Use of Green Functions in Atomic and Molecular Calculations. VI. The First-Order Perturbation to the Eigenfunction of the Helium-Atom Ground State

Abstract

We present an analytical expression for the first-order perturbation correction to the eigenfunction of the He-atom ground state. The expression is derived from the previously obtained He-atom Green function and it has the form of a series expansion in terms of Legendre polynomials Pn(cosθ12) where θ12 is the angle between the position vectors of the two electrons. The coefficients of the expansion, which are functions of the electron coordinates (r1, r2), are obtained in the form of integral representations.