4 particle descriptions. In conclusion, we have shown that a quantum- statistical model of nuclear matter, that includes the formation of clusters at densities below nuclear satura- tion, describes quite well the low-density symmetry en- ergy which was extracted from the analysis of heavy-ion collisions. Within such a theoretical approach the com- position and the thermodynamic quantities of nuclear matter can be modeled in a large region of densities, temperatures and asymmetries that are required, e.g., in supernova simulations. Acknowledgement : This research was supported by the DFG cluster of excellence “Origin and Structure of the Universe”, by CompStar, a Research Networking Pro- gramme of the European Science Foundation, by US De- partment of Energy contract No. DE-AC02-06CH11357 (TK) and grant No. DE-FG03-93ER40773 (Texas A& M) and by Robert A. Welch Foundation grant No. A0330 (JBN). DB acknowledges support from the Polish Min- istry for Research and Higher Education, grant No. N N 202 2318 37 and from the Russian Fund for Basic Re- search, grant No. 08-02-01003-a. that the underlying RMF model for the quasiparticle de- scription with n$_{0}$ = 0 . 149 fm $^{$_{−}$3}$, E$_{sym}$ ( n$_{0}$ ) = 32 . 73 MeV gives a reasonable behavior at high density similar to the MDI, x =0 parametrization. We thus see that our approach successfully interpolates between the cluster- ing phenomena at low density and a realistic description around normal density. In the right panel of Fig. 2 we compare to the ex- perimental results, full (red) circles (Tab. I, col. 6) in an expanded low-density region. Besides the MDI parametrization we show the QS results [8] for T =1, 4, and 8 MeV, which are in the range of the temperatures in the experiment. The QS results including cluster forma- tion agree well with the experimental data points, as seen in detail in Fig. 1. We conclude that medium-dependent cluster formation has to be considered in theoretical mod- els to obtain the low-density dependence of the symmetry energy that is observed in experiments. The temperatures and densities of columns 2 and 3 in Tab. I will be modified if medium effects on the light clusters are taken into account [24]. We have carried out a self-consistent determination of the temperatures T sc and densities n sc taking into account the medium- dependent quasiparticle energies as specified in Ref. [12] (columns 9 and 10 of Tab. I). Compared to the Albergo method results [20], the temperatures T sc are about 10 % lower. Significantly higher values are obtained for the in- ferred densities n sc which are more sensitive to the inclu- sion of medium effects. We have also calculated the free and internal symmetry energies corresponding to these self-consistent values of T sc and n sc according to Ref. [8] (columns 11 and 12 of Tab. I). These results are also shown in the right panel of Fig. 2 as open (purple) cir- cles. The resultant internal symmetry energies are 15 to 20 % higher than the QS model values for T and n given in columns 2 and 3 in Tab. I. We have restricted our present work to that region of the phase diagram where heavier clusters with A > 4 are not relevant. The generalization of the given approach to account for clusters of arbitrary size would lead to an improvement in the low-density, low-temperature re- gion when nuclear statistical equilibrium is assumed. Al- ternatively, one can introduce the formation of heavier nuclei in the presence of a nucleon and cluster gas, cf. Refs. [25, 26]. The simplest approach to model the formation of heavy clusters is to perform inhomogeneous mean-field calcu- lations in the Thomas-Fermi approximation assuming spherical Wigner-Seitz cells. 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