Investigation of possible correlation betweenα-particle preformation probability and energy levels forαemitters with74≤Z≤83

Abstract

The preformation probability of an $\ensuremath{\alpha}$ cluster inside radioactive parent nuclei is investigated. The calculations are employed in the framework of the density-dependent cluster model for both even-even and odd-$A$ isotopes with $74\ensuremath{\le}Z\ensuremath{\le}83$. A realistic density-dependent nucleon-nucleon ($NN$) interaction with a finite-range exchange part is used to calculate the microscopic $\ensuremath{\alpha}$-nucleus potential in the well-established double-folding model. The main effect of antisymmetrization under exchange of nucleons between the $\ensuremath{\alpha}$ and daughter nuclei has been included in the folding model through the finite-range exchange part of the $NN$ interaction. The calculated potential is then implemented to find both the assault frequency and the penetration probability of the $\ensuremath{\alpha}$ particle by means of the Wentzel-Kramers-Brillouin approximation in combination with the Bohr-Sommerfeld quantization condition. We investigated the correlation between the $\ensuremath{\alpha}$-particle preformation probability, ${S}_{\ensuremath{\alpha}}$, and the energy levels of the parent nucleus for $\ensuremath{\alpha}$ emitters with atomic number $74\ensuremath{\le}Z\ensuremath{\le}83$. Based on the similarity in the behavior of ${S}_{\ensuremath{\alpha}}$ with the neutron number for two nuclei, we try to predict or confirm the unknown or doubted nuclear spins and parities in this mass region.