On the determination of radial electron–electron distribution functions

The problem of evaluating the radial electron–electron distribution function P 0 ( r 12 ) from the spin‐free 2‐particle density matrix P (2) ( r 1 , r 2 I r' 1 , r' 2 ) is considered in detail. The analysis is first applied to 2‐electron S ‐type functions built from l 2 configurations. For the special case l = 0, the expression for P 0 ( r 12 ) reduces to the result obtained by Coulson and Neilson. For non‐spherically symmetric states of N ‐electron atoms, the angular integrations are handled by a procedure used by Calais and Löwdin in their evaluation of atomic integrals containing functions of r 12 . Consideration is also given to the evaluation of necessary radial integrals.