Relativistic Kramers-Pasternack Recurrence Relations

Details Relativistic Kramers-Pasternack Recurrence Relations Relativistic Kramers-Pasternack Recurrence Relations

2009-08-20

arxiv.org/abs/0908.3021v5

Physics

Mathematical Physics

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

Scientific paper

Recently we have evaluated the matrix elements $$,$ where $O$ $={1,\beta, i\mathbf{\alpha n}\beta} $ 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 $_{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.

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