New Procedure for Evaluation of U(3) Coupling and Recoupling Coefficients
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916242085904384 |
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| author | Dang, Phong Draayer, Jerry P. Pan, Feng Becker, Kevin S. |
| author_facet | Dang, Phong Draayer, Jerry P. Pan, Feng Becker, Kevin S. |
| contents | A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group-subgroup chains is presented. While the canonical U(3)->U(2)->U(1) coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3)->SO(3) coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and hence provides faster and more accurate output of requested results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Arne Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. A C++ library built on this new methodology will be published in a complementary journal that specializes in the management and distribution of such programs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_06843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Procedure for Evaluation of U(3) Coupling and Recoupling Coefficients Dang, Phong Draayer, Jerry P. Pan, Feng Becker, Kevin S. Mathematical Physics Nuclear Theory Quantum Physics A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group-subgroup chains is presented. While the canonical U(3)->U(2)->U(1) coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3)->SO(3) coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and hence provides faster and more accurate output of requested results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Arne Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. A C++ library built on this new methodology will be published in a complementary journal that specializes in the management and distribution of such programs. |
| title | New Procedure for Evaluation of U(3) Coupling and Recoupling Coefficients |
| topic | Mathematical Physics Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2405.06843 |