New sum rules for Wigner 3jm symbols: application to expectation values of hydrogenic ions
| Autor: | Pain, Jean-Christophe, Gilleron, Franck |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1361-6455/abde18 |
| Popis: | 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. Comment: submitted to J. Phys. B: At. Mol. Opt. Phys |
| Databáze: | arXiv |
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