Davydov–Chaban Hamiltonian with deformation-dependent mass term for the sextic potential

This paper presents analytical expressions for spectra and wave functions derived from a Davydov–Chaban Hamiltonian, which models the collective motion of nonaxial nuclei within a sextic potential and incorporates the Deformation-Dependent Mass (DDM) formalism. The resulting solution, termed the Sextic and DDM Approach ([Formula: see text]-SDDMA), is attained through the combined application of Quasi-Exact Solvability (QES) and a Quantum Perturbation Method (QPM). Spectra and [Formula: see text] transition rates are provided for a selection of 15 nuclei: [Formula: see text]Xe, [Formula: see text]Pt and [Formula: see text]Pd, demonstrating a notable agreement with experimental data. Notably, the DDM parameter plays a crucial role in representing, for the first time, the [Formula: see text] band levels [Formula: see text] and [Formula: see text] as well as the higher levels within the natural ordering, resolving a previously identified anomaly present in all models related to the Davydov–Chaban Hamiltonian. Additionally, we explore the impact of DDM on the staggering effect of the [Formula: see text] band, moments of inertia, and shape phase transition, focusing on the prominent isotopic chains of Xe, Pt and Nd where some of the best candidates are obtained. Moreover, the DDM effect is found to facilitate the emergence of the backbending phenomenon in select nuclei in contrast with other models.