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

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 $k\ge 1$. 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.

submitted to J. Phys. B: At. Mol. Opt. Phys

References in corpus (2)

• Two Non-Commutative Binomial Theorems
• The Moments of the Hydrogen Atom by the Method of Brackets