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

Abstract

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.

Excited states of odd-mass nuclei with different deformation-dependent mass coefficients

“…Exact separation of variables β and γ can be achieved for potentials using the convenient form [12] V (β, γ) = U (β) + f 2 W (γ)/β 2 , in which the potential depending only on γ has a minimum around γ = 0. In the same context, the total wave function can be constructed as…”

“…The purpose of the present work is to investigate a new generalized version of the collective quadrupole Bohr Hamiltonian with different deformation-dependent mass parameters, firstly developed in [12]. We will then propose a combination of the first and second approach mentioned above.…”

Exact solutions of deformed Schrödinger equation with a class of non-central physical potentials

“…The AIM, an increasingly popular method, has proved to be a powerful, efficient and easily handling method in the treatment of problems in physics involving Schrödinger, Klein-Gordon and Dirac equations [36][37][38][39][40][41][42][43] .…”

Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model

“…As already mentioned, the asymptotic iteration method (AIM) [10,11] has been proposed and applied [16][17][18][19][20][21] to solve the second-order homogeneous differential equation of the form…”