Analytical study of conformable fractional Bohr Hamiltonian with Kratzer potential

Abstract

New analytical solutions of the conformable fractional Bohr Hamiltonian appropriate for triaxial nuclei, involving the Kratzer potential in β-part of the collective nuclear potential and the steep harmonic oscillator in γ-part, are developed. The analytical expressions for energy spectra and wave functions are derived using a new algorithm of the conformable fractional Nikiforov-Uvarov method. The relationship between the conformable fractional spectra of the Kratzer potential and the spectrum of the Z(5) model is discussed. The evolution of the spectra in correspondence with the fractional derivative order and the potential parameters is investigated. The normalized calculated spectra and B(E2) transition rates are compared with the available experimental data and the existing theoretical predictions from various models. The predictions produced well the experimental data for 120,126,128,130Xe, 192,194,196Pt, and 112,114,116Pd.