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

Abstract

The Deformation Dependent Mass (DDM) Kratzer model is constructed by considering the Kratzer potential in a Bohr Hamiltonian, in which the mass is allowed to depend on the nuclear deformation, and solving it by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Analytical expressions for spectra and wave functions are derived for separable potentials in the cases of γ-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. 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, moderates the 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 …”

“…For this purpose and in order to find exact analytical results for Eq. (4.1) we are going to consider for the deformation function the special form 20,22 :…”

“…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.…”

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.…”

Microscopic description of energy-levels for even-even 124-134Xe isotopes

“…The ground-state band GSB with I π =0+, 2+, 4+, ..., and the negative parity band NPB with I π =1 − , 3 − , 5 − .... in even-even nuclei are interwoven, forming a single octupole band with levels characterized by I π =0+, 1−, 2+, 3−, 4+, .... [12][13][14][15][16][17]. This is an example of odd-even staggering or I=1 staggering; the latter term being due to the fact that each energy level with angular momentum I is displaced relatively to its neighbors with angular momenta I= 1 [15].…”