Couplings and recouplings of four angular momenta: Alternative 9j symbols and spin addition diagrams
| Autor: | Cecilia Coletti, Ana Carla P. Bitencourt, Vincenzo Aquilanti, Robenilson F. Santos, Annalisa Marzuoli, Mirco Ragni, Frederico V. Prudente |
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| Rok vydání: | 2016 |
| Předmět: |
Physics
010308 nuclear & particles physics Organic Chemistry Structure (category theory) Binary number Semiclassical physics Fano plane 01 natural sciences Catalysis Computer Science Applications Inorganic Chemistry Theoretical physics Computational Theory and Mathematics Reaction dynamics Quantum mechanics 0103 physical sciences Angular momentum coupling Spin network Physical and Theoretical Chemistry 010306 general physics Spin (physics) |
| Zdroj: | Journal of molecular modeling. 23(4) |
| ISSN: | 0948-5023 |
| Popis: | The Wigner 9j symbols of the first kind-also known as Fano X-coefficients-serve to connect different addition schemes of four angular momenta, widely known examples being the LS and the jj couplings in atomic, molecular, and nuclear spectroscopies. Here, we also consider alternative sequences of binary couplings of four angular momenta, which are dealt through the 9j symbols of the second kind, and are explicitly given by the pentagonal (or Biedenharn-Elliott) identity. These coefficients are essential ingredients in the quantum-mechanical treatments of rotational and polarization phenomena in reaction dynamics and photoinduced processes. We also emphasize the combinatorial structure underlying the extended construction of a previously introduced truncated icosahedral "abacus", and provide extensions useful for algebraical manipulations, semiclassical interpretations, and computational applications, including all the 120 addition schemes. |
| Databáze: | OpenAIRE |
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