Bohr Hamiltonian with an energy-dependent $\gamma$ γ -unstable Coulomb-like potential

Abstract

An exact analytical solution for the Bohr Hamiltonian with an energy dependent Coulomb-like γ-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in the asymptotic limit of the slope parameter resembles the spectral structure of the spherical vibrator, however with a different state degeneracy. The parameter free energy spectrum as well as the transition rates for this case are given in closed form and duly compared with those of the harmonic U (5) dynamical symmetry. The model wave functions are found to exhibit properties that can be associated to shape coexistence. A possible experimental realization of the model is found in few medium nuclei with a very low second 0 + state known to exhibit competing prolate, oblate and spherical shapes.

Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

“…where the energy slope parameter  must be positive definite in order to describe a physical system 27 .…”

Collective Excitations in Atomic Nuclei with Energy-Dependent Potentials.

“…Such a solution was for example given in Ref. [9]. A parameter-free energy spectrum imply the existence of a symmetry in the system.…”

Untitled

“…Model calculations for actual nuclei and comparison to experimental data were performed in Refs. [9,12] with hyperbolic and Kratzer potentials, and in Refs. [8,10,11] for the Davidson potential.…”

“…This useful feature of quantum systems can be extended by considering quasi-exactly solvable potentials [1], or inducing an energy dependence into the usually exactly solvable potentials [2,3,4]. Both these approaches were successfully used in various instances of the Bohr-Mottelson model [5,6] to describe the collective energy levels in even-even nuclei [7,8,9,10,11,12]. Here one will focus on the Bohr model solutions with energy-dependent potentials.…”