Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T14:29:11.178Z Has data issue: false hasContentIssue false
  • English
  • Français

Relativistic wave-functions and K-capture for a modified coulomb field

Published online by Cambridge University Press:  24 October 2008

I. Malcolm  and
C. Strachan
I. Malcolm
Affiliation:
Department of Natural PhilosophyUniversity of Aberdeen
C. Strachan
Affiliation:
Department of Natural PhilosophyUniversity of Aberdeen
Get access Rights & Permissions [Opens in a new window]

Extract

In the theory of beta-decay, as is well known, when the electron is described by relativistic wave-functions, e.g. in a Coulomb field, a difficulty arises when these become infinite at the centre of force, r = 0. The wave-functions are then evaluated at the nuclear radius, r = R, and in many formulae there appears (1) a rather sensitive dependence on R. For the capture of an orbital electron by a nucleus the results of calculation depend strongly on the behaviour of the wave-function of the bound electron near the nucleus. The nature of the potential energy near the nucleus will thus affect such quantities as the ratio of K-capture to positron emission. Wannier (2) has discussed a similar problem for the Schrödinger equation, but the singular behaviour of the solutions of the Dirac equation for the ground state makes it desirable to have the solution for the relativistic case. In the following, relativistic wave-functions are derived and used for a potential energy which is Coulombian outside the nucleus and constant inside. Similar problems have been considered by others, Breit et al. (3), Racah (4), in application to the calculation of hyperfine structure, and also by Broch (5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 3 , July 1951 , pp. 610 - 616
Copyright
Copyright © Cambridge Philosophical Society 1951

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Konopinski, E.J. Rev. Mod. Phys. 15 (1943), 209.CrossRefGoogle Scholar
(2)Wannier, G. H.Phys. Rev. 64 (1943), 358.CrossRefGoogle Scholar
(3)Rosenthal, J. and Breit, G.Phys. Rev. 41 (1932), 459.CrossRefGoogle Scholar
Breit, G. and Brown, G. E.Phys. Rev. 76 (1949), 1307.CrossRefGoogle Scholar
(4)Racah, G.Nuovo Cim. 8 (1931), 178.CrossRefGoogle Scholar
(5)Broch, E. K.Arch. Math. Naturv. B 48, no. 1 (1945).Google Scholar
(6)Slater, J. C.Phys. Rev. 36 (1930), 57.CrossRefGoogle Scholar
(7)Reitz, J. R.Phys. Rev. 77 (1950), 10.CrossRefGoogle Scholar
(8)Rose, M. E.Phys. Rev. 51 (1937), 484.CrossRefGoogle Scholar
(9)Whittaker, E. T. and Watson, G. N.Modern analysis (Cambridge, 1927).Google Scholar
(10)Watson, G. N.Theory of Bessel functions (Cambridge, 1944).Google Scholar
(11)Rosenfeld, L.Nuclear forces (Amsterdam, 1948).Google Scholar
(12)Kramers, H. A.Theorien des Aufbaues der Materie (Leipzig, 1933).Google Scholar
(13)Hill, E. L. and Landshoff, R.Rev. Mod. Phys. 10 (1938), 87.CrossRefGoogle Scholar
(14)Bethe, H.Handbuch der Physik, 24, 1 (Berlin, 1933).Google Scholar
(15)Bouchez, R., de Groot, S. R., Nataf, R. and Tolhoek, H. A.J. Phys. Radium, 11 (1950), 105.CrossRefGoogle Scholar