Favored $\alpha$-decay half-lives of odd-$A$ and odd-odd nuclei using an improved density-dependent cluster model with anisotropic surface diffuseness

We extend the improved density-dependent cluster model (DDCM+) of our recent work [Wang et al., Phys. Rev. C 105, 024327 (2022)] to study the favored $\alpha$ decays of odd-$A$ and odd-odd nuclei with $Z⩾82$. In this work, the effective $\alpha$-core interactions are determined using the double-folding potential with a realistic M3Y-Reid nucleon-nucleon interaction plus proton-proton Coulomb interaction, in which a deformation-dependent diffuseness correction is validated to address the surface anisotropy and polarization effects in nucleon density distribution. It is found that calculations within the anisotropic diffuseness would yield longer calculated $\alpha$ decay half-lives and suggest larger estimated $\alpha$-preformation factors, which is quite consistent with the conclusions obtained for the even-even $\alpha$ emitters. Meanwhile, the theoretical half-lives agree very well with the experimental data for the favored $\alpha$ decays of the odd-$A$ and odd-odd nuclei with a mean factor of 1.94 and 1.61, respectively. Remarkably, the experimental $\alpha$-decay half-life of the new thorium isotope ${}^{207}\mathrm{Th}$ [Yang et al., Phys. Rev. C 105, L051302 (2022)] is also well reproduced with a factor of about 2.50. Furthermore, we present the quantitative predictions on the favored $\alpha$-decay half-lives of ${}^{293,294}119$ and ${}^{294,295}120\alpha$-decay chains in this work, which are expected to serve as useful references for the synthesis of new isotopes in the future.

Figure 1

(a) The sum of nuclear and Coulomb potential versus the distance between the center of mass of the $\alpha$ cluster and core nucleus for the $\alpha$ decay of ${}^{253}\mathrm{Es}\to {}^{249}\mathrm{Bk}+\alpha$. The blue solid line, black dashed line, and red dot-dash line denote the total interactions at three orientation angles $\xi =0, \pi /4$, and $\pi /2$, respectively. The green dashed line at 6.739 MeV denotes the $\alpha$-decay energy of ${}^{253}\mathrm{Es}$. (b) The strength factor $\lambda \left(\xi \right)$ of double-folding nuclear potential varies with the orientation angles for the systems of ${}^{249}\mathrm{Bk}\otimes \alpha$ (blue circles), ${}^{212}\mathrm{At}\otimes \alpha$ (black squares), and ${}^{202}\mathrm{Fr}\otimes \alpha$ (red triangles), respectively.

Figure 2

The average strength factor $\langle \lambda \rangle$ over the all orientation angles versus the mass number of daughter nuclei with the choices of (a) $G=20$ and (b) $G=22$, respectively. Note the Gaussian-like fitted curves in red are to guide the eyes.

Figure 3

(a) The form factors of anisotropic diffuseness $a^{\tau }\left(\theta \right)/a_0^{\tau }$ (blue solid line) and half-density radius $R^{\tau }\left(\theta \right)/R_0^{\tau }$ (red dashed line) as a function of angle $\theta$ for ${}^{249}\mathrm{Bk}$. (b) The position and (c) the height of $\alpha$-core effective potential barrier versus the orientation angle $\xi$ for the decay channel ${}^{253}\mathrm{Es}\to {}^{249}\mathrm{Bk}+\alpha$. The theoretical results calculated with the isotropic diffuseness $a_0^{\tau }$ are denoted by the blue solid lines, while ones calculated with anisotropic diffuseness $a^{\tau }\left(\theta \right)$ are denoted by the red dashed lines in each panel.

Figure 4

The logarithmic deviations between the experimental data and the theoretical results given by DDCM+ for (a) odd-$A$ and (b) odd-odd nuclei. The black dot-dash lines in each panel correspond to the deviation between the theoretical results and the experimental data with a factor of three, while the red solid line denotes the neutron number of $N=126$. The red star in (a) denotes the logarithmic deviation of new isotope ${}^{207}\mathrm{Th}$.