Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T00:43:43.615Z Has data issue: false hasContentIssue false
  • English
  • Français

The dispersion electrons of lithium

Published online by Cambridge University Press:  24 October 2008

J. Hargreaves
J. Hargreaves
Affiliation:
Clare College
Get access Rights & Permissions [Opens in a new window]

Extract

An attempt has been made in the work described in the present paper to use the method initiated by Hartree, for the numerical solution of the Schrödinger wave equation for an atom with a non-Coulomb field of force, to estimate the number of dispersion electrons (hereinafter denoted by “ƒ” for brevity), corresponding to the lines of the principal series of the optical spectrum of lithium, and also to the continuous spectrum at the head of the series. Various attempts have been made to do this for hydrogen and other atoms by an application of the Correspondence Principle, but the first successful attempt at a complete description was made by Sugiura†, who has calculated ƒ for the Lyman, Balmer, and Paschen series and the corresponding continuous spectra, by using the known analytical solutions of the wave equation for an electron in a Coulomb field. The same author has also calculated ƒ for the first two lines of the principal series of sodium, by the utilisation of an empirical field of force in the atom calculated from the observed term-values by a method based on the old quantum theory. He has estimated the contribution to Σƒ (summed for the whole series) due to the continuous spectrum by the theorem that Σƒ = 1 in the one-electron problem§. This property provides a useful check on the work when ƒ for the continuous spectrum is also calculated. In the present paper ƒ for the continuous spectrum is actually calculated and it is found that Σƒ = 1 to a good approximation.

Type
Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 1 , January 1929 , pp. 75 - 96
Copyright
Copyright © Cambridge Philosophical Society 1929

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

* Hartree, , Proc. Gamb. Phil. Soc. XXIV, 89–132 (1928). See also 426–437.CrossRefGoogle Scholar

† Sugiura, , Journ. de Phys. VIII, 113 (1927).Google Scholar

‡ Sugiura, , Phil. Mag. IV, 495 (1927).CrossRefGoogle Scholar

§ See London, Zeit. für Phys. XXXIX, 322 (1926).Google Scholar

* See, e.g., Richardson, , Electron Theory of Matter, ch. VIII,Google Scholar or Lorentz, , Problems of Modern Physics, p. 169et seq.Google Scholar

† Lorentz, , loc. cit., esp. equations 215, 216.Google Scholar

‡ See below, p. 79.

§ Schrödinger, , Ann. der Phys. LXXXI, 109 (1926).CrossRefGoogle Scholar

║ London, F., Zeit. f. Phys. XXXIX, 322 (1926).CrossRefGoogle Scholar

* Ladenburg, , Zeit. f. Phys. IV, 451 (1921).CrossRefGoogle Scholar Also Ladenburg, and Reiche, , Naturwiss. XI, 584 (1923).CrossRefGoogle Scholar

† Einstein, , Verh. Deuts. Physikal. Gesells. Jahrg. XVIII, 318 (1916).Google Scholar See also Phys. Zeit. XVIII, 121 (1917).Google Scholar

‡ Einstein, loc. cit.

* Dirac, , Proc. Roy. Soc. CXIV, 243 (1927).CrossRefGoogle Scholar

* Kuhn, , Zeit. f. Phys. XXXIII, 408 (1925).CrossRefGoogle Scholar Also Thomas, , Naturwiss. XIII, 627 (1925),CrossRefGoogle Scholar and Reiche, and Thomas, , Zeit. f. Phys. XXXIV, 510 (1925).CrossRefGoogle Scholar

† London, loc. cit.

‡ Kronig, and Kramers, , Zeit. f. Phys. XLVIII, 174 (1928).CrossRefGoogle Scholar

* Milne, , Phil. Mag. XLVII, 209 (1924).CrossRefGoogle Scholar

† Lorentz, loc. cit.

* Hartree, loc. cit.

† Sugiura, Journ. de Phys., loc. cit.

* Loc. cit. p. 92, equation (2·3).

* Loc. cit. pp. 111–114.

‡ Report on Series Spectra (1922).

* The equation for δε is

† The asymptotic form of the equation, viz. p″ − ∈p=0, gives a circular function as solution.

* Fues, , Ann. d. Phys. LXXXI, 281 (1926).CrossRefGoogle Scholar

* See Whittaker, and Watson, , Modern Analysis, p. 188.Google Scholar

* Hartree, , loc. cit. p. 428, equation (3·1) et seq.Google Scholar

† Whittaker, and Watson, , loc. cit. p. 343.Google Scholar

‡ Ibid p. 253.

* Loc. cit.

† Hartree, , loc. cit. p. 436.Google Scholar See also Sugiura, Journ. de Phys., loc. cit.

* Sommerfeld, , Atomic Structure and Spectral Lines, p. 448 (1923).Google Scholar

† Sugiura, Journ. de Phys., loc. cit.

* Zeit. f. Phys. L, 228 (1928).Google Scholar

† Phil. Mag., loc. cit.

† Trumpy, , Zeit. f. Phys. XLIV, 575 (1927).CrossRefGoogle Scholar

* In the figures the P's are not normalised to unity, but are taken with the arbitrary constant chosen so that, for small r, P is the same for all states of the same l, i.e. is the same for all three lines at the origin.

* I have to thank Dr R. W. Ditchburn for this information.