  Experimental data indicate that the mass tensor of collective Bohr
Hamiltonian cannot be considered as a constant but should be considered as a
function of the collective coordinates. In this work our purpose is to
investigate the properties of low-lying collective states of the odd nuclei
$^{173}$Yb and $^{163}$Dy by using a new generalized version of the collective
quadrupole Bohr Hamiltonian with deformation-dependent mass coefficients. The
proposed new version of the Bohr Hamiltonian is solved for Davidson potential
in $\beta$ shape variable, while the $\gamma$ potential is taken to be equal to
the harmonic oscillator. The obtained results of the excitation energies and
B(E2) reduced transition probabilities show an overall agreement with the
experimental data. Moreover, we investigate the effect of the deformation
dependent mass parameter on energy spectra and transition rates in both cases,
namely: when the mass coefficients are different and when they are equal.
Besides, we will show the positive effect of the present formalism on the
moment of inertia.
