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

## TL;DR

This study uses heavy-ion collision data and Bayesian analysis to constrain the nuclear symmetry energy, effective mass splitting, and isovector mean-field potential, providing new insights into nuclear matter properties.

## Contribution

It introduces a Bayesian framework combining experimental ratios to simultaneously constrain symmetry energy parameters and nucleon effective masses.

## Key findings

- Effective mass splitting is nearly independent with a value of -0.05 ± 0.09.
- Symmetry energy at a specific density is constrained to 16.8 ± 1.2 MeV.
- Strong correlation found between isoscalar and isovector effective masses.

## 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, $m_s^* - m_v^*$ are strongly correlated. The linear correlation observed in $m_s^* - m_v^*$ yields a nearly independent constraint on the effective mass splitting $\Delta m_{np}^*= (m_n^*-m_p^*)/m_N = -0.05_{-0.09}^{+0.09}\delta$. The correlated constraint on the standard symmetry energy, $S_0$ and the slope, $L$ at saturation density yields the values of symmetry energy $S(\rho_s)=16.8_{-1.2}^{+1.2}$ MeV at a sensitive density of $\rho_s/\rho_0 = 0.43_{-0.05}^{+0.05}$.