Nuclear spin of odd-oddαemitters based on the behavior ofα-particle preformation probability

Abstract

The preformation probabilities of an $\ensuremath{\alpha}$ cluster inside radioactive parent nuclei for both odd-even and odd-odd nuclei are investigated. The calculations cover the isotopic chains from Ir to Ac in the mass regions $166\ensuremath{\le}A\ensuremath{\le}215$ and $77\ensuremath{\le}Z\ensuremath{\le}89$. The calculations are employed in the framework of the density-dependent cluster model. 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. The correlation of the $\ensuremath{\alpha}$-particle preformation probability and the neutron and proton level sequences of the parent nucleus as obtained in our previous work is extended to odd-even and odd-odd nuclei to determine the nuclear spin and parities. Two spin coupling rules are used, namely, strong and weak rules to determine the nuclear spin for odd-odd isotopes. This work can be a useful reference for theoretical calculation of undetermined nuclear spin of odd-odd nuclei in the future.