Relativistic Kramers-Pasternack Recurrence Relations

Abstract

Recently we have evaluated the matrix elements $<O{r}^p>$,$where$O={1,β, i\mathbf{αn}β} $arethestandardDiracmatrixoperatorsandtheangularbracketsdenotethequantum-mechanicalaveragefortherelativisticCoulombproblem,intermsofgeneralizedhypergeometricfunctions$_{3}F_{2}(1) $ for all suitable powers and established two sets of Pasternack-type matrix identities for these integrals. The corresponding Kramers--Pasternack three-term vector recurrence relations are derived here.

12 pages, no figures Will appear as it is in Journal of Physics B: Atomic, Molecular and Optical Physics, Special Issue on Hight Presicion Atomic Physics

References in corpus (2)

• The Hahn polynomials in the nonrelativistic and relativistic Coulomb problems
• Expectation Values in Relativistic Coulomb Problems

Cited by in corpus (2)

• Coulomb expectation values in $D=3$ and $D=3-2\epsilon$ dimensions
• Expression of relativistic expectation values of powers of $r$ in terms of Clebsch-Gordan coefficients