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 freeparameter Bonatsos potentials, b 2, n 2 close completely the gaps between the classical spectra of the vibrational ( ) U 5 dynamical symmetry, the ( ) b -E 5 n 2 models, and the ( ) E 5 critical point symmetry. The ground effective sextic potential, which generates both the ground state and the b 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 g-unstable ( ) O 6 energy level sequence to the spectrum of ( )-b E 5 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 96 Mo nucleus are discussed in the framework of the conformable fractional Bohr Hamiltonian. 106 Cd, 106 Mo, 108 Cd, 124 Te, 128 Xe, and 134 Ba have been identified as the empirical realizations of the ( ) E 5 .Recently, the author of the present work [21] introduced a new class of CPSs called the conformable fractional ( ) a E 5 CPS, where a is the order of the derivative in the conformable fractional BH. The analytic eigenvalue and eigenfunction solutions of conformable fractional BH (utilizing ISWP in b variable) were RECEIVED

Shape Coexistence in Even–Even Nuclei: A Theoretical Overview

“…While in the standard fractional calculus [475][476][477], fractional derivatives do not obey the familiar basic properties of derivatives, the conformable fractional derivatives [478] do obey them, thus offering obvious analytical advantages. Analytical models using conformable fractional derivatives contain an extra parameter, the order of the derivative, which allows closer approach to the data of critical nuclei [474,[479][480][481].…”