Hexadecapole Interaction and the Delta I=4 Staggering Effect in   Rotational Bands
  A role of the multipole interaction in the description of the $\triangle I$=4 staggering phenomenon is investigated in a model consisting of a single-$j$ shell filled by identical nucleons. Exact diagonalization of the quadrupole-plus-hexadecapole Hamiltonian shows that the hexadecapole-hexadecapole interaction can produce a $\triangle I$=4 periodicity in the yrast sequence. 
K. Burzynski, P. Magierski, J. Dobaczewski, and W. Nazarewicz