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The effect of the orbital velocity of the electrons in heavy atoms on their stopping of α-particles

Published online by Cambridge University Press:  24 October 2008

L. H. Thomas
L. H. Thomas
Affiliation:
Trinity College
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Extract

Henderson proposed a theory of the stopping of swift α-particles by matter. He treated the electrons in the atoms as free and at rest and ignored all collisions of the α-particle with them except those in which the electron would on that assumption gain sufficient energy to leave the atom. Fowler has shown that Henderson's theory gives stopping-powers only of about 60% of those observed. Fowler also made a calculation of the stopping-power of hydrogen by combining the effects of close collisions treating the electron as free and slight collisions as perturbations of the electron's motion in a circular orbit. He obtained much better agreement. This method is, of course, the natural extension of Bohr's original theory to that model.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 23 , Issue 6 , April 1927 , pp. 713 - 716
Copyright
Copyright © Cambridge Philosophical Society 1927

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References

* Henderson, , Phil. Mag., vol. XLIV (1922), p. 680.CrossRefGoogle Scholar

† Fowler, , Proc. Camb. Phil. Soc., vol. xxi (1923), p. 521.Google Scholar

‡ Ibid., vol xxii (1925), p. 792.

§ Bohr, , Phil. Mag., vol. xxv (1913), p. 10, vol. xxx (1915), p. 581.CrossRefGoogle Scholar

∥ Hartree, , Proc. Camb. Phil. Soc., vol. xxi (1923), p. 625. I am indebted to Mr Hartree for his kindness in giving me unpublished numerical values for these fields and orbits.Google Scholar

Gumey, , Proc. Roy. Soc. A. 107 (1925), pp. 332, 340.Google Scholar

* Cf. Jeans, The Dynamical Theory of Gases, p. 209Google Scholar

* The extra term 4k/3j in this expression when the velocity of the electron is taken into account depends on limiting the collisions by a restriction on q. In Fowler's calculation (loc. cit.) for hydrogen the close collisions are in effect separated from the others at a value of p. The only alteration that taking the velocity in close collisions into account makes in his result is to replace V 3 in the numerator of the argument of the logarithm in his formula ((1), p. 794, loc. cit.) by V 2(V 2−ν2)½.