An expansion method for calculating atomic properties. VIII. Transitions in the Hartree-Fock approximation

Abstract

According to Brillouin’s theorem, diagonal matrix elements of one-electron operators are given correct to first order by the Hartree-Fock approximation. Transition matrix elements of one-electron operators are not given correct to first order because of the contributions from virtual excitations involving a change in the azimuthal quantum number of the active electron but no change in the principal quantum number. The electric dipole matrix elements connecting the 1 s 2 s 1,3 S states of helium to the 1 s 2 p 1,3 P states are calculated exactly to first order in inverse powers of the nuclear charge and the differences from the Hartree-Fock approximation are shown explicitly to correspond to virtual transitions of the inner shell 1 s electron of the type 1 s — np . A generalization of the Hartree-Fock approximation is discussed which eliminates most of the first order error.