Contracted symplectic model with ds-shell applications
Abstract
A contracted version of the symplectic model, with the raising and lowering generators of Sp(6, R) replaced by boson creation and annihilation operators, is presented. The symmetry of this scheme is shown to be Ub(6) × Us(3) where Us(3) is the familiar 0/khω Elliott shell-model symmetry and Ub(6) is the group of the six-dimensional oscillator that is generated by bilinear products of the boson (l = 0 and 2) creation and annihilation operators. While this boson symmetry is realized in the same way as the U(6) group of the IBA model, they are different theories because in the present case the bosons are associated with intershell excitations and not intrashell ones. This scheme is also known as the U(3) boson model. Mathematical justification for the simplifying assumptions is provided through an application of the group deformation mechanism. A simple hamiltonian that takes into account the shell structure, couplings to major shells through a quadrupole-quadrupole interaction, and a residual rotor term is expressed in terms of generators of the Ub(6) × Us(3) model. Calculated excitation spectra and E2 transition strengths for the ds-shell nuclei 20Ne, 22Ne and 24Mg are compared with the available experimental numbers. © 1989.