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In this work, we modify the Davydov-Chaban Hamiltonian describing thecollective motion of a $\gamma$-rigid atomic nucleus by allowing the mass todepend on nuclear deformation. Exact analytical expressions are derived forenergy spectra as well as normalized wave functions for Davidson potential. Themodel, called Z(4)-DDMD (Deformation Dependent Mass with Davidson potential),is achieved by using the Asymptotic Iteration Method (AIM). The numericalcalculations for energy spectra and B(E2) transition probabilities are comparedto the experimental data of $^{192-196}$Pt isotopes. The obtained results showan overall agreement with the experiment and an important improvement inrespect to other models.

Davydov-Chaban Hamiltonian within the formalism of deformation-dependent effective mass for Davidson potential