New recursion relations of matrix elements of r^λ and βr^λ between relativistic hydrogenic eigenstates

2003/04/12 by R. P. Martı́nez-y-Romero, Martínez-y-Romero, R. P., H. N. Núñez‐Yépez +3
Physics and Astronomy · #Quantum and Classical Electrodynamics #Crystallography and Radiation Phenomena #Atomic and Molecular Physics

paper · pdf · doi:10.48550/arxiv.physics/0304049

Abstract

We determine exact recurrence relations which help in the evaluation of matrix elements of powers of the radial coordinate between Dirac relativistic hydrogenic eigenstates. The power λ can be any complex number as long as the corresponding term vanishes faster than r^-1 as r → ∞. These formulas allow determining recursively any matrix element of radial powers --r^λ or βr^λ, β is a Dirac matrix-- in terms of the two previous consecutive elements. The results are useful in relativistic atomic calculations.

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