Perturbation theory Z expansion for many-electron autoionising states of atomic systems. I. Calculations of the energy

Abstract

A theory for calculating energies and wavelengths using the Z-expansion technique is presented; it is suitable for degenerate autoionisation states of many-electron ions. The Hartree-Fock energy, correlation energy and relativistic corrections have been taken into account. To calculate the relativistic part the first non-zero term of the expansion in powers of Z alpha was considered, which, in fact, is described by the Breit Hamiltonian. Four-electron systems are considered as an example. Results of calculations of the wavelengths as well as the theory and numerical results for autoionisation rates and radiative transition probabilities will be given in future papers.