Coexistence and fluctuations phenomena with Davidson-like potentials in quadrupole–octupole deformed nuclei

Abstract

The energy spectra of three types of two-dimensional potentials (we will call them ‘Davidson-like potentials’ (DLPs)), characterized by four minima separated by barriers, are investigated. The predictions for spectra and wave functions are obtained by using the nine-point finite-difference method. For these potentials, with the existence of a single configuration, a transition of spectra, as a function of barrier height, is covered from tunneling splitting modes to fluctuations phenomena, with equal peaks wave functions, crossing to the spectra of purely anharmonic oscillator potentials (AOPs). A different type of phase transition occurs when two (or more) configurations coexist. With the change of the parameters, a transition of spectra is covered from coexistence phenomena of two distinct quantum tunneling modes to fluctuations phenomena, with unequal peaks wave functions, crossing to the spectra of purely AOPs. Using DLPs, a particular application of the coherent quadrupole–octupole model to describe energy bands with alternating parity of the nuclei 100Mo, 146,148Nd, 148,150Sm, 220Ra, 220,222Rn, and 220,222Th is presented. The global parametrization of the model for the selected nuclei is achieved.

Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials

“…Moreover, the exactly separable (ES) models provide a detailed description of nuclei near to or far away from the CPSs, for example the ES-X( 5) [8] model. The most frequently used potentials include Davidson [9][10][11][12][13], Woods-Saxon [14], Sextic [15][16][17][18][19][20][21][22][23][24], Kratzer [25][26][27], Hulthen [28], and Pöschl-Teller [29].…”

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

“…However, the conformable fractional spectra of these potentials close all the gaps between the classical spectra of the 𝑈(5), 𝐸(5) − 𝛽 2𝑛 , and 𝐸( 5) models. The second potential considered in this study is the sextic potential in the 𝛽 variable [24][25][26][27][28][29][30][31][32]. It is characterized by, depending on the values of its parameters, a single spherical minimum, a deformed minimum, or simultaneous spherical and deformed minima separated by a barrier.…”