Attempt to link the neutron skin thickness of ${}^{208}\mathrm{Pb}$ with the symmetry energy through cluster radioactivity

Exotic cluster radioactivity is proposed to constrain neutron skin thickness of ${}^{208}\mathrm{Pb}$ and the density slope of symmetry energy $L\left({\rho }_0\right)$. Based on the density-dependent cluster model (DDCM) with the M3Y effective nucleon-nucleon interaction, the neutron skin thickness of ${}^{208}\mathrm{Pb}$ is closely related to the density slope $L\left({\rho }_0\right)$ where the cluster radioactivity serves as a link between them. The single-nucleon potential constructed from the M3Y nucleon-nucleon interaction, especially its isovector part, is found to be particularly important in determining the neutron skin in a finite nucleus and the density slope parameter $L\left({\rho }_0\right)$ in nuclear matter. The correlation between the neutron skin thickness of ${}^{208}\mathrm{Pb}$ and the density slope parameter is obtained from cluster radioactivity where the standard Fermi-form density parameterizations and the standard M3Y effective interactions are assumed in DDCM.

Figure 1

(Top) Neutron and proton density distributions of ${}^{208}\mathrm{Pb}$ with neutron skin thickness $S=0\mathrm{fm}$ (Case I) and $S=0.33\mathrm{fm}$ (Case II). (Bottom) Cluster-${}^{208}\mathrm{Pb}$ potentials for cluster emitter ${}^{222}\mathrm{Ra}$ with $S=0\mathrm{fm}$ (Case I) and $S=0.33\mathrm{fm}$ (Case II).

Figure 2

(Top) The double-folding nuclear potential $V_N\left(R\right)$ in the region from 8 to 22 fm for Case I (blue solid line) and Case II (red dotted line). (Bottom) The corresponding Coulomb barrier of cluster radioactivity for Case I (blue solid line) and Case II (red dotted line). The black dashed lines denote the decay energies for the cluster emitters.

Figure 3

The variation of cluster radioactivity half-lives of ${}^{222}\mathrm{Ra},{}^{228}\mathrm{Th},{}^{232}\mathrm{U},{}^{236}\mathrm{Pu}$, and ${}^{242}\mathrm{Cm}$ as a function of the neutron skin thickness of ${}^{208}\mathrm{Pb}$.

Figure 4

The schematic diagram of constraining the neutron skin thickness of ${}^{208}\mathrm{Pb}$ and the slope parameter $L\left({\rho }_0\right)$ by cluster radioactivity.

Figure 5

The variation of neutron skin thickness of ${}^{208}\mathrm{Pb}$ as a function of the slope parameter $L\left({\rho }_0\right)$ constrained by cluster radioactivities of ${}^{222}\mathrm{Ra},{}^{228}\mathrm{Th},{}^{232}\mathrm{U},{}^{236}\mathrm{Pu}$, and ${}^{242}\mathrm{Cm}$.

Figure 6

The density slope parameter $L\left({\rho }_0\right)$ constrained by cluster radioactivity half-lives of ${}^{222}\mathrm{Ra},{}^{228}\mathrm{Th},{}^{232}\mathrm{U},{}^{236}\mathrm{Pu}$, and ${}^{242}\mathrm{Cm}$ where the surface part contribution to the neutron skin thickness of ${}^{208}\mathrm{Pb}$ is taken into account.