Recurrence relations for relativistic two centre matrix elements

Abstract

Recursion formulae are derived for the calculation of two centre matrix elements of a radial function in relativistic quantum mechanics. The recursions are obtained between not necessarily diagonal radial eigensates using arbitrary radial potentials and any radial functions. The only restriction is that the potentials have to share a common minimum. Among other things, the relations so obtained can help in evaluating relativistic corrections to transition probabilities between atomic Rydberg states.