The matrix coherent-state approach of the interacting boson model with configuration mixing is used to study the geometry of the platinum isotopes. With a parameter set determined in previous studies, it is found that the absolute minimum of the potential for the Pt isotopes evolves from spherical to oblate and finally to prolate shapes when the neutron number decreases from $N=126$ (semi-magic) to $N=104$ (mid-shell). Shape coexistence is found in the isotopes ${}^{182,184,186,188}\mathrm{Pt}$. A phase diagram is constructed that shows the coexistence region as a function of the number of bosons and the strength of the mixing parameter.

• Received 26 February 2008

DOI:https://doi.org/10.1103/PhysRevC.78.024303