Constraining the symmetry energy with heavy-ion collisions and Bayesian analyses

Abstract

Efficiency corrected single ratios of neutron and proton spectra in central ${}^{112}$Sn+${}^{112}$Sn and ${}^{124}$Sn+${}^{124}$Sn collisions at 120 MeV/u are combined with double ratios to provide constraints on the density and momentum dependencies of the isovector mean-field potential. Bayesian analyses of these data reveal that the isoscalar and isovector nucleon effective masses, $m_s^{\ast }-m_v^{\ast }$ are strongly correlated. The linear correlation observed in $m_s^{\ast }-m_v^{\ast }$ yields a nearly independent constraint on the effective mass splitting $\hat{I}”m_{np}^{\ast }=(m_n^{\ast }-m_p^{\ast })/m_N=-0.05_{-0.09}^{+0.09}\hat{I}´$. The correlated constraint on the standard symmetry energy, $S_0$ and the slope, $L$ at saturation density yields the values of symmetry energy $S(\ddot{I}{}_s)=16.8_{-1.2}^{+1.2}$ MeV at a sensitive density of $\ddot{I}{}_s/\ddot{I}{}_0=0.43_{-0.05}^{+0.05}$.