Solution of the nuclear shell model by symmetry-dictated truncation

Abstract

The dynamical symmetries of the Fermion Dynamical Symmetry Model are used as a principle of truncation for the spherical shell model. Utilizing the usual principle of energy-dictated truncation to select a valence space, and symmetry-dictated truncation to select a collective subspace of that valence space, we are able to reduce the full shell model space to one of manageable dimensions with modern supercomputers, even for the heaviest nuclei. The resulting shell model then consists of diagonalizing an effective Hamiltonian within the restricted subspace.This theory is not confined to any symmetry limits, and represents a full solution of the original shell model if the appropriate effective interaction of the truncated space can be determined.As a first step in constructing that interaction, we present an empirical determination of its matrix elements for the collective subspace with no broken pairs in a representative set of nuclei with 130 ≤ A ≤ 250. We demonstrate that this effective interaction can be parameterized in terms of a few quantities varying slowly with particle number, and is capable of describing a * Review article prepared for the Journal of Physics G. Solution of the Nuclear Shell Model by Symmetry-Dictated Truncation1 broad range of low-energy observables for these nuclei. Finally we give a brief discussion of extending these methods to include a single broken collective pair.. In other fermion theories, such as the Elliott model [24] or

Universality of Symmetry and Mixed-Symmetry Collective Nuclear States

“…This procedure is carried out until a good match to the experimental spectra and a smooth trend in particle number was found for the Hamiltonian parameters. Similar calculations have been described in [16,10] and details of the present fitting process will be discussed in a forthcoming paper [17].…”