New sum rules for Wigner 3jm symbols: application to expectation values of hydrogenic ions

Abstract

Abstract We present new sum rules for 3jm coefficients, which involve, in addition to the usual weighting factor (2j + 1) where j is an angular momentum, the quantity [j(j + 1)] k with k ⩾ 1. The sum rules appear for instance in the statistical modeling of rotational spectra within the theory of moments, and enable one to deduce the expectation values of r k (used in the theory of Stark effect for hydrogenic ions) in parabolic coordinates from the expectation values of r k in spherical coordinates.