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

Abstract

It is shown that, in the relativistic hydrogenic approximation, expectation values of the type $⟨n\ell j|r^k|n\ell j⟩$ 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] in the non-relativistic hydrogenic case.

submitted to "Optics ans spectroscopy"

References in corpus (4)

• Relativistic Kramers-Pasternack Recurrence Relations
• Expectation Values in Relativistic Coulomb Problems
• Mathematical Structure of Relativistic Coulomb Integrals
• Modeling penetrating collisions in the standard line broadening impact theory for hydrogen

Cited by in corpus (1)

• Some properties of Wigner $3j$ coefficients: non-trivial zeros and connections to hypergeometric functions