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Журнал технической физики

Expression of relativistic expectation values of powers of r in terms of Clebsch-Gordan coefficients-=SUP=-*-=/SUP=-

Jean‐Christophe Pain

Published Jan 1, 2020• 0 citations
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Abstract

It is shown that, in the relativistic hydrogenic approximation, expectation values of the type < nlj|rk|nlj> can be expressed in terms of Clebsch-Gordan coefficients or 3jm symbols. This generalizes the results obtained by Varshalovich and Karpova [Opt. Spectrosc. 118, 1-5 (2015); Opt. Spektrosk. 118, 3-7 (2015)] in the non-relativistic hydrogenic case. Keywords: relativistic hydrogenic approximation, expectation values of powers of r. Clebsch-Gordan coefficents.

DOI
10.21883/os.2020.08.49704.1016-20

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It is shown that, in the relativistic hydrogenic approximation, expectation values of the type < nlj|rk|nlj> can be expressed in terms of Clebsch-Gordan coefficients or 3jm symbols. This generalizes the results obtained by Varshalovich and Karpova [Opt. Spectrosc. 118, 1-5 (2015); Opt. Spektrosk. 118, 3-7 (2015)] in the non-relativistic hydrogenic case. Keywords: relativistic hydrogenic approximation, expectation values of powers of r. Clebsch-Gordan coefficents.
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