Conformable fractional Bohr Hamiltonian with Bonatsos and double-well sextic potentials

Abstract

Using the conformable fractional calculus, a new formulation of the Bohr Hamiltonian is introduced. The conformable fractional energy spectra of free- and two- parameters anharmonic oscillator potentials are investigated. The energy eigenvalues and wave functions are calculated utilizing the finite-difference discretization method. It is proved that the conformable fractional spectra of the free-parameter Bonatsos potentials, close completely the gaps between the classical spectra of the vibrational dynamical symmetry, the models, and the critical point symmetry. The ground effective sextic potential, which generates both the ground state and the excited states is considered to have two degenerate minima. In this case, the conformable fractional spectra of sextic potentials show a change, as a function of barrier height, from -unstable energy level sequence to the spectrum of model and simultaneously provide new features. The shape coexistence phenomena in the ground band states are identified. The energy spectrum and shape coexistence with mixing phenomena in 96Mo nucleus are discussed in the framework of the conformable fractional Bohr Hamiltonian.