The X(3) model for the modified Davidson potential in a variational approach

Abstract

In this work, we investigate the [Formula: see text]-rigid version of Bohr–Hamiltonian for the modified Davidson potential. Since the corresponding wave equation cannot be solved analytically, we apply the variational method. The related wave function, energy spectra and transition rates are determined. In order to evaluate our results, we fit the formula for the energy spectra to the available experimental data for some nuclei and compare the obtained standard error with the corresponding one in other similar work. Moreover, we study the collective behavior of these nuclei through the evolution of two quantities [Formula: see text] and [Formula: see text] in terms of number of valence nucleons.