The interpolation of atomic fields

Abstract

ABSTRACTZ(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.