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Generalized q-Deformed Symplectic sp(4) Algebra for Multi-shell Applications

K. D. Sviratcheva·A. I. Georgieva·J. P. Draayer
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Abstract

A multi-shell generalization of a fermion representation of the q-deformed compact symplectic sp_q(4) algebra is introduced. An analytic form for the action of two or more generators of the Sp_q(4) symmetry on the basis states is determined and the result used to derive formulae for the overlap between number preserving states as well as for matrix elements of a model Hamiltonian. A second-order operator in the generators of Sp_q(4) is identified that is diagonal in the basis set and that reduces to the Casimir invariant of the sp(4) algebra in the non-deformed limit of the theory. The results can be used in nuclear structure applications to calculate beta-decay transition probabilities and to provide for a description of pairing and higher-order interactions in systems with nucleons occupying more than a single-j orbital.

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K. D. Sviratcheva, A. I. Georgieva, J. P. Draayer. 2003-04-14. Generalized q-Deformed Symplectic sp(4) Algebra for Multi-shell Applications. https://doi.org/10.1088/0305-4470%2F36%2F27%2F310

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