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The Statistical Theory of Dissociation and Ionization by Collision, with applications to the capture and loss of electrons by α-particles

Published online by Cambridge University Press:  24 October 2008

R. H. Fowler
R. H. Fowler
Affiliation:
Fellow and Lecturer in Trinity College, Cambridge
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Extract

In two recent papers in the Philosophical Magazine the statistical theory of collisions of electrons with atoms has been considered, and applied to explain the observed features of the capture and loss of electrons by α-particles. The basis of that discussion can however be improved. Firstly, interactions with the core of any atom entered by the α-particle were explicitly ignored. Such interactions—or rather interactions with the general intra-atomic field as distinct from individual electrons—might be expected to be (and are) important, and it has been found possible to include them in this paper. Secondly, the frequency laws for the processes concerned were based on the classical Thomson-Bohr theory of ionization by collision. This theory—it is well known—does not completely reproduce experimental facts at α-particle velocities, and a less restrictive form can be given to the frequency laws which appears to be in accord with all the known facts. The application to the capture and loss of electrons by α-particles proves to be unaffected.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 3 , 20 September 1924 , pp. 253 - 272
Copyright
Copyright © Cambridge Philosophical Society 1924

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References

* Fowler, , Phil. Mag., 47, 257, 415 (1924).CrossRefGoogle Scholar

† For example, Pauli, , Zeit. für Phys., 18, 272 (1923)CrossRefGoogle Scholar; Einstein, and Ehrenfest, , Zeit. für Phys., 19, 301 (1923)CrossRefGoogle Scholar; and, to a less extent, Einstein, , Phys. Zeit., 18, 121 (1917)Google Scholar.

† Jeans, , Dynamical theory of gases, 3rd ed., p. 251Google Scholar, equation (699).

* This particular specification of leads to the simplest forms in applications for where εrel. is the energy of the relative motion of the bodies 0 and 2 after dissociation.

* Fowler, , Phil. Mag., 45, 27 (1923)Google Scholar, equation (9·82).

† Fowler, loc. cit. (1).

‡ Fowler, loc. cit. (1), p. 271, equation C.

* See for example Fowler, , Proc. Camb. Phil. Soc., 21, 526 (1923)Google Scholar.

† Fowler, loc. cit. (1), p. 273, transposed to the present notation.

* Fowler, , Proc. Camb. Phil. Soc., 21, 531 (1923)Google Scholar.

† Fowler, loc. cit.; Wilson, C. T. R., Proc. Roy. Soc., A, 104, 1, 192 (1923)CrossRefGoogle Scholar, especially p. 200.

‡ Dr J. Chadwick informs me that he has been able to make a rough count of this nature, which, so far as it goes, confirms the classical V 2-factor.

§ Bohr, , The Fundamental Postulates, Chap. 1; Camb. Phil. Soc. Proc. (Supplement).Google Scholar

* Bohr, , Phil. Mag., 24, 10 (1913)Google Scholar; 30, 581 (1915).

† Blackett, , Proc. Roy. Soc., A, 103, 68 (1923)CrossRefGoogle Scholar. The V 3-law appears to hold when the logarithmic factors are ignored. This is not the place to enter into details, but when the logarithmic factors are included the factor V 2 in the denominator of (3·41) must not actually be replaced by V to give an adequate representation of the observed velocity variation, but by a factor more like . The logarithmic factors in fact themselves vary effectively in these ranges more or less like V ½.

* Geiger, , Proc. Boy. Soc., A, 82, 486 (1909)CrossRefGoogle Scholar; Taylor, , Phil. Mag., 26, 402 (1913)CrossRefGoogle Scholar.

† Smyth, , Proc. Roy. Soc., A, 105, 116 (1924).CrossRefGoogle Scholar

‡ Proc. Camb. Phil. Soc., loc. cit.

§ The theoretical value of s is of course 2, and the theoretical value of the constant 1·0 × 10−28.

* See Hartree, D. R., Camb. Phil. Soc. Proc., 21, 625 (1923)Google Scholar for a discussion and numerical values.

* Hartree, loc. cit.

* It would actually be somewhat better with the classical value of f (V), about 1·3 times too large. But we have no justification for using the classical value.