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Chemical constants extracted from $^{124}$Xe+ $^{124}$Sn collisions at 32AMeV are compared to the predictions of an extended Nuclear StatisticalEquilibrium model including mean-field interactions and in-medium bindingenergy shifts for the light ($Z\leq 2$) clusters. The ion species and densitydependence of the in-medium modification is directly extracted from theexperimental data. We show that the shift increases with the mass of thecluster and the density of the medium, and we provide a simple linear fit forfuture use in astrophysical simulations in the framework of the CompOSE database. The resulting mass fractions are computed in representative thermodynamicconditions relevant for supernova and neutron star mergers. A comparison to theresults of a similar analysis of the same data performed in the framework of arelativistic mean-field model shows a good agreement at low density, butsignificant discrepancies close to the Mott dissolution of clusters in thedense medium.

Binding energy shifts from heavy-ion experiments in a nuclear statistical equilibrium model