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The Quantum Theory of electronic scattering by Helium

Published online by Cambridge University Press:  24 October 2008

N. F. Mott
N. F. Mott
Affiliation:
St John's College
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Extract

The problem of the collision between an electron and an atom was first considered on the Quantum theory by Born, who has worked out in detail the case of atomic hydrogen, and has obtained formulae giving the variation of scattering with angle both for elastic and inelastic collisions. Born's solution is only approximate. The purpose of this note is to discuss the physical nature of the approximations used by him, and also to extend his results to Helium, for which experimental evidence is now available. It is found that the theoretical curve agrees with the experimental as well as the approximations used would lead one to expect. We shall confine ourselves to elastic collisions.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 3 , July 1929 , pp. 304 - 309
Copyright
Copyright © Cambridge Philosophical Society 1929

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References

* Born, M., Zeit. f. Physik, Vol. XXXVIII, p. 803 (1926);CrossRefGoogle ScholarGöttinger Nachrichten. p. 146 (1926), referred to as loc. cit.Google Scholar

† Dymond, and Watson, , Proc. Roy. Soc. A, Vol. CXII, p. 571 (1928).Google Scholar

‡ Born, , loc. cit. Equation (8).Google Scholar

§ Hartree, , Proc. Camb. Phil. Soc., Vol. XXIV, p. 89 (1928).CrossRefGoogle Scholar

* Oppenheimer, , Phys. Rev., Vol. XXXII, p. 361 (1928).CrossRefGoogle Scholar

† Cf. Faxen, and Holtzmark, , Zeit. f. Physik, Vol. XLV, p. 307 (1927).CrossRefGoogle Scholar

* Cf. Blackett, P. M. S., Proc. Camb. Phil. Soc., Vol. XXIII, pp. 698–702 (1927)CrossRefGoogle Scholar

† By the total number scattered, we mean

* Born, loc. cit. Equation (23).Google Scholar

† In these units, the unit of length, which is all that concerns us, is h2/4π2mε2.Google Scholar

* This curve gives the classical scattering by the field V(r). The calculations were carried out by Dymond. I am very much indebted to him for providing me with this curve, and also for informing me of his experimental results.Google Scholar

* Cf. Faxen, and Holtzmark, , loc. cit.;Google ScholarMott, N. F., Proc. Roy. Soc., A, Vol. CXVIII, p. 544 (1928).Google Scholar