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The influence of screening on the creation and stopping of electrons

Published online by Cambridge University Press:  24 October 2008

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

The cross-sections for the emission of radiation by very fast electrons (energy great compared with mc2) and for the production of pairs of positive and negative electrons by very hard γ-rays is calculated, considering the screening of the atomic field in which the processes happen. The main part of the paper deals with the integration of the differential cross-section over the angles. It is found that the integral cross-section increases steadily with increasing energy of the primary particle, reaching an asymptotic value for extremely high energies.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 30 , Issue 4 , October 1934 , pp. 524 - 539
Copyright
Copyright © Cambridge Philosophical Society 1934

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References

* Proc. Roy. Soc. London, in press.Google Scholar Quoted as R.

* E.g. Bethe, H., Ann. d. Phys. 5 (1930), 385.Google Scholar

* By a more careful analysis it can be shown that our calculation is correct to the order (μ/E 0)2.

* Actually, only values of x comparable with μ2 contribute appreciably (cf. § VIII), which would be still more favourable for our argument.

† Only the values of x smaller than √(E 0μ) contribute appreciably to the cross-section. See above.

* It is actually the most troublesome and least interesting part of the calculation to show that the terms neglected in (23) really correspond only to a correction of the order μ2/E 02.

* The argument is similar to that leading to the neglect of (17).

* Of course, E 0, E and hν are still assumed to be large compared with mc 3.

* We have not made use of this fact in § II, because (72) does not follow immediately from the calculation carried out in this paper.