Recurrence relations for relativistic atomic matrix elements

Recurrence formulae fur arbitrary hydrogenic radial matrix elements are obt ained in the Dirac form of relativistic quantum mechanics. Our approach is inspired by the relativistic extension of the second hypervirial method tha t has been successfully employed to deduce an analogous relationship in non -relativistic quantum mechanics. We first obtain the relativistic extension of the second hypervirial and then the relativistic recurrence relation. F urthermore, we use this relation to deduce relativistic versions of the Pas ternack-Sternheimer rule and of the virial theorem.