The α decay spectroscopic factor of heavy and superheavy nuclei

Abstract

The spectroscopic factor which refers to the preformation probability of an α cluster inside parent radioactive nuclei is investigated. The study is based on the cluster model of α decay that is extended to account for the deformation degrees of freedom. The calculations are carried out for 179 even(Z)-even(N) parent nuclei in the mass region of A = 144–294. Taking into account the deformations of daughter nuclei, the semi-microscopic calculations of the α–daughter interaction potential are performed using the Hamiltonian energy density approach in terms of the SLy4 Skyrme-like effective interaction. The calculated potential is then implemented to find both the assault frequency and the penetration probability of the α particle by means of the Wentzel–Kramers–Brillouin approximation at different orientations of the deformed daughter. By averaging the obtained decay widths over different orientations, the half-lives of the mentioned α decays are then estimated. Taking into account the errors on both the released energy and the experimental half-life times, the extracted half-lives are employed in turn to deduce the α spectroscopic factor. The results show a periodic behaviour of the spectroscopic factor as a function of the charge and neutron numbers characterized by several local maxima and minima. The predicted minima are mainly related to the proton and neutron shell and subshell closures. In addition to the well-known closed shells of the nucleonic numbers 50, 82, and 126, the obtained values of the spectroscopic factor give some evidence for the presence of closed subshells of nucleonic numbers 70, 102 (104) and 152 (150). A simple formula is suggested to roughly estimate the spectroscopic factor in terms of the numbers of protons and neutrons of the parent nucleus outside its closed shells. The parameters of this formula are fitted to the deduced values of the spectroscopic factor.