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Ionization Power of a Neutrino with Magnetic Moment

Published online by Cambridge University Press:  24 October 2008

H. A. Bethe
H. A. Bethe
Affiliation:
University of Manchester
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Extract

The number of ions produced by a neutral particle of small mass with a magnetic moment equal to n Bohr magnetons has been calculated (I–III) and found to be 103n2 per km. path in air at N.T.P., being practically independent of the mass and energy of the particle (IV). A comparatively large fraction of the secondary electrons produced have high energy and may therefore be counted if they are produced in the wall of the Geiger counter instead of in the counter itself. This fact should facilitate the experimental detection of the ionization considerably (V).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 1 , January 1935 , pp. 108 - 115
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

† Fermi, E., Zeits. Physik. 88 (1934), 161.CrossRefGoogle Scholar

‡ Bethe, H. A. and Peierls, R., Nature, 133 (1934), 532.CrossRefGoogle Scholar

§ Oppenheimer, and Carlson, , Phys. Rev. 41 (1932), 763.Google Scholar

† Møller, C., Zeits. Physik. 70 (1931), 786.CrossRefGoogle Scholar

† E. Fermi, loc. cit.

‡ The problem is connected with the incoherent scattering of X-rays, since is proportional to the probability that the atom is excited to the state W by an X-ray of wavelength λ which is scattered through an angle θ, where

The total probability for the incoherent scattering through a given angle, i.e. the sum of over all excited states W of the atom, has been calculated by W. Heisenberg (Phys. Zeits. 32 (1931), 735), and by Bewilogua (Ibid. 740), using Fermi's statistical model. The result is

where the function S (υ) has been tabulated by Bewilogua, and

For large values of υ, all the scattering is incoherent, so that S (υ) = 1 (cf. (19)). Therefore we may write

The quantity υ0 defined here is connected with the average excitation potential A by the relation

where I H is the ionization potential of hydrogen. From the Bewilogua table we have calculated υ0 =0·081 and therefore volt.

† The actual calculations were done for Cu. For other substances, the extra path L would be very nearly proportional to 1/Z M.

† If Ra B+C only is used, the extra path for zero neutrins mass is 2·46 cm., whereas for Ra D+E it is 0·70 cm.

‡ Proc. Cambridge Phil. Soc. 31 (1935), 99.Google Scholar