Analytic Approach to Electron Correlation in Atoms

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 $\text{dN\hspace{0.17em}−\hspace{0.17em}1}$ 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.