Shape phase transition in the Xe and Ba isotope chains with the sextic oscillator potential

Exact analytical solutions for the low-lying eigenfunctions and eigenvalues of the Bohr Hamiltonian using a sextic potential were presented recently in J. Phys. G: Nucl. Part. Phys. 48, 085102 (2021). Here, they are applied to describe even-even Xe and Ba isotopes with mass numbers from A = 124 to 134 and A = 126 to 136, respectively. The aim of this study is to investigate the possible transition in these isotopic chains from deformed \(\gamma \)-independent to spherical shape phases. For this purpose, a detailed analysis of each isotope, including excitation energies and B(E2) transition rates, is presented. Special attention is paid to transitions from the first two excited \(0^+\) levels to the \(2^+_1\) and \(2^+_2\) levels, as these transitions assume different values for vibrating spherical and deformed nuclei, offering insights into possible shape phase transitions. The three parameters of the Hamiltonian have been determined using a weighted least squares fit procedure. This produces the corresponding energy surface for each isotope. This analysis shows that all studied isotopes are deformed, with moderate deformations, except for the heaviest studied isotope in each isotopic chain, which is calculated to be spherical. In addition to energy excitations and B(E2) transitions, other observables such as nuclear radii are also calculated.