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arXiv · 2504.11567

On summation of $3j$-Wigner symbols

Alexey N. Hopersky·Alexey M. Nadolinsky·Rustam V. Koneev
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Abstract

Within the framework of the theory of irreducible tensor operators, using well-known general analytical results for double sums ($\sum_{jm}$) of products of two $3j$-Wigner symbols, analytical expressions for single sums ($\sum_m$) for the values $j_1 = j_2 = 1$ and $j = 2$ parameters of the upper row $3j$-Wigner symbol are specified. The expressions obtained supplement the well-known analytical results of the theory of angular momentum and are in demand in solving, in particular, such problems of atomic physics as the construction of a nonrelativistic quantum theory of single and double bremsstrahlung when a photon is scattered by an atom (atomic ion) (Hopersky et al [6,7,8]) and two-photon resonance single ionization of the deep shell of an atomic ion (Hopersky et al [9]).

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Alexey N. Hopersky, Alexey M. Nadolinsky, Rustam V. Koneev. 2025-04-15. On summation of $3j$-Wigner symbols. https://arxiv.org/abs/2504.11567

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