Experimental determination of the symmetry energy of a low density nuclear gas

Experimental analyses of moderate-temperature nuclear gases produced in the violent collisions of 35 MeV/nucleon $^{64}\mathrm{Zn}$ projectiles with $^{92}\mathrm{Mo}$ and $^{197}\mathrm{Au}$ target nuclei reveal a large degree of \ensuremath{\alpha} particle clustering at low densities. For these gases, temperature- and density-dependent symmetry energy coefficients have been derived from isoscaling analyses of the yields of nuclei with $A\ensuremath{\leqslant}4$. At densities of 0.01 to 0.05 times the ground-state density of symmetric nuclear matter, the temperature- and density-dependent symmetry energies range from 9.03 to 13.6 MeV. This is much larger than those obtained in mean-field calculations and reflects the clusterization of low-density nuclear matter. The results are in quite reasonable agreement with calculated values obtained with a recently proposed virial equation of state calculation.