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The equation of state with light clusters for nuclear and stellar matter isdetermined using chemical equilibrium constants evaluated from the analysis ofthe recently published (Xe$+$Sn) heavy ion data, corresponding to threereactions with different isotopic contents of the emission source. The measuredmultiplicities are used to extract the thermodynamic properties, and anin-medium correction to the ideal gas internal partition function of theclusters is included in the analysis. This in-medium correction and itsrespective uncertainty are calculated via a Bayesian analysis, with the uniquehypothesis that the different nuclear species in a given sample must correspondto a unique common value for the density of the expanding source. Differentparameter sets for the correction are tested, and the effect of the radius ofthe clusters on the thermodynamics and on the chemical equilibrium constants isalso addressed. It is shown that the equilibrium constants obtained are almostindependent of the isospin content of the analysed systems. Finally, acomparison with a relativistic mean field model proves that data are consistentwith a universal in-medium correction of the scalar $\sigma$-meson coupling fornucleons bound in clusters. The obtained value, $g_s/g_s^0 = 0.92 \pm 0.02$, islarger than that obtained in a previous study not including in-medium effectsin the data analysis. This result implies a smaller effect on the bindingenergy of the clusters and, as a consequence, larger melting densities, and anincreased cluster contribution in supernova matter.

Improved method for the experimental determination of in-medium effects from heavy-ion collisions