Density slope of the symmetry energy L(ρ0) constrained by proton radioactivity

Background: Recently, the cluster radioactivity of heavy nuclei decaying to $^{208}\mathrm{Pb}$ was successfully used to constrain the density slope of the symmetry energy $L({\ensuremath{\rho}}_{0})$ at saturation density ${\ensuremath{\rho}}_{0}$.Purpose: By using well-measured experimental decay energy and half-life, proton radioactivity is proposed to further constrain $L({\ensuremath{\rho}}_{0})$ in this work.Method: From the Hugenholtz--Van Hove theorem, $L({\ensuremath{\rho}}_{0})$ is found to be directly related to the magnitude of the symmetry potential, which can be extracted from the proton radioactivity within the density-dependent cluster model.Results: By investigating the radioactivity of proton emitters with large isospin asymmetry, the value of the density slope is found to be $L({\ensuremath{\rho}}_{0})=51.8\ifmmode\pm\else\textpm\fi{}7.2$ MeV.