Description of the prolate nuclei within deformation-dependent mass and energy-dependent Davidson potential formalisms

In this work, we generalize our earlier formalism, which couples an energy-dependent Davidson potential with a deformation-dependent mass term, from the γ\gammaγ-unstable regime to axially symmetric, prolate-deformed nuclei, treated within the framework of the Bohr Hamiltonian. The approach is tested on a set of 62 nuclei, spanning 13 actinides and 49 rare earth isotopes. Four free parameters enter the description and are determined by a least-squares fit to measured energy spectra. We focus in particular on the N=90N = 90N=90 isotones $^{150}$Nd, $^{152}$Sm, $^{154}$Gd, and $^{156}$Dy, which are widely regarded as the prime empirical realizations of the X(5) critical point symmetry. The calculations yield a marked improvement relative to earlier treatments, most notably by correcting the well-known overestimation of β\betaβ-band-level spacings that affects the standard Davidson potential. Examining the resulting effective potentials, we identify clear fingerprints of criticality: the wells associated with the $0^+_{\beta}statesbecomedeeper,whiletheminimaofthegroundand states become deeper, while the minima of the ground and statesbecomedeeper,whiletheminimaofthegroundand\gamma$ band-head states grow more widely separated. The model further reproduces $B(E2)$ transition ratios reasonably well, albeit with some overestimation of interband transition strengths. Overall, our findings indicate that jointly incorporating energy dependence and a deformation-dependent mass provides a richer and more consistent description of collective nuclear behavior throughout transitional regions, and points toward broader applications in nuclear structure studies.