Bohr Hamiltonian with a deformation-dependent mass term for the Davidson potential

Abstract

Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for separable potentials consisting of a Davidson potential in the β variable, in the cases of γ-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. The solution, called the Deformation Dependent Mass (DDM) Davidson model, is achieved by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, reduces the rate of increase of the moment of inertia with deformation, removing a main drawback of the model.

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

“…The aim of this section is to present a theoretical background of the position-dependent effective mass formalism (PDEMF) 20,[22][23][24] . In the PDEMF, for Schrödinger equation, the mass operator …”

“…Later on, this formalism has been widely used in different fields of physics such as quantum liquids 2 , 3 H e clusters 3 , quantum wells, wires and dots 4,5 , metal clusters 6 , graded alloys and semiconductor heterostructures [7][8][9][10][11][12][13] , the dependence of energy gap on magnetic field in semiconductor nano-scale quantum rings 14 , the solid state problems with the Dirac equation 15 and others [16][17][18][19][20][21] . Recently, it has been applied to study nuclear collective states within Bohr Hamiltonian with Davidson potential and Kratzer potential [22][23][24] . The advantage of this formalism resides in its ability to enhance the numerical calculation precision of physical observables, particularly the energy spectrum.…”

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

“…Despite this small defect in the β band, as we can see in Fig. 5 the Manning-Rosen potential has proved its ability to reproduce adequately the experimental energy spectrum of 238 U in comparison with the calculated spectrum with Davison potential within the deformation dependent mass formalism (DDMF) [34] bearing in mind that the DDMF [34,35] introduces an extra fitting parameter which allows enhancing the precision of the numerical results, while our calculations have been carried out only with a constant mass parameter.…”

The X(3) model for the modified Davidson potential in a variational approach

“…This description has been achieved through its analytical 3-9 or approximated solutions. [10][11][12][13][14] Indeed, different models of this Hamiltonian, corresponding to the different dynamical symmetries, describe the various deformed nuclei. In order to obtain the best agreement with the experimental data, various potentials are inserted in these models.…”