Electron correlations in atomic shells. III. Algebraic form of the Hamiltonian matrix.

Abstract

The hyperspherical coordinate representation of N-electron atoms is developed and applied to simple systems. Algebraic expressions are given for Coulomb radial integrals, analogous to standard forms for spin and angular matrix elements. Numerical evaluation of the algebraic forms is tractable over a sizable range of the hyperspherical quantum numbers, as demonstrated by pilot calculations for beryllium and carbon. Correlation diagrams connecting hyperspherical and independent-electron classification schemes are presented and discussed.