Interaction of symbolic states in atomic structure computations

Abstract

We derive general equations for angular coefficients needed to carry out atomic structure computations using symbolic state expansions. In this new approach the energy is expressed, not in terms of kinetic energy and Slater integrals, but in terms of two-electron matrix elements, with coefficients that are independent of the one-electron quantum numbers involved in these matrix elements. Specific results are given for the matrix elements of a symmetric scalar two-body operator involving single-replacement and double-replacement symbolic states. The derivations use jj coupling, coefficients of fractional parentage for nonequivalent electrons, and diagrammatic angular momentum algebra.
Keywords: atomic structure theory, symbolic state expansion, angular momentum algebra
PACS: 31.15.-p