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

Details New recursion relations of matrix elements of $r^λ$ and $β r^λ$ between relativistic hydrogenic eigenstates New recursion relations of matrix elements of $r^λ$ and $β r^λ$ between relativistic hydrogenic eigenstates

2003-04-12

arxiv.org/abs/physics/0304049v1

Physics

Atomic Physics

16 pages, no figures

Scientific paper

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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