Quadrupole and hexadecapole correlations in rotating nuclei studied within the single-$j$ shell model

The influence of quadrupole and hexadecapole residual interactions on rotational bands is investigated in a single-$j$ shell model. An exact shell-model diagonalization of the quadrupole-plus-hexadecapole Hamiltonian demonstrates that the hexadecapole-hexadecapole interaction can sometimes produce a staggering of energy levels in the yrast sequence; however, long and regular $\Delta I=2\mathrm{}$ sequences are not obtained. The shell-model results are discussed in terms of the intrinsic deformations extracted by means of the self-consistent Hartree-Fock method. The angular momentum dependence of intrinsic quadrupole and hexadecapole moments $Q_{2\mu }$ and $Q_{4\mu }$ is investigated.