SOLUTION OF THE NUCLEAR SHELL-MODEL BY SYMMETRY-DICTATED TRUNCATION

The dynamical symmetries of the fermion dynamical symmetry model are u sed as a principle of truncation for the spherical shell model. Utiliz ing the usual principle of energy-dictated truncation to select a vale nce space, and symmetry-dictated truncation to select a collective sub space of that valence space, we are able to reduce the full shell mode l space to one of manageable dimensions with modem supercomputers, eve n 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 determinati on of its matrix elements for the collective subspace with no broken p airs in a representative set of nuclei with 130 less than or equal to A less than or equal to 250. We demonstrate that this effective intera ction can be parametrized in terms of a few quantities varying slowly with particle number, and is capable of describing a broad range of lo w-energy observables for these nuclei. Finally we give a brief discuss ion of extending these methods to include a single broken collective p air.