Relativistic Kramers–Pasternack recurrence relations

Abstract

Recently we have evaluated the matrix elements ⟨Orp⟩, where O are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem in terms of generalized hypergeometric functions 3F2(1) for all suitable powers and established two sets of Pasternack-type matrix identities for these integrals. The corresponding Kramers–Pasternack-type three-term vector recurrence relations are derived.