Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-07-06T19:17:36.507Z Has data issue: false hasContentIssue false
  • English
  • Français

The interpolation of atomic fields

Published online by Cambridge University Press:  24 October 2008

E. Cicely Ridley
E. Cicely Ridley
Affiliation:
The University Mathematical Laboratory*Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Z(nl; r) is the contribution to Z(r) from an electron in the (nl) wave function. The Z(nl; r) vary systematically with atomic number and, as N becomes large, tend to the corresponding hydrogen-like functions, ZH(nl; r). A two-parameter method of fitting the Z(nl; r) to the ZH(nl; r) is described. This involves a ‘screening constant’ and a ‘slope constant’, both of which are defined. From published data, the two parameters have been obtained as functions of atomic number. The parameters for an unsolved atom can then be found by interpolation and approximate Z(nl; r) derived by appropriate adjustment of the functions for the nearest atom in the periodic table for which they are known. The method has been tested by interpolating for the (3d) function between Cu+ and Rb+ and by preparing estimates of the Z(nl; r) for the unknown structure Mo+. The results were good for all but Z(4d; r) for Mo+, where the number of values of the screening and slope constants already known was insufficient for reliable interpolation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 4 , October 1955 , pp. 693 - 701
Copyright
Copyright © Cambridge Philosophical Society 1955

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)Condon, E. U. and Shortley, G. H.The theory of atomic spectra (Cambridge, 1953), chap. V, 2, p. 114.Google Scholar
(2)Hartree, D. R.The calculation of atomic structures. Rep. Progr. Phys. 11 (1948), 113.Google Scholar
(3)Hartree, D. R.The interpolation of atomic wave functions. Proc. Camb. phil. Soc. 51 (1955), 684.CrossRefGoogle Scholar
(4)Henry, W. G.The self-consistent field for Au+. Proc. phys. Soc. A, 67 (1954), 789.CrossRefGoogle Scholar
(5)Ridley, E. C.The self-consistent field for Mo+. Proc. Camb. phil. Soc. 51 (1955), 702.CrossRefGoogle Scholar