New recursion relations of matrix elements of $r^\lambda$ and $\beta r^\lambda$ between relativistic hydrogenic eigenstates

R. P. Martínez-y-Romero; H. N. Núñez-Yépez; A. L. Salas-Brito

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New recursion relations of matrix elements of $r^\lambda$ and $\beta r^\lambda$ between relativistic hydrogenic eigenstates

R. P. Martínez-y-Romero·H. N. Núñez-Yépez·A. L. Salas-Brito

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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 $\lambda$ can be any complex number as long as the corresponding term vanishes faster than $r^{-1}$ as $r \to \infty$. These formulas allow determining recursively any matrix element of radial powers --$r^\lambda$ or $\beta r^\lambda$, $\beta$ is a Dirac matrix-- in terms of the two previous consecutive elements. The results are useful in relativistic atomic calculations.

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R. P. Martínez-y-Romero, H. N. Núñez-Yépez, A. L. Salas-Brito. 2003-04-12. New recursion relations of matrix elements of $r^\lambda$ and $\beta r^\lambda$ between relativistic hydrogenic eigenstates. https://arxiv.org/abs/physics/0304049

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