Rotational bands from shell-model Hamiltonians

Abstract

Shell-model Hamiltonians with eigenstates forming rotational bands are considered. Such states have eigenvalues proportional to J( J+ 1) and can be projected from a Slater determinant of deformed orbitals. The latter are linear combinations of single-nucleon wave functions of j-orbits in a major shell. Conditions on matrix elements and single-nucleon energies are obtained in terms of the deformation parameters. An actual effective interaction is constructed yielding exact ground-state rotational bands for 20Ne and 24Mg which gives reasonable agreement with energies of other sd shell nuclei. Unlike the case of SU(3) symmetry, spin-orbit interaction and different single-nucleon energies can be accommodated and the procedure is not confined to oscillator major shells. Other welcome departures of our effective interaction from the SU(3) picture are the absence of rotational spectra in oxygen isotopes and that the 24Mg ground-state band is projected from a Nilsson-type deformed state with axial symmetry.