Measurements of the density dependence of the symmetry free energy in low-density clustered matter have been extended using the Neutron Ion Multidetector for Reaction Oriented Dynamics at Texas A&M University. Thermal coalescence models were employed to extract densities $\mathrm{<ruby><rb>\rho </rb><rt>ろー</rt></ruby>}$ and temperatures $T$ for evolving systems formed in collisions of 47$A$ MeV ${}^{40}$Ar+${}^{112}$Sn,${}^{124}$Sn and ${}^{64}$Zn+${}^{112}$Sn, ${}^{124}$Sn. Densities of $0.03⩽\mathrm{<ruby><rb>\rho </rb><rt>ろー</rt></ruby>}/{\mathrm{<ruby><rb>\rho </rb><rt>ろー</rt></ruby>}}_0⩽0.2$ and temperatures in the range 5–10 MeV have been sampled. The symmetry free energy coefficients are found to be in good agreement with values calculated using a quantum statistical model. Values of the corresponding symmetry free energy coefficient are derived from the data using entropies derived from the model.

• Received 22 October 2011

DOI:https://doi.org/10.1103/PhysRevC.85.064618