Algebraic realization of the quantum rotor - odd-A nuclei

An algebraic realization of the quantum rotor for non-zero spin values (integer as well as half-integer) is established by constructing a model Hamiltonian out of rotationally invariant functions of the generators of SU(3). The eigenvalues of this Hamiltonian in the leading normal-SU(3) symmetry for 25Mg and the so-called leading pseudo-SU(3) symmetries for 159Dy and 165Er are compared with the corresponding rotor results. For spinfree systems the internal symmetry group of the rotor and its SU(3) realization are known to be D2, the Vierergruppe. This symmetry extends to integral spin values, while for half-integer spins the rotor and its SU(3) realization are shown to display an internal quaternion group symmetry. The theory points to a microscopic (manyparticle shell-model) picture of nuclear rotational motion with spin degrees of freedom taken fully into account. An algebraic realization of the many-particle Nilsson model for odd-A nuclei, with the orbit-orbit and spin-orbit terms included, is given and applied to 23Na. PACS: 21.60Cs; 21.60Ev: 21.60Fw