Quadrupole moment of the $\gamma$-soft $^{196}$Pt

The $^{196}$Pt nucleus is considered to be one of the best examples of the O(6) $\gamma$-soft symmetry in the Interacting Boson Model (IBM) based on energies and B(E2) values, especially the $2^+_2 \rightarrow 0^+_1 / 2^+_2 \rightarrow 2^+_1$ B(E2) ratio, which is close to the O(6) limit of 0. However, the quadrupole moment of $^{196}$Pt (and that of neighboring $^{194}$Pt) is known to be positive and sizeable, which hints at a considerable oblate deformation of the nucleus. It is impossible to describe the O(6)-like features and the nonzero quadrupole moment simultaneously within the commonly-used consistent-Q formalism in the IBM-1, in which the same quadrupole operator is used in the Hamiltonian and the E2 transition operator. Therefore, IBM-1 calculations were performed breaking the consistent-Q formalism. An alternative approach was taken in the proton-neutron version of the IBM (IBM-2), choosing different parameters for the proton and neutron quadrupole operators, thus introducing triaxiality by different deformations of the proton and neutron bodies. Work supported by US DOE grant number DE-FG02-91ER-40609 and the Perspectives on Science Program of Yale University.