On the algebraic formulation of collective models III. The symplectic shell model of collective motion

Abstract

The symplectic model is a microscopic theory which provides a practical technique for identifying the shell configurations necessary for the description of quadrupole and monopole vibrations as well as collective rotations of the nucleus. The model is based on the non-compact symplectic algebra sp(3, R) and is a natural generalization of Elliott's su(3) model to include many major oscillator shells in addition to core excitations. It is also simultaneously the shell model adaptation of the collective rotational [ R 5] so(3), the Bohr-Mottelson cm(3) = [ R 6] sl(3) and the mass quadrupole collective MQC = [ R 6] gl(3) models. In contrast to the su(3) algebra, the sp(3, R) algebra makes no 0ħω approximations and treats all observables in the algebra exactly, thereby achieving a microscopic theory of large amplitude collective motion. The observables in the algebra include the quadrupole and monopole moments, the kinetic energy, the harmonic oscillator Hamiltonian and the angular and vibrational momenta. Numerical results are reported for 20Ne using an 8 ħω truncation and a phenomenological potential V( β, γ). Satisfactory agreement with experiment is obtained for the absolute B( E2) rates without resorting to an effective charge.