Nuclear spin of odd-odd $\alpha$ emitters based on the behavior of $\alpha$-particle preformation probability

The preformation probabilities of an $\alpha$ 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 $166\le A\le 215$ and $77\le Z\le 89$. The calculations are employed in the framework of the density-dependent cluster model. A realistic density-dependent nucleon-nucleon $\left(NN\right)$ interaction with a finite-range exchange part is used to calculate the microscopic $\alpha$-nucleus potential in the well-established double-folding model. The main effect of antisymmetrization under exchange of nucleons between the $\alpha$ 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 $\alpha$ particle by means of the Wentzel-Kramers-Brillouin approximation in combination with the Bohr-Sommerfeld quantization condition. The correlation of the $\alpha$-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.

Figure 1

Extracted $\alpha$-preformation probability, $S_{\alpha }$, for different Ir isotopes $\left(Z=77\right)$ with the parent neutron number $N$.

Figure 2

The same as Fig. 1 but for Au isotopes. Panel (b) presents the extracted alpha preformation factors with their uncertainties for different Au isotopes using the experimental data of Refs. [49, 50]

Figure 3

The same as Fig. 1 but for Bi isotopes.

Figure 4

The same as Fig. 1 but for At isotopes.

Figure 5

The same as Fig. 1 but for Fr isotopes.

Figure 6

The same as Fig. 1 but for Ac isotopes.

Figure 7

Deviation of the calculated partial half-lives with the corresponding experimental data for both odd-odd and odd-$A$ nuclei.