Conformable Fractional Bohr Hamiltonian With Bonatsos And Double-Well Sextic Potentials

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, beta(2n)/2, close completely the gaps between the classical spectra of the vibrational U(5) dynamical symmetry, the E(5) - beta(2n) models, and the E(5) critical point symmetry. The ground effective sextic potential, which generates both the ground state and the beta excited states 0(+), 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 gamma-unstable O(6) energy level sequence to the spectrum of E(5)-beta(6) 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 Mo-96 nucleus are discussed in the framework of the conformable fractional Bohr Hamiltonian.