Universality of Symmetry and Mixed-symmetry Collective Nuclear States

The global correlation in the observed variation with mass number of the $E2$ and summed $M1$ transition strengths is examined for rare earth nuclei. It is shown that a theory of correlated $S$ and $D$ fermion pairs with a simple pairing plus quadrupole interaction leads naturally to this universality. Thus a unified and quantitative description emerges for low-lying quadrupole and dipole strengths.Comment: In press, Phys. Rev. Lett. 199

Solution of the Nuclear Shell Model by Symmetry-Dictated Truncation

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 $130\le A \le 250$. 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 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.Comment: invited paper for J. Phys. G, 57 pages, Latex, 18 figures a macro are available under request at [email protected]