Properties of platinum isotopes in framework of particle rotor model and IBM

We introduce a model that consists of an axially symmetric core plus two particles occupying the lowest two sublevels $i_{13/2}$ orbital. The exact solution of this model has been calculated by diagonalizing $4\times 4$ matrices. By fitting the experimental single particle spectrum in these nuclei, a new set of Nilsson parameters and deformation parameter are proposed. Since the excitation energy spectrum of the core is very difficult to simulate through any simple energy angular momentum relationship, we use the variable moment of inertia (VMI) core formalism. The calculated kinematic moment of inertia, rotational frequency and the component of angular momentum along an axis perpendicular to the symmetry axis reproduce quite well the backbending of the yrast band in ^180-192Pt. Nuclei exhibit an anomaly along the yrast line around angular momentum ${10}^{+}$ to ${12}^{+}$. An apparent change of structure occurs when transiting from ¹⁸⁶Pt to ¹⁸⁸Pt. It is more appropriate to describe Pt nuclei within the IBM Hamiltonian based on the intrinsic coherent state to generate the potential energy surfaces (PES's) to identify the shape transition. The equilibrium values of shape parameter β are obtained by minimizing the PES and also the location of the critical points are obtained. The isotopic chain ^180-192Pt evolves from prolate to oblate shapes between ¹⁸⁶Pt (prolate) and ¹⁸⁸Pt (oblate). The PES's for both ^188,190Pt are γ-soft having the minimum on the oblate side.