Electronic wave functions IV. Some general theorems for the calculation of Schrödinger integrals between complicated vector-coupled functions for many-electron atoms

Abstract

A scheme of theorems is developed which enables an important class of integrals of the Schrödinger Hamiltonian between antisymmetric vector-coupled functions of the Russell-Saunders type to be expressed in terms of integrals corresponding to smaller numbers of electrons. These integrals form the most important class occurring in problems of atomic spectra and the structure of atoms, but only particular reduction methods have been available previously. The analysis is based on the usual commutation properties of the angular operators, but some new formal rearrangements of the couplings within integrals are made, which give the essential reduction relations. The expansions are in terms of certain coefficients denoted by V and W , which must be evaluated numerically, but the particular values of which can be used repeatedly for unlimited numbers of special cases. These relations provide an important part of a general scheme of reduction of all Schrödinger integrals.