A Perturbation Treatment of the Unrestricted Hartree-Fock Equations for the Ground State of Lithium-like Ions

The unrestricted Hartree-Fock integro-differential equations for the ground state 1s 2 2s 2 S of lithium-like ions are solved by a perturbation expansion in ascending powers of 1/ Z . The zero- and first-order functions are obtained analytically and energies up to the third order are calculated. These are compared with the corresponding expansion for the restricted Hartree-Fock energy, obtained by Linderberg (1961). Some of the difficulties in using these functions for calculating the hyperfine splitting are briefly discussed.