Constraints on both the symmetry energy $E_2\left({\rho }_0\right)$ and its density slope $L_2\left({\rho }_0\right)$ by cluster radioactivity

Within the density-dependent cluster model (DDCM), the decay half-lives of 22 cluster emitters are calculated by using experimental decay energies. Based on our previous study on cluster radioactivity [Phys. Rev. C 90, 064310 (2014)], not only the quadratic symmetry energy $E_2\left({\rho }_0\right)$ and its slope $L_2\left({\rho }_0\right)$ but also the quartic symmetry energy $E_4\left({\rho }_0\right)$ and its slope $L_4\left({\rho }_0\right)$ at the saturation density ${\rho }_0$ are constrained by considering the neutron skin thicknesses in the daughter nuclei. With the extracted values of $E_2\left({\rho }_0\right)$ and $L_2\left({\rho }_0\right)$, the exponent $\gamma$ of the quadratic density-dependent symmetry energy $E_2\left(\rho \right)=E_2\left({\rho }_0\right){(\rho /{\rho }_0)}^{\gamma }$ is estimated. Moreover, the symmetry energy coefficient of nuclei $a_{\mathrm{sym}}\left(A\right)$ and the ratio $\kappa$ of the surface symmetry coefficient to the volume symmetry coefficient are extracted as well.

Figure 1

Variation of the decay half-life difference ${\mathrm{\Delta }}_T$ with the proton number $Z$ of the mother nucleus.

Figure 2

Results of the symmetry energies $E_{2,4}\left({\rho }_0\right)$ and their density slopes $L_{2,4}\left({\rho }_0\right)$ constrained by cluster radioactivity.

Figure 3

Values of $a_{\mathrm{sym}}\left(A\right)=S_A=S\left({\rho }_A\right)$ at the reference density ${\rho }_A=0.1{\mathrm{fm}}^{-3}$ for the nucleus ${}^{208}\mathrm{Pb}$.