Regular perturbation theory for two-electron atoms

Abstract

Regular perturbation theory (RPT) for the ground and excited states of two-electron atoms or ions is developed. It is shown for the first time that summation of the matrix elements from the electron–electron interaction operator over all intermediate states can be calculated in a closed form by means of the two-particle Coulomb Green’s function constructed in the Letter. It is shown that the second order approximation of RPT includes the main part of the correlation energy both for the ground and excited states. This approach can be also useful for description of two-electron atoms in external fields.