Correlation Splitting in Helium-Like Ions

Abstract

The correlation effects in the ground state of the He‐like ions are investigated by using the idea that the two electrons may occupy different orbitals in space. By using a scale factor η and a splitting parameter v, a radial function [open phi][r] is split into two different orbitals, [open phi][η(1+v)r] and [open phi][η(1—v)r], following Hylleraas [E. A. Hylleraas, Z. Physik 54, 347 (1929)], and Eckart [C. Eckart, Phys. Rev. 36, 878 (1930)]. It is shown that by using orbitals obtained by splitting a simple exponential function, a surprisingly large amount of the radial correlation energy may be taken into account, whereas an attempt to split the atomic self‐consistent field function for He led to a negative result. The lowest triplet state is also treated by using the same approach.