  Chemical constants extracted from $^{124}$Xe+ $^{124}$Sn collisions at 32
AMeV are compared to the predictions of an extended Nuclear Statistical
Equilibrium model including mean-field interactions and in-medium binding
energy shifts for the light ($Z\leq 2$) clusters. The ion species and density
dependence of the in-medium modification is directly extracted from the
experimental data. We show that the shift increases with the mass of the
cluster and the density of the medium, and we provide a simple linear fit for
future use in astrophysical simulations in the framework of the CompOSE data
base. The resulting mass fractions are computed in representative thermodynamic
conditions relevant for supernova and neutron star mergers. A comparison to the
results of a similar analysis of the same data performed in the framework of a
relativistic mean-field model shows a good agreement at low density, but
significant discrepancies close to the Mott dissolution of clusters in the
dense medium.
