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The energy flux of the corpuscular cosmic radiation
846
THE
BARTOL R E S E A R C H
FOUNDATION.
[J. F. I.
electrons through assumption of the classical force equation. If the invariant J were incorporated, it would not be T - e(E.u) which would be conserved. We should, in fact, have
T/dO
=
It is true t h a t the neutrino manifests itself in connection with particle energies far below those concerned in cosmic-rays, energies comparable with a million electron volts. It is to be observed, however, t h a t there is nothing to require t h a t J should change monotonically with increase of the velocity of the particle. It m u s t further be pointed o u t t h a t there is little to necessitate regarding the ordinary expression (3) as having anything to do with the q u a n t i t y which we speak of in energy transitions in atomic structure problems. T h e assignm e n t of energy levels in atoms, and the subsequent determination of frequencies by their differences, for example, are things which do n o t involve T as given by (3) having any relation to t h a t which should be conserved in the processes involved. T h e energy magnitudes concerned in atomic structure problems come, for the most part, from a consideration of magnitudes of constants which determine the characteristic solutions of ~k equations. It is quite true t h a t experiments on critical potentials and the like form a bridge between kinetic energy as born of the force equation and energy as it occurs in problems of atomic structure; b u t this bridge can hardly be considered to have been established for energies as high even as a million electron volts. However, it is not our purpose here to stress to the realm of the neutrino the considerations here presented. The main purpose of the paper concerns the cosmic-ray particles. T H E E N E R G Y FLUX OF T H E CORPUSCULAR COSMIC RADIATION.* BY C. G. M O N T G O M E R Y A N D
D. D. MONTGOMERY.
The recent advances in cloud chamber technique have made possible the m e a s u r e m e n t of such high energies of * Condensed from a paper which was published in full in the 53, x93 (1938).
Physical Review,
June, ~939.]
THE
BARTOL R E S E A R C H FOUNDATION.
847
cosmic-ray corpuscles t h a t one is led to inquire h o w much of the total energy of the cosmic radiation appears in a measurable form in the cloud chamber. It is possible to estimate the total flux of cosmic-ray energy across a unit surface, since all of this energy m u s t e v e n t u a l l y appear at points below the unit surface in the form of ionization and the excitation of atoms. T h u s if we k n o w the ionization at each point below our surface, we can integrate it and so obtain the total flux of energy through the surface. If we k n o w also the n u m b e r of corpuscular rays, we can obtain the mean energy per r a y at a n y point. This can then be directly compared to the cloud c h a m b e r observations. T h e values of the mean energy found from the ionization d a t a are illustrated in Fig. I. C u r v e A gives the mean FIG. I.
~2 ~
0
~
P
I
.5
7"
I
lO
A-VERTIC.m_ RAY,,~
B-ALLRAY5
I
IS
I
ZO
I
2S
NIET"C/P,~ O F 14/AIT"~'R The mean energiesof cosmic-rayparticles at various depths in the atmosphere.
energy of the vertical rays, curve B the mean energy of all the rays crossing a horizontal square centimeter. It will be noted t h a t the mean energy increases with increasing h. This is representative of the fact t h a t there is a distribution of energies in the p r i m a r y cosmic radiation, since the mean energy of the r a y s produced b y a p r i m a r y of a given energy m u s t always decrease with increasing h. T h e mean energy at 0.664 m e t e r below the t o p of the a t m o s p h e r e is 1.46 )< TO9 volts, and since the earth's magnetic field excludes vertically
848
T n ~ BARTOL RESEARCH FOUNDATION.
[J. F. I.
incident rays of energy less than 6 X lO 9 volts, the mean energy must increase to some value of this order at the top of the atmosphere. This rise is indicated by the dotted portion of curve B. For the cloud chamber observations, we chose those of Blackett who measures the energy distribution of the vertical rays up to energies of 2 X lOTM volts. Using his energy distribution, one finds that the total energy of the lOl 5 rays of energy less than 2 X lOTM volts is 2.44 X lOTM volts. He observes in addition 42 rays of energy greater than 2 X lOTM volts, which must have a total energy greater than 0.84 X lO12 volts. Therefore the mean energy will be somewhat greater than (2.44 + 0.84) X lO12/lO57, or 3.11 X lO 9 volts. This m a y be compared directly to the value calculated for vertical rays at sea level, viz. : 3.04 X lO 9 volts. These figures agree closely with each other, and we are led to the conclusion that, at sea level, practically all of the
energy in the cosmic-ray beam is carried by charged corpuscles. These figures rule out the possibility of any appreciable contribution of energy by photons, neutrons, or other nonionizing entities. The above conclusion is based on the assumption t h a t all the energy of the cosmic radiation is eventually dissipated in ionizing and exciting atoms. If there are other means by which cosmic rays can lose energy, such a s by the production of neutrinos, then the energy lost in this way must be carried by non-ionizing particles at sea level. The circumstance that, in the cloud chamber results, we are dealing with the penetrating component of the cosmic radiation which m a y consist of particles with higher rest masses than electrons, has only a very small effect on the measured energies, since the energies under consideration are high compared to the rest mass of the particles. The condition t h a t most of the energy be carried by charged corpuscles would not obtain on the present theory of the passage of a beam of high energy electrons and their secondaries through, matter. In t h a t case we should expect approximately equal amounts of energy to be carried by electrons and by photons. If suitable cloud chamber observations were available, taken at a high elevation, this point could be directly tested, as has been done above for sea level.
THE
BARTOL R E S E A R C H
FOUNDATION.
[J. F. I.
electrons through assumption of the classical force equation. If the invariant J were incorporated, it would not be T - e(E.u) which would be conserved. We should, in fact, have
T/dO
=
It is true t h a t the neutrino manifests itself in connection with particle energies far below those concerned in cosmic-rays, energies comparable with a million electron volts. It is to be observed, however, t h a t there is nothing to require t h a t J should change monotonically with increase of the velocity of the particle. It m u s t further be pointed o u t t h a t there is little to necessitate regarding the ordinary expression (3) as having anything to do with the q u a n t i t y which we speak of in energy transitions in atomic structure problems. T h e assignm e n t of energy levels in atoms, and the subsequent determination of frequencies by their differences, for example, are things which do n o t involve T as given by (3) having any relation to t h a t which should be conserved in the processes involved. T h e energy magnitudes concerned in atomic structure problems come, for the most part, from a consideration of magnitudes of constants which determine the characteristic solutions of ~k equations. It is quite true t h a t experiments on critical potentials and the like form a bridge between kinetic energy as born of the force equation and energy as it occurs in problems of atomic structure; b u t this bridge can hardly be considered to have been established for energies as high even as a million electron volts. However, it is not our purpose here to stress to the realm of the neutrino the considerations here presented. The main purpose of the paper concerns the cosmic-ray particles. T H E E N E R G Y FLUX OF T H E CORPUSCULAR COSMIC RADIATION.* BY C. G. M O N T G O M E R Y A N D
D. D. MONTGOMERY.
The recent advances in cloud chamber technique have made possible the m e a s u r e m e n t of such high energies of * Condensed from a paper which was published in full in the 53, x93 (1938).
Physical Review,
June, ~939.]
THE
BARTOL R E S E A R C H FOUNDATION.
847
cosmic-ray corpuscles t h a t one is led to inquire h o w much of the total energy of the cosmic radiation appears in a measurable form in the cloud chamber. It is possible to estimate the total flux of cosmic-ray energy across a unit surface, since all of this energy m u s t e v e n t u a l l y appear at points below the unit surface in the form of ionization and the excitation of atoms. T h u s if we k n o w the ionization at each point below our surface, we can integrate it and so obtain the total flux of energy through the surface. If we k n o w also the n u m b e r of corpuscular rays, we can obtain the mean energy per r a y at a n y point. This can then be directly compared to the cloud c h a m b e r observations. T h e values of the mean energy found from the ionization d a t a are illustrated in Fig. I. C u r v e A gives the mean FIG. I.
~2 ~
0
~
P
I
.5
7"
I
lO
A-VERTIC.m_ RAY,,~
B-ALLRAY5
I
IS
I
ZO
I
2S
NIET"C/P,~ O F 14/AIT"~'R The mean energiesof cosmic-rayparticles at various depths in the atmosphere.
energy of the vertical rays, curve B the mean energy of all the rays crossing a horizontal square centimeter. It will be noted t h a t the mean energy increases with increasing h. This is representative of the fact t h a t there is a distribution of energies in the p r i m a r y cosmic radiation, since the mean energy of the r a y s produced b y a p r i m a r y of a given energy m u s t always decrease with increasing h. T h e mean energy at 0.664 m e t e r below the t o p of the a t m o s p h e r e is 1.46 )< TO9 volts, and since the earth's magnetic field excludes vertically
848
T n ~ BARTOL RESEARCH FOUNDATION.
[J. F. I.
incident rays of energy less than 6 X lO 9 volts, the mean energy must increase to some value of this order at the top of the atmosphere. This rise is indicated by the dotted portion of curve B. For the cloud chamber observations, we chose those of Blackett who measures the energy distribution of the vertical rays up to energies of 2 X lOTM volts. Using his energy distribution, one finds that the total energy of the lOl 5 rays of energy less than 2 X lOTM volts is 2.44 X lOTM volts. He observes in addition 42 rays of energy greater than 2 X lOTM volts, which must have a total energy greater than 0.84 X lO12 volts. Therefore the mean energy will be somewhat greater than (2.44 + 0.84) X lO12/lO57, or 3.11 X lO 9 volts. This m a y be compared directly to the value calculated for vertical rays at sea level, viz. : 3.04 X lO 9 volts. These figures agree closely with each other, and we are led to the conclusion that, at sea level, practically all of the
energy in the cosmic-ray beam is carried by charged corpuscles. These figures rule out the possibility of any appreciable contribution of energy by photons, neutrons, or other nonionizing entities. The above conclusion is based on the assumption t h a t all the energy of the cosmic radiation is eventually dissipated in ionizing and exciting atoms. If there are other means by which cosmic rays can lose energy, such a s by the production of neutrinos, then the energy lost in this way must be carried by non-ionizing particles at sea level. The circumstance that, in the cloud chamber results, we are dealing with the penetrating component of the cosmic radiation which m a y consist of particles with higher rest masses than electrons, has only a very small effect on the measured energies, since the energies under consideration are high compared to the rest mass of the particles. The condition t h a t most of the energy be carried by charged corpuscles would not obtain on the present theory of the passage of a beam of high energy electrons and their secondaries through, matter. In t h a t case we should expect approximately equal amounts of energy to be carried by electrons and by photons. If suitable cloud chamber observations were available, taken at a high elevation, this point could be directly tested, as has been done above for sea level.