Novel energy spectra of Xenon isotope with the coupling of supersymmetric quantum mechanics and conformable fractional method

Abstract

The coupling of the quantum supersymmetric method to the critical point symmetry called [Formula: see text](5) conformable fractional critical point symmetry has been used to obtain new expressions for the energy spectrum and associated eigenwave functions. We studied the solutions of the [Formula: see text]-part of the Bohr Hamiltonian equation with this technical tool in the presence of a modified Morse and Yukawa potential. We obtained the new energy states by varying the fractional terms. We also studied the effect of this potential on the mean-square deviation and normalized eigenenergies of the ground state band, [Formula: see text]-band and [Formula: see text]-band of [Formula: see text]Xe atomic nuclei isotopes. We proved that the conformable fractional parameters allowed us to influence the nuclear interactions of nuclei, especially and improved the results of the energy spectra and quadrupole transitions of triaxial nuclei. [Formula: see text] transition rates are calculated for the latter potential. Furthermore, our numerical results are compared with experimental data and other previous works using a few indicators, namely the root mean square and the [Formula: see text]-band staggering.