Bohr Hamiltonian with energy-dependent (ED) inverse square potential for \(\gamma \)-unstable nuclei

In this paper, analytical solutions of Bohr Hamiltonian for \(\gamma \)-unstable nuclei via energy-dependent (ED) inverse square potential are obtained. A linear ED potential is employed to minimize the \(\beta \)-fluctuation which occurs during the \(\beta \) collective excitation motion of the nuclei. The ED inverse square potential is shown to override the general problem associated with ED and also with the standard version of Bohr Hamiltonian without ED. The present model is well represented by \(^{118-134}\)Xe isotope chain. For \(^{132}\)Xe and \(^{134}\)Xe spectra fits, standard errors of \(\sigma =0.32\) and \(\sigma =0.13\) are recorded, respectively, compared to \(\sigma =0.42\) and \(\sigma =0.19\) from previous studies using inverse square potential without ED. Within the framework of Bohr Hamiltonian for \(\gamma \)-unstable nuclei, these results indicate that the present ED model can serve as a corrective approach to previous work using inverse square potential without energy dependence.