Medium effects on light clusters from heavy-ion collisions within a relativistic mean-field description

TL;DR

This study probes how light nuclear clusters behave in heavy-ion collisions within a relativistic mean-field framework, focusing on in-medium modifications captured by cluster–meson couplings. Using Bayesian inference on INDRA Xe+Sn data, it tests two pictures of cluster quenching: reduced binding via $x_s$ and enhanced repulsion via $x_ omega$, finding both describe the data comparably well and revealing a robust, quasi-universal freeze-out density near $\rho \approx 0.015$ fm$^{-3}$ with a temperature-driven evolution of the couplings. The work demonstrates a degeneracy between scalar and vector channels in the RMF description, with $x_s(T)$ decreasing or $x_ omega(T)$ increasing as $T$ grows, and shows that the inferred thermodynamic parameters are resilient to the chosen RMF functional (FSU vs DD2). Estimating out-of-equilibrium effects by excluding deuterons indicates no strong evidence for non-equilibrium contributions; including deuteron data helps tighten constraints and supports a statistical-equilibrium interpretation. Overall, the findings provide a robust, model-dependent yet consistent picture of light-cluster production in low-density nuclear matter, suggesting avenues for future transport calculations to connect static fits with dynamical evolution.

Abstract

Central $^{136,124}$Xe$+^{124,112}$Sn collisions from INDRA data are analysed using a Bayesian inference on light nuclei multiplicities to estimate the thermodynamical parameters and in-medium modification of the cluster self-energies within a relativistic mean-field model. An excellent description of experimentally measured abundances of H and He isotopes is obtained. We examine two possible modelling of in-medium effects as an increased in-medium effective mass, or an increased vector repulsion. We show that these physical pictures cannot be discriminated by the data. In both cases, the temperature dependence of the meson couplings leads to a faster weakening of the light cluster abundances with temperature than previous studies predicted. Possible systematic errors due to out-of-equilibrium effects affecting the experimental abundances, are considered by repeating the Bayesian inference with reduced information. The abundance prediction of the species excluded from the constraint is well compatible with the experimental data, suggesting that there is no a priori need of accounting for non-equilibrium effects or finite state interactions that potentially affect the deuteron yield.

Figures (15)

• Figure 1: Experimental (dots) and theoretical (bands) mass fractions for the colliding system $^{136}$Xe$+^{124}$Sn, considering the parametric form Eqs.(\ref{['eq:rho_alex_quadratic']},\ref{['eq:T_alex_quadratic']}) for the density and temperature, for the FSU RMF model, according to Ref.Alex_Thesis_2024. Both experimental dots and theoretical bands are represented with 1-$\sigma$ uncertainty.
• Figure 2: Comparison between extracted values of temperature and baryonic density, for the $^{136}$Xe$+^{124}$Sn entrance channel, performed considering: the modified ideal gas assumption from Refs.Pais2020Pais2020prl (black); density and temperature as quadratic functions of $v_{\text{surf}}$ as in Section \ref{['section:alex_quadratic_fit']} (red); the result of dividing the experimental points in two groups of low and high $v_{\text{surf}}$ performed in Section \ref{['section:intermediate_step']} (green); and the extracted density and temperature values obtained in Ref.Custodio_prl_2025 (orange). All four scenarios considered an FSU RMF model and the error bars represent 1-$\sigma$ uncertainty.
• Figure 3: Experimental (black symbols) and theoretical (bands) nuclear species mass fractions for the different colliding systems $^{136,124}$Xe$+^{124,112}$Sn and with the optimised ${\theta_1}=\{\rho_1,x_{s1},T_{4.1},T_{4.3},T_{4.5},T_{4.7},T_{4.9},T_{5.1},T_{5.3}\}$ and ${\theta_2}=\{\rho_2,x_{s2},T_{5.5},T_{5.7},T_{5.9},T_{6.1},T_{6.3},T_{6.5}\}$ parameter distributions displayed in Figs.\ref{['fig:T_vs_rho_intermediate']},\ref{['fig:fig_xs_intermediate']}, for the FSU RMF model. Both experimental black symbols and theoretical bands are represented with 2-$\sigma$ uncertainty.
• Figure 4: Bayesian estimation of the density and temperatures belonging to the parameter sets ${\theta_1}=\{\rho_1,x_{s1},T_{4.1},T_{4.3},T_{4.5},T_{4.7},T_{4.9},T_{5.1},T_{5.3}\}$ and ${\theta_2}=\{\rho_2,x_{s2},T_{5.5},T_{5.7},T_{5.9},T_{6.1},T_{6.3},T_{6.5}\}$, for each entrance channel. Note that each panel includes the results of the two different bayesian inferences on ${\theta_1}$ and ${\theta_2}$, since they consider different $v_{\text{surf}}$ bins. Each colour represents a different $v_{\text{surf}}$(cm/ns) bin and is identified on the upper left panel. For each band, the 1,2-$\sigma$ uncertainty regions are shown for the FSU RMF model.
• Figure 5: Posterior distributions histogram of the effective cluster coupling parameter $x_s$ corresponding to ${\theta_1}=\{\rho_1,x_{s1},T_{4.1},T_{4.3},T_{4.5},T_{4.7},T_{4.9},T_{5.1},T_{5.3}\}$ (solid) and ${\theta_2}=\{\rho_2,x_{s2},T_{5.5},T_{5.7},T_{5.9},T_{6.1},T_{6.3},T_{6.5}\}$ (dashed) parameter sets, for the FSU RMF model. Each colour corresponds to a different entrance channel.