Shell Model Theory for Light and Medium Mass Nuclei

A hybrid shell-model scheme for studying collective features of light to medium-mass nuclei is considered. The theory takes maximum advantage of Wigner's Supermultiplet Theory, wherein the complete model space is factorized into a direct product of its spatial [U(3) symmetry dominated] and its spin-isospin [U(4) symmetry dominated] parts. This co-joining of the S and T features under the U(4) symmetry is shown to lead to a simpler understanding of the collective phenomena found in light nuclei (sd shell and below) as well as medium-mass nuclei (fp and gds shells). Based upon first results of such analyses, it seems the same approach may prove to be useful when the theory is extended upward into the rare-earth and actinide regions of the Chart of the Nuclides, and quite possibly even beyond up into the domains of heavy and super-heavy nuclei. The major advantage of this hybrid approach is that it can be used to gain an excitation spectra that can be organized easily into rotational bands, while the Pauli principle and conservation of electric charge are already guaranteed from the construction of the model space. Furthermore, the model also holds a potential answer to the question of whether a shell model can reproduce realistic predictions for binding energies under a Bethe-Weizsacker-type mass formula embedded within the U(4)-driven supermultiplet scheme.