This article is cited in 3 papers

Spectroscopy and physics of atoms and molecules

Expression of relativistic expectation values of powers of $r$ in terms of Clebsch–Gordan coefficients

J. C. Pain

CEA, DAM, DIF, Arpajon, France

Abstract: It is shown that, in the relativistic hydrogenic approximation, expectation values of the type $\langle nlj|r^k|nlj\rangle$ can be expressed in terms of Clebsch-Gordan coefficients or 3$jm$ symbols. This generalizes the results obtained by Varshalovich and Karpova [Opt. Spectrosc. $\mathbf{118}$, 1-5 (2015); Opt. Spektrosk. $\mathbf{118}$, 3–7 (2015)] in the non-relativistic hydrogenic case.

Keywords: relativistic hydrogenic approximation, expectation values of powers of $r$, Clebsch–Gordan coefficents.

Received: 22.01.2020
Revised: 04.04.2020
Accepted: 15.04.2020

Language: English

 English version: Optics and Spectroscopy, 2020, 128:8, 1105–1109

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