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arXiv · 2102.06133

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

Jean-Christophe Pain·Franck Gilleron
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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.

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Jean-Christophe Pain, Franck Gilleron. 2021-02-11. New sum rules for Wigner 3jm symbols: application to expectation values of hydrogenic ions. https://doi.org/10.1088/1361-6455/abde18

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