Study of odd-A nuclei with an energy-dependent $$\gamma $$-unstable harmonic-oscillator-like potential and deformation-dependent mass term

Abstract

Investigation of the Bohr Hamiltonian with Bose–Fermi dynamical symmetry is considered for odd–even nuclei near the critical point of the spherical to deformed $$\gamma $$-unstable phase transition $$[E(5|2j+1)]$$. This evaluation is modified by the energy-dependent harmonic-oscillator-like potential for $$\beta $$ part of the Hamiltonian in the presence of the deformation-dependent mass term, the spin–orbit interaction and the degeneracy-breaking terms. The Hamiltonian equation is solved using techniques of supersymmetric quantum mechanics (SUSYQM). The excitation energy spectra, the electromagnetic transition strengths, quadrupole moments and dipole moments for this case are given for $$^{191}\hbox {Ir}$$.