Description of the isotope chain ${}^{180-196}$Pt within some solvable approaches

Abstract

Energies of the ground, $\beta$ and $\gamma$ bands as well as the associated B(E2) 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), respectively. While the first three methods were formulated in some earlier papers of the present authors, ISWMA is an inedited 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.

arXiv comment18 pages, 1 figure

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Cited by in corpus (6)

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• Bohr Hamiltonian with Hulth?en plus Ring shaped potential for triaxial nuclei
• Electric quadrupole transitions of the Bohr Hamiltonian with Manning-Rosen potential
• Bohr Hamiltonian with an energy dependent $\gamma$-unstable Coulomb-like potential
• Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential