Analytic Approach to Electron Correlation in Atoms

Abstract

A novel perturbative treatment of electron correlation in N-electron atoms is devised. The unperturbed starting point is a central-force “hydrogenic” problem in the full dN-dimensional configuration space (d = dimensionality). The central potential in this solvable “hydrogenic” problem is obtained by averaging the actual electron–electron and electron–nucleus potentials over all dN − 1 hyperspherical polar angles in the configuration space. The relevant projected Green's functions are computed for the ground states of the model one-dimensional two-electron atom (with delta function interactions), as well as for the real three-dimensional helium isoelectronic sequence. The corresponding first-order wavefunctions exhibit weakly singular logarithmic behavior (at three-particle confluence) of the type first advocated by Fock. Second-order energies are evaluated for both of these two-electron problems. The basic ingredients of our hyperspherical coordinate method for three-electron atoms are displayed, in preparation for later application. Explicit suggestions are made for inclusion of singular terms in high-accuracy atomic and molecular variational wavefunctions.