Sp(6)

Abstract

The basis states generated in the sp(6)[contains]u(3) algebra of the fermion dynamical symmetry model (FDSM) are studied. The assumption made in the FDSM that the lowest-lying states of even nuclei are states with [ital u]=0 and the largest SU(3) quantum numbers is analyzed. A pairing plus quadrupole-quadrupole interaction is diagonalized for valence nucleons of the actinide region in (i) a complete basis for two protons and two neutrons, (ii) a truncated FDSM basis for 10 protons and 14 neutrons, and (iii) a strongly-coupled FDSM basis for 24 nucleons. The existence of a multiplicity of FDSM bases is taken into account. In all cases, the overlap between the truncated FDSM subspace and the full shell model space is very small for the [ital n]-identical-particle calculations. This implies that a complicated renormalization of shell model effective interactions is required before they can be used in the individual proton and and neutron spaces. However, with the proper forced choice of proton and neutron bases, a strong proton-neutron quadrupole-quadrupole interaction drives the states with the largest possible FDSM-SU(3) quantum numbers to lie lowest in energy. This leads to a rotational band structure in actinide nuclei with excited rotational bands ordered by the FDSM-SU(3) quantummore » numbers in the strong coupling limit.« less