o 2) for lead and copper but, as he remarks himself, the uncertainty in his result was too great to allow him to conclude that the decrease could not be proportional to the electron density. From another more accurate experiment with lead, iron and marble Street, Woodward and Stevenson!) ‘drew the conclusion that the decrease of the primaries was proportional to the electron-density but that the absorption per nucleus increases somewhat more rapidly than linearly with atomic number. The arrangement of Alocco, and of Street, Woodw a r d and S t e v e n s o n, was in principle the same. Three or four counters at great distances w.ere separated by a column of lead or other material between them and the great distance between th’e counters made the cone of rays counted in the apparatus very small, Physica IV
521 339
522
J. CLAY,
J. T. WIERSMA
AND
E.
M.
BRUINS
so that it took a long period of counting to attain a sufficient accuracy. We had in our former experiment a different arrangement, namely of three counters separated by only 10 cm. of lead in a cavity, in which an ionisation chamber could also be placed and our geometry was much more complicated so that on this grourrd our result could perhaps not be compared with theirs.We therefore mentioned already that we wished to measure the decrease of the hardprimariesin a way, more similar to that of the other observers. But we wished to compare the decrease in various materials, also in those sorts of which we had but a small supply. In order to overcome this difficulty and attain a sufficient accuracy we made an arrangement as given in fig. 1. The counters had an inner diameter of 4 cm. and an active length of 28 cm.
Fig. 1. Arrangement of the counters under layers of different thickness.
The distance between the axes of the counters was 16,5 cm. and’ blocks of material of 10 cm. height could be inserted between them. We had enough lead and iron to fill up the volumes E and F. During the experiment the same lead block was always in A. To find the decrease in a layer of 20 cm. mercury we had therefore only to take two iron buckets filled with mercury and place them in B and C and fill the other spaces with lead and iron to be sure that we .had only to deal with hard primaries and that we could compare this decrease with, the one, when lead blocks were in B and C. Similarly, when
DECREASE
OF HARD
PRIMARY
COSMIC
RAYS
523
IN MATTER
experimenting with Sn and Sulphur we filled only the spaces B, C and D. In this way we could compare the various decreases in Sulphur, Sn, Fe, Pb and Hg and be sure that the decreases themselves belonged to identical layers of the various materials. The average path through the layers is 4,8% more than the vertical distance. The results are given in the table I. TABLE
Coinc. per min.
Layer
10 cm Pb +20cm ,I +33cmSn ,, +32cm ,, +48cmS ,f
I
Pb Fe
7560’ 5345’ 5465’ 5950’ 2210’
53 cm Fe + 40 cm Pb 12240’ + 20 cm Pb 2995’ 0 ,, + 33 cm Sn 1920’ ,, II +32 cm Fe 4640’ I, ,, + 18cmHg 1380’ ,I II
22742 14014 14142
3,008
Uncertainty
2,622
5 0,020 j, 0,022
0,386
2,588
*to,022
0,420
15408
2,590
j,O,O21
0,418
6559
2,968 -~
&0,037
0,040
33170 7236 4633 11117 3354
2,710 2,416 2,413 2,396 2,430
*0,015 +0,028 &-0,036 f 0,023 f 0,042
0,294 0,297 0,314
0,280
0,ooosa
f 0,00006 6
59 3: 0,00049
f 0,00012 46
48
13
.IO
43
For lead the decrease for different layers up to 1300 gr. per cm2 is measuredespecially. Now we see that, reduced to their values per gram cm2, the results for the various materials are the same, more closely than we could expect from the computed -uncertainty. Only for sulphur is the uncertainty very large. Although we employed a layer of 50 cm. thickness the decrease of the counted number of coincidences was so slight that only the order of magnitude could be found. We may remark that the value for water, which is known more accurately as it is found from thicker layers by ‘our earlier experiments 3, fits very well in the series of the other values and the same is true for the coefficient of decrease for a layer of 30 m. of clay under which Follett and Crawshaw6) have measured coincidences. They give a density of 2 for the layer and then we find for the. coefficient of decrease the value 0,00048 per gr/cm”. When we now compare the coefficients of decrease given in table I for various materials and we plot them against the specific density, we see that there is a very good agreement, whereas, on plotting the coefficients against the electron density we observe that the diffefences are larger than the uncertainty of thevalues. We may, therefore,
17
524
J. CLAY,
J. T. WIERMSA
AND
E. M.
BRUINS
exclude this relation, in view of the accuracy obtained with water, iron and lead. There is also certainly not a direct relation with the crosssectionof the nuclei of the atoms (0) .We may conclude, therefore, that the decrease of the hard primaries takes place simply as if matter consisted of neutrons and protons and that the concentration in atoms plays nearly no part. That charge also is not of first importance. 8 x10-3 WClll. I
6
!!!l
9
20
0
0.05
! as
0.1
30 0.2
I 0.25
50 XIO?E
40
a3
Fig. 2. Coefficient of decrease in various,substances.in relation mass (0) the elddt’ron den&y (C) and the total cioss-section nuclei (0) (between 700 and 900 &cm*) TABLE
Density P
Atomic weight
Atomic number 2.
A.
13,b 11,3 73 7,8
Pb Sn Fe S I-W
The
w 190
total
cross-section
201 207 119
ii 50 26
ii
UsI
1:
is calculated
AL
$.
A
“:
z. N. lo**
I’ 0,0676 0,0546 0,0612 0,139 0,062s 0,0556
frdm /f“’ * ( APb 1
to their of the
II
I
Hg
c.m: T .
the
32,8 27 0 18,6 21,9 6,06 3,40.
Total crosssection of nuclei cm*. p. cm. 0,23 0,20 0,15 0,20 0,064 0,058
p.lO-a p. cm.
5,8 5,4 8 0;56 0,45
formula
. 5,8 . K+.
We must call the attention of the reader to another fact, namely, that the coefficients of decrease are not constant, as they seemed at first, under a layer of about 400 gr/cm2 but that the value is steadily going down, just as with water. As matters stand we feel.inclined to suggest the following solution.
DECREASE
OF HARD
PRIMARY
COSMIC
RAYS
IN
525
MATTER
The protons coming from outside the atmosphere are gradually replaced by neutrons, while they penetrate in matter and collide with the protons and neutrons of matter. The possibility of anexchange proton-neutron and vice versa was already suggested by B h a b h a 6). Our present supposition however, is that the decrease of the protons is twofold. In the first place, they are replaced by neutrons by collision and in the second place they lose part of their energy by ionisation, showers and radiation. On the other hand the neutrons will partly produce protons by the impact with the constituent3 of matter. As a first approximation we suppose that the energy of the neutrons is but very slightly decreased by ionisation etc.
-( I TABLE
:oinc. Per ITIlL
Layer
40 cm Pb + 20 cm Pb 60 h
Pb
+30 cm Pb 33 c& Fe +60 cm Pb +90cm Pb ,*
;560’ 5345’ 5345’ 2840’ 2995 2810’
22742 14014 14014
6294 7236 6021
3,008
2,622 2,622 2,216 2,416 2,143
III Uncertainty f f f f f f
0,020 0,022 0,022 0,028 0,028 0,028
10-L
Coeff. of decrease
Uncertaiuty
0,386
0,00058
f 0,00006
0,406
0,00048
f0,00012
0,273
0,00033
f 0,00015
When P is the number of protons of a certain definite energy and N the number of neutrons, we have the following ‘relations: dP -=--(A+v)P+pN ax and dN -= -pN+AP. dx The coefficients A and lo measure the transformation proton-neutron and, neutron-proton. The coefficients v,.A and l.~ will depend on the energy
Fig. 3. The coefficient of decrease in lead for layers of different thickness.
520
DECREASE
OF HARD
PRIMARY
COSMIC
RAYS
IN MATTER
As we measure the number of coincidences at different find only the decrease of the protons and we see that
depths we
1 dP --=(A + 4 + !g P a& that means that the apparent absorption coefficient decreases as the ratio N/P increases, as it will do in the first part of the path of the particles through matter. And after a certain layer conditions may become such that this coefficient of decrease nearly vanishes just as we found in water and in the earth at a depth between 230 and 330 m-water-aequivalent. We shall give the comparison between this theory and our experimental results in a following paper. Received,
April
28, 1937.
REFERENCES 1) J. Clay, Physica3,332,1936;.J. Clay, A.v. Gemert 3, 627, 1936. 2) G. -4 1 o cc o, Nature 135, 36, 1935. 3) J.C. S-treat, Woodward and&C. Stevenson, 4) J. C 1 a y and P. H. C 1 a y, Physica 8, 1042, 1935. 5) D. H. F o 11 e t t and J. D. C r a w s h a w,. Proc. roy. 6) H. J. B h a b ha, Nature 134, 934, 1934.
andJ.T.
Wiersma,
Phys.Rev.67,891,1935 Sot. 155,
546, 1936.
IV, no 7
Juli
DECREASE
OF HARD PRIMARY RAYS IN MATTER
by J. CLAY, J. T. WIERSMA Natuurkundig
Laboratorium
1937
COSMIC
and E. M. BRUINS Amsterdam
Summary The decrease of hard cosmic primaries is determined in mercury, lead, iron, tin, sulphur and water under layers up to 1300 gr/cm*. We were able to establish that the decrease depends on the mass and not on the electron density or the dimension of the nucleus. The coefficient of decrease is decreasing with the thickness of the layers. On account of these two facts and the constancy found of the number of coincidences between 230 and 330 m. water equivalent, it is suggested that the protons are partly replaced by neutrons and partly lost by energy-loss in ionisation, showers and radiation.
In a former publication 1) we gave the coefficient of decrease of the hard primary cosmic rays in lead and in iron under layers up to 700 gram/cm2. We came to the conclusion that the coefficients of lead, iron and water were proportional to the- density of the layer. This relation was found first by A 1 o c c o 2) for lead and copper but, as he remarks himself, the uncertainty in his result was too great to allow him to conclude that the decrease could not be proportional to the electron density. From another more accurate experiment with lead, iron and marble Street, Woodward and Stevenson!) ‘drew the conclusion that the decrease of the primaries was proportional to the electron-density but that the absorption per nucleus increases somewhat more rapidly than linearly with atomic number. The arrangement of Alocco, and of Street, Woodw a r d and S t e v e n s o n, was in principle the same. Three or four counters at great distances w.ere separated by a column of lead or other material between them and the great distance between th’e counters made the cone of rays counted in the apparatus very small, Physica IV
521 339
522
J. CLAY,
J. T. WIERSMA
AND
E.
M.
BRUINS
so that it took a long period of counting to attain a sufficient accuracy. We had in our former experiment a different arrangement, namely of three counters separated by only 10 cm. of lead in a cavity, in which an ionisation chamber could also be placed and our geometry was much more complicated so that on this grourrd our result could perhaps not be compared with theirs.We therefore mentioned already that we wished to measure the decrease of the hardprimariesin a way, more similar to that of the other observers. But we wished to compare the decrease in various materials, also in those sorts of which we had but a small supply. In order to overcome this difficulty and attain a sufficient accuracy we made an arrangement as given in fig. 1. The counters had an inner diameter of 4 cm. and an active length of 28 cm.
Fig. 1. Arrangement of the counters under layers of different thickness.
The distance between the axes of the counters was 16,5 cm. and’ blocks of material of 10 cm. height could be inserted between them. We had enough lead and iron to fill up the volumes E and F. During the experiment the same lead block was always in A. To find the decrease in a layer of 20 cm. mercury we had therefore only to take two iron buckets filled with mercury and place them in B and C and fill the other spaces with lead and iron to be sure that we .had only to deal with hard primaries and that we could compare this decrease with, the one, when lead blocks were in B and C. Similarly, when
DECREASE
OF HARD
PRIMARY
COSMIC
RAYS
523
IN MATTER
experimenting with Sn and Sulphur we filled only the spaces B, C and D. In this way we could compare the various decreases in Sulphur, Sn, Fe, Pb and Hg and be sure that the decreases themselves belonged to identical layers of the various materials. The average path through the layers is 4,8% more than the vertical distance. The results are given in the table I. TABLE
Coinc. per min.
Layer
10 cm Pb +20cm ,I +33cmSn ,, +32cm ,, +48cmS ,f
I
Pb Fe
7560’ 5345’ 5465’ 5950’ 2210’
53 cm Fe + 40 cm Pb 12240’ + 20 cm Pb 2995’ 0 ,, + 33 cm Sn 1920’ ,, II +32 cm Fe 4640’ I, ,, + 18cmHg 1380’ ,I II
22742 14014 14142
3,008
Uncertainty
2,622
5 0,020 j, 0,022
0,386
2,588
*to,022
0,420
15408
2,590
j,O,O21
0,418
6559
2,968 -~
&0,037
0,040
33170 7236 4633 11117 3354
2,710 2,416 2,413 2,396 2,430
*0,015 +0,028 &-0,036 f 0,023 f 0,042
0,294 0,297 0,314
0,280
0,ooosa
f 0,00006 6
59 3: 0,00049
f 0,00012 46
48
13
.IO
43
For lead the decrease for different layers up to 1300 gr. per cm2 is measuredespecially. Now we see that, reduced to their values per gram cm2, the results for the various materials are the same, more closely than we could expect from the computed -uncertainty. Only for sulphur is the uncertainty very large. Although we employed a layer of 50 cm. thickness the decrease of the counted number of coincidences was so slight that only the order of magnitude could be found. We may remark that the value for water, which is known more accurately as it is found from thicker layers by ‘our earlier experiments 3, fits very well in the series of the other values and the same is true for the coefficient of decrease for a layer of 30 m. of clay under which Follett and Crawshaw6) have measured coincidences. They give a density of 2 for the layer and then we find for the. coefficient of decrease the value 0,00048 per gr/cm”. When we now compare the coefficients of decrease given in table I for various materials and we plot them against the specific density, we see that there is a very good agreement, whereas, on plotting the coefficients against the electron density we observe that the diffefences are larger than the uncertainty of thevalues. We may, therefore,
17
524
J. CLAY,
J. T. WIERMSA
AND
E. M.
BRUINS
exclude this relation, in view of the accuracy obtained with water, iron and lead. There is also certainly not a direct relation with the crosssectionof the nuclei of the atoms (0) .We may conclude, therefore, that the decrease of the hard primaries takes place simply as if matter consisted of neutrons and protons and that the concentration in atoms plays nearly no part. That charge also is not of first importance. 8 x10-3 WClll. I
6
!!!l
9
20
0
0.05
! as
0.1
30 0.2
I 0.25
50 XIO?E
40
a3
Fig. 2. Coefficient of decrease in various,substances.in relation mass (0) the elddt’ron den&y (C) and the total cioss-section nuclei (0) (between 700 and 900 &cm*) TABLE
Density P
Atomic weight
Atomic number 2.
A.
13,b 11,3 73 7,8
Pb Sn Fe S I-W
The
w 190
total
cross-section
201 207 119
ii 50 26
ii
UsI
1:
is calculated
AL
$.
A
“:
z. N. lo**
I’ 0,0676 0,0546 0,0612 0,139 0,062s 0,0556
frdm /f“’ * ( APb 1
to their of the
II
I
Hg
c.m: T .
the
32,8 27 0 18,6 21,9 6,06 3,40.
Total crosssection of nuclei cm*. p. cm. 0,23 0,20 0,15 0,20 0,064 0,058
p.lO-a p. cm.
5,8 5,4 8 0;56 0,45
formula
. 5,8 . K+.
We must call the attention of the reader to another fact, namely, that the coefficients of decrease are not constant, as they seemed at first, under a layer of about 400 gr/cm2 but that the value is steadily going down, just as with water. As matters stand we feel.inclined to suggest the following solution.
DECREASE
OF HARD
PRIMARY
COSMIC
RAYS
IN
525
MATTER
The protons coming from outside the atmosphere are gradually replaced by neutrons, while they penetrate in matter and collide with the protons and neutrons of matter. The possibility of anexchange proton-neutron and vice versa was already suggested by B h a b h a 6). Our present supposition however, is that the decrease of the protons is twofold. In the first place, they are replaced by neutrons by collision and in the second place they lose part of their energy by ionisation, showers and radiation. On the other hand the neutrons will partly produce protons by the impact with the constituent3 of matter. As a first approximation we suppose that the energy of the neutrons is but very slightly decreased by ionisation etc.
-( I TABLE
:oinc. Per ITIlL
Layer
40 cm Pb + 20 cm Pb 60 h
Pb
+30 cm Pb 33 c& Fe +60 cm Pb +90cm Pb ,*
;560’ 5345’ 5345’ 2840’ 2995 2810’
22742 14014 14014
6294 7236 6021
3,008
2,622 2,622 2,216 2,416 2,143
III Uncertainty f f f f f f
0,020 0,022 0,022 0,028 0,028 0,028
10-L
Coeff. of decrease
Uncertaiuty
0,386
0,00058
f 0,00006
0,406
0,00048
f0,00012
0,273
0,00033
f 0,00015
When P is the number of protons of a certain definite energy and N the number of neutrons, we have the following ‘relations: dP -=--(A+v)P+pN ax and dN -= -pN+AP. dx The coefficients A and lo measure the transformation proton-neutron and, neutron-proton. The coefficients v,.A and l.~ will depend on the energy
Fig. 3. The coefficient of decrease in lead for layers of different thickness.
520
DECREASE
OF HARD
PRIMARY
COSMIC
RAYS
IN MATTER
As we measure the number of coincidences at different find only the decrease of the protons and we see that
depths we
1 dP --=(A + 4 + !g P a& that means that the apparent absorption coefficient decreases as the ratio N/P increases, as it will do in the first part of the path of the particles through matter. And after a certain layer conditions may become such that this coefficient of decrease nearly vanishes just as we found in water and in the earth at a depth between 230 and 330 m-water-aequivalent. We shall give the comparison between this theory and our experimental results in a following paper. Received,
April
28, 1937.
REFERENCES 1) J. Clay, Physica3,332,1936;.J. Clay, A.v. Gemert 3, 627, 1936. 2) G. -4 1 o cc o, Nature 135, 36, 1935. 3) J.C. S-treat, Woodward and&C. Stevenson, 4) J. C 1 a y and P. H. C 1 a y, Physica 8, 1042, 1935. 5) D. H. F o 11 e t t and J. D. C r a w s h a w,. Proc. roy. 6) H. J. B h a b ha, Nature 134, 934, 1934.
andJ.T.
Wiersma,
Phys.Rev.67,891,1935 Sot. 155,
546, 1936.