Energies of the ground, $\beta$ and $\gamma$ bands as well as the associated $B\left(E2\right)$ values are determined for each even-even isotope of the ${}^{180-196}$Pt chain by the exact solutions of some differential equations which approximate the generalized Bohr-Mottelson Hamiltonian. The emerging approaches are called the sextic and spheroidal approach (SSA), the sextic and Mathieu approach (SMA), the infinite square well and spheroidal approach (ISWSA), and the infinite square well and Mathieu approach (ISWMA). While the first three methods were formulated in some earlier papers, ISWMA is an unedited approach of this work. Numerical results are compared with those obtained with the so-called X(5) and Z(5) models. A contour plot for the probability density as function of the intrinsic dynamic deformations is given for a few states of the three considered bands with the aim of evidencing the shape evolution along the isotope chain and pointing out possible shape coexistence.

• Received 15 October 2013
• Revised 9 December 2013

DOI:https://doi.org/10.1103/PhysRevC.88.064328