On summation of $3j$-Wigner symbols
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910912086016000 |
|---|---|
| author | Hopersky, Alexey N. Nadolinsky, Alexey M. Koneev, Rustam V. |
| author_facet | Hopersky, Alexey N. Nadolinsky, Alexey M. Koneev, Rustam V. |
| contents | 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]). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11567 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On summation of $3j$-Wigner symbols Hopersky, Alexey N. Nadolinsky, Alexey M. Koneev, Rustam V. Atomic Physics 00A81 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]). |
| title | On summation of $3j$-Wigner symbols |
| topic | Atomic Physics 00A81 |
| url | https://arxiv.org/abs/2504.11567 |