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.