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The energy loss by radiation of fast electrons in a Coulomb field

Published online by Cambridge University Press:  24 October 2008

J. C. Jaeger
J. C. Jaeger
Affiliation:
The University of Tasmania
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Extract

The problem of the energy loss by radiation of an electron in a Coulomb field has been solved, using relativistic equations and the Born approximation, by Bethe and Heitler, and, using exact non-relativistic equations, by Sommerfeld; the first of these solutions is valid only for relatively high and the second for relatively low energies. In this paper an exact solution of the problem is given using the relativistic Coulomb wave functions, but depending on a final stage of numerical computation. The method is an extension of that used to determine cross-sections for pair production.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 39 , Issue 2 , June 1943 , pp. 127 - 130
Copyright
Copyright © Cambridge Philosophical Society 1943

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References

* Proc. Roy. Soc. A, 146 (1934), 83.Google Scholar

† Ann. der Physik, 11 (1931), 257.Google Scholar

‡ Jaeger, & Hulme, , Proc. Roy. Soc. A, 148 (1935), 708CrossRefGoogle Scholar; 153 (1936), 443. These papers will be referred to as I and II respectively.

§ Electrons passing at a distance of more than 1 cm. from the nucleus, corresponding to values of k > 2πp/h, are of course quite negligible.

* Dashes are used in I to denote an initial state of negative energy, here to denote an initial state of positive energy.

† Appell, and Kampé, de Fériet, , Fonctions hypergeometriques, p. 28.Google Scholar

* Jaeger, , Journ. London Math. Soc. 13 (1938), 254.CrossRefGoogle Scholar

† The value 13 × 1024 was given for hν 0 = 1·5 in Nature, 140 (1937), 108Google Scholar. A small error has been corrected and the extrapolation improved.

* Cf. I, Table 1, and Jaeger, , Nature, 137 (1936), 781.CrossRefGoogle Scholar

† Phys. Rev. 52 (1937), 63.Google Scholar