Generalized q-Deformed Symplectic sp(4) Algebra for Multi-shell Applications
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.
Cite
@article{arxiv.nucl-th/0304044,
title = {Generalized q-Deformed Symplectic sp(4) Algebra for Multi-shell Applications},
author = {K. D. Sviratcheva and A. I. Georgieva and J. P. Draayer},
journal= {arXiv preprint arXiv:nucl-th/0304044},
year = {2008}
}
Comments
10 pages