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

Dennis Bonatsos, P. E. Georgoudis, N. Minkov, D. Petrellis, and C. Quesne

Phys. Rev. C 88, 034316 – Published 18 September 2013

Abstract

The deformation-dependent mass 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 $B (E 2)$ 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.

Received 27 May 2013

DOI:https://doi.org/10.1103/PhysRevC.88.034316

Authors & Affiliations

Dennis Bonatsos¹, P. E. Georgoudis¹, N. Minkov², D. Petrellis¹, and C. Quesne³

¹Institute of Nuclear and Particle Physics, National Centre for Scientific Research “Demokritos,” GR-15310 Aghia Paraskevi, Attiki, Greece
²Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, 1784 Sofia, Bulgaria
³Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229,Boulevard du Triomphe, B-1050 Brussels, Belgium

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Vol. 88, Iss. 3 — September 2013

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Images

Figure 1
The Kratzer (left) and Davidson (right) potentials. The quantities shown are dimensionless, while all free parameters have been set equal to unity for the sake of simplicity.Reuse & Permissions
Figure 2
Effective potentials [Eq. (23)] for $L = 4$ for some Xe (a) and Ba (b) isotopes, corresponding to the parameters of Table . The quantities shown are dimensionless. Rescaling has been carried out, according to Appendix , using the rescaling parameters $A$ given in Table . The rescaled effective potentials are given by Eq. (G17), while the rescaled abscissa, $\tilde{β}$ , is given by Eq. (G1).Reuse & Permissions
Figure 3
Dependence of the effective potentials of Eq. (23) on the parameter $a$ (a) and on the angular momentum $L$ (b). The quantities shown are dimensionless. The effective potential for the $L = 4$ state of the ground-state band of $^{130}$ Xe (corresponding to the parameters of Table ), plotted in both panels, is used as the basis of the comparison. Rescaling has been carried out, according to Appendix , using the rescaling parameters $A$ given in Table . The rescaled effective potentials are given by Eq. (G17), while the rescaled abscissa, $\tilde{β}$ , is given by Eq. (G1).Reuse & Permissions
Figure 4
Effective potentials [Eq. (23)] for $L = 4$ for some Gd (a) and Dy (b) isotopes, corresponding to the parameters of Table . The quantities shown are dimensionless. Rescaling has been carried out, according to Appendix , using the rescaling parameters $A$ given in Table . The rescaled effective potentials are given by Eq. (G17), while the rescaled abscissa, $\tilde{β}$ , is given by Eq. (G1).Reuse & Permissions
Figure 5
Effective potentials [Eq. (23)] for $L = 4$ for the $N = 90$ isotones being good examples of the X(5) critical point symmetry, corresponding to the parameters of Table . The quantities shown are dimensionless. Rescaling has been carried out, according to Appendix , using the rescaling parameters $A$ given in Table . The rescaled effective potentials are given by Eq. (G17), while the rescaled abscissa, $\tilde{β}$ , is given by Eq. (G1).Reuse & Permissions
Figure 6
Dependence of the effective potentials of Eq. (23) on the parameter $a$ (a) and on the angular momentum $L$ (b). The quantities shown are dimensionless. The effective potential for the $L = 4$ state of the ground-state band of $^{154}$ Gd (corresponding to the parameters of Table ), plotted in both panels, is used as the basis of the comparison. Rescaling has been carried out, according to Appendix , using the rescaling parameters $A$ given in Table . The rescaled effective potentials are given by Eq. (G17), while the rescaled abscissa, $\tilde{β}$ , is given by Eq. (G1).Reuse & Permissions

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