Vibrational and rotational excited states within a Bohr Hamiltonian with a deformation-dependent mass formalism

In a recent work [Phys. Rev. C 84, 044321 (2011)] M. J. Ermamatov and P. R. Fraser have studied rotational and vibrational excited states of axially symmetric nuclei within the Bohr Hamiltonian with different mass parameters. However, the energy formula that the authors have used contains some inaccuracies. So the numerical results they obtained seem to be controversial. In this paper, we revisit all calculations related to this problem and determine the appropriate formula for the energy spectrum. Moreover, in order to improve such calculations, we reconsider this problem within the framework of the deformation-dependent mass formalism. Also, unlike the work of Bonatsos et al. [Phys. Rev. C 83, 044321 (2011)], in which the mass parameter has not been considered, we will show the importance of this parameter and its effect on numerical predictions.