Unveiling nuclear energy excitations and staggering effect in the <b>γ</b>-band of the isotope chain 180−196Pt

In this study, we introduce a new model where the interaction potential explicitly depends on the energy of the system. We analytically solve the Bohr Hamiltonian incorporating an energy-dependent Killingbeck potential in the [Formula: see text]-part, employing the extended Nikiforov–Uvarov method to derive expressions for the energy eigenvalues and corresponding wave functions. With the impact of the energy dependence parameter on the standard deviation [Formula: see text] and normalized eigenenergies in the ground, [Formula: see text] and [Formula: see text] bands are examined across a wide range of platinum isotopes ([Formula: see text]Pt). Additionally, [Formula: see text] transition rates are calculated for various values of the energy dependence parameter [Formula: see text]. Our theoretical predictions show good overall agreement with experimental data and other theoretical models, as indicated by the values of [Formula: see text]. The impact of energy dependence on the spectra of triaxial nuclei is investigated and compared with results obtained using the classical Killingbeck potential. To further evaluate the degree of triaxiality, we examine characteristic signatures such as the staggering pattern in the [Formula: see text]-band. A comparable zig-zag behavior is observed around the [Formula: see text] axis, with experimental staggering patterns accurately reproduced by our model, particularly for lower values of the parameter [Formula: see text], notably at [Formula: see text].