Nucleon pairing correlations and theαcluster preformation probability inside heavy and superheavy nuclei

Abstract

The presence of paired or unpaired protons and neutrons in the open-shell radioactive \ensuremath{\alpha} emitter affects the preformation probability of the \ensuremath{\alpha} cluster inside it. The \ensuremath{\alpha}-preformation probability inside the $\mathrm{odd}(Z)\text{\ensuremath{-}}\mathrm{even}(N)$, $\mathrm{even}(Z)\text{\ensuremath{-}}\mathrm{odd}(N)$, and $\mathrm{odd}(Z)\text{\ensuremath{-}}\mathrm{odd}(N)$ \ensuremath{\alpha} emitters is investigated. The study is restricted to those decays with no angular momentum transfer to make a precise prediction about the mere pairing effect. The extended cluster model of \ensuremath{\alpha} decay and the WKB approximation are used by taking into account the deformation degrees of freedom to carry out the calculations for 105 parent nuclei in the mass region of $A=175--289.$ The $\ensuremath{\alpha}$ + daughter interaction potential is calculated by using the Hamiltonian energy-density approach in terms of the SLy4 Skyrme-like interaction, then it is implemented to find the average decay width over the different orientations. The half-life of the decay is then estimated and employed in turn to extract the \ensuremath{\alpha}-preformation probability by taking account of errors on both the released energy and the experimental half-life time. According to the present calculations, it is found that the \ensuremath{\alpha} cluster preformation probability inside the nuclei which have unpaired nucleons is less than it would be in the neighboring nuclei of the same shell and subshell closures but have no unpaired nucleons. In particular, the effect of the single unpaired neutron in the $\mathrm{even}(Z)\text{\ensuremath{-}}\mathrm{odd}(N)$ nuclei is slightly larger than that of the single unpaired proton in the $\mathrm{odd}(Z)\text{\ensuremath{-}}\mathrm{even}(N)$ ones. The effect of the unpaired nucleons appears more clearly in the $\mathrm{odd}(Z)\text{\ensuremath{-}}\mathrm{odd}(N)$ nuclei which have both an unpaired neutron and an unpaired proton. Based on the obtained results, an empirical pairing term is added to the empirical formula [J. Phys. G 40, 105102 (2013)] that relates the \ensuremath{\alpha} cluster preformation probability to the proton and neutron numbers outside the closed shells of the parent nucleus.