Effects of differences between neutron and proton density distributions on $\alpha$-decay half-lives

The neutron skin of heavy nuclei is one of the hot topics in contemporary nuclear physics. In this article, effects of differences between neutron and proton density distributions on $\alpha$ decay are investigated. $\alpha$-decay calculations are performed within the generalized density-dependent cluster model, where the $\alpha$-core potential is determined in the double-folding model using the neutron and proton density distributions of daughter nuclei. The proton and neutron density distributions, assumed to be of two-parameter Fermi form, are constrained by the experimental nuclear charge radii as well as the neutron skin thickness of heavy nuclei. The resulting distribution of daughter nuclei results in an improved $\alpha$-core potential which is important for $\alpha$-decay calculations. It is found that the neutron skin thickness plays an important role in reducing the calculated $\alpha$-decay half-lives, implying a smaller $\alpha$ preformation factor. The calculations with neutron skin thickness show good agreement with the available experimental data for even-even nuclei including the known heaviest nuclei.

Figure 1

Schematic sketch of the total potential $V\left(r\right)=V_N\left(r\right)+V_C\left(r\right)$ between $\alpha$ particles and core nuclei for the $\alpha$ decay of ${}^{212}\mathrm{Po}$. Black solid line: the case without consideration of neutron skin thickness (i.e., $\mathrm{\Delta }{r}_{np}=0$); red dotted line: the “neutron skin-type” distribution with $\mathrm{\Delta }{r}_{np}=0.174$ fm; blue dashed line: the “neutron halo-type” distribution with $\mathrm{\Delta }{r}_{np}=0.174$ fm. Note that the $\alpha$-decay energy $Q_{\alpha }$ is indicated by dash-dotted lines and the interaction potential in the range of $r=8.0\text{–}11.5$ fm is magnified for clarity in the small figure.

Figure 2

Dependence of the theoretical $\alpha$-decay half-life of ${}^{212}\mathrm{Po}$ on the neutron skin thickness $\mathrm{\Delta }{r}_{np}$ of ${}^{208}\mathrm{Pb}$: (a) the “neutron skin-type” distribution and (b) the “neutron halo-type” distribution. Calculations are performed in the extreme cluster model (i.e., $P_{\alpha }=1$). The red zone corresponds to $\mathrm{\Delta }{r}_{np}=0.{33}_{-0.18}^{+0.16}$ fm deduced from parity-violating electron scattering [49], and the blue zone corresponds to $\mathrm{\Delta }{r}_{np}=0.15\pm 0.03{(\mathrm{stat}.)}_{-0.03}^{+001}(\mathrm{sys}.)$ fm deduced from coherent pion photoproduction cross sections [50].

Figure 3

(Top) Comparison of the calculated $\alpha$-decay half-lives with the experimental data versus the neutron number $N$ of parent nuclei, where black hollow squares denote the experimental data and red solid stars denote the calculated results. (Bottom) Logarithm of the ratio $T^{\mathrm{calc}}/T^{\mathrm{expt}}$ versus the neutron number $N$ of parent nuclei, showing the strong shell effect at the neutron magic number $N=126$.

Figure 4

Deviations of the theoretical results from the experimental $\alpha$-decay half-lives versus the neutron number of parent nuclei for the isotopic chains of Ra, Th, and U. Black squares: the case without consideration of neutron skin thickness (i.e., $\mathrm{\Delta }{r}_{np}=0$); red circles: the “neutron skin-type” distribution with $\mathrm{\Delta }{r}_{np}\ne 0$; blue triangles: the “neutron halo-type” distribution with $\mathrm{\Delta }{r}_{np}\ne 0$.