Constraints on both the symmetry energy E2(ρ0) and its density slope L2(ρ0) 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 ${E}_{2}({\ensuremath{\rho}}_{0})$ and its slope ${L}_{2}({\ensuremath{\rho}}_{0})$ but also the quartic symmetry energy ${E}_{4}({\ensuremath{\rho}}_{0})$ and its slope ${L}_{4}({\ensuremath{\rho}}_{0})$ at the saturation density ${\ensuremath{\rho}}_{0}$ are constrained by considering the neutron skin thicknesses in the daughter nuclei. With the extracted values of ${E}_{2}({\ensuremath{\rho}}_{0})$ and ${L}_{2}({\ensuremath{\rho}}_{0})$, the exponent $\ensuremath{\gamma}$ of the quadratic density-dependent symmetry energy ${E}_{2}(\ensuremath{\rho})={E}_{2}({\ensuremath{\rho}}_{0}){(\ensuremath{\rho}/{\ensuremath{\rho}}_{0})}^{\ensuremath{\gamma}}$ is estimated. Moreover, the symmetry energy coefficient of nuclei ${a}_{\mathrm{sym}}(A)$ and the ratio $\ensuremath{\kappa}$ of the surface symmetry coefficient to the volume symmetry coefficient are extracted as well.