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

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.Comment: 10 page

An Algebraic Pairing Model with Sp(4) Symmetry and its Deformation

A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0^+ ground states, they also have a large effect on the energies of excited states, including especially excited 0^+ states. In this article we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp_{(q)}(4) to different realizations of u_{(q)}(2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0^{+} states of even-even and odd-odd nuclei in the 1d_{3/2}, 1f_{7/2}, and 1f_{5/2}2p_{1/2}2p_{3/2}1g_{9/2} shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Sp_{q}(4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton-neutron interaction along with non-linear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0^{+} energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking, and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher-order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei.Comment: 19 pages, 5 figures minor changes; improvements to achieve a better and clearer presentation of our messages and idea

On the new quasiparticle factorization of the j-shell

The new Elliott-Evans classification scheme by means of a quasiparticle factorization of the j-shell of both protons and neutrons is developed further. The needed reduced matrix elements follow from the equivalence between quasiparticle isospins and quasiparticle quasispins. The transformation to states of good particle number n is simplified by imbedding the quasiparticle quasispins in the five-dimensional quasispin group R(5). This leads to a factoring of the transformation coefficients. One factor is independent of J and other subgroup labels of Sp(2j + 1) and carries the dependence on the subgroup labels of R(5). Simple recursion formulae are derived from which this factor can be calculated in complete generality. The second factor carries the dependence on the subgroup labels of Sp(2j + 1) and must be calculated for each j. Since it is independent of n and T it is sufficient to calculate this factor for particular (most convenient) values of n and T. A calculation of the coefficients is illustrated with for which complete tables are given. An extension of the quasiparticle factorization technique to the nuclear LST scheme is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32642/1/0000005.pd

Factorization of the j = 7/2 shell of neutrons and protons : Transformation coefficients to states of good particle number

Complete tabulations are given, for the j = 7/2 nuclear shell, of the transformation coefficients to states of good particle number needed in a new method of nuclear spectroscopy based on a quasiparticle factorization of the j-shell. The method leads to a classification scheme in which total angular momentum and isospin are good quantum numbers and in which the calculation of matrix elements can be carried out simply by standard techniques of Racah algebra, without the use of coefficients of fractional parentage and with the use of only a very small number of reduced matrix elements. These reduced matrix elements also are tabulated. A few sample calculations show how matrix elements of one- and two-body operators, single nucleon and pair creation operators, ..., can be calculated with this technique and the present tabulations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21980/1/0000389.pd