IMF production and symmetry energy in heavy ion collisions near Fermi energy

The symmetry energy at the time of the production of intermediate mass fragments (IMFs) is studied using experimentally observed IMF multiplicities combined with quantum statistical model calculations (QSM of Hahn and Stocker). The ratios of difference in chemical potentials between neutrons and protons relative to the temperature, (mu(n)-mu(p))/T, and the double ratio temperature, T, were extracted experimentally in the reactions of Zn-64,Zn-70, Ni-64+Ni-58,Ni-64, Sn-112,Sn-124, Au-197, Th-232 at 40A MeV. The extracted (mu(n)-mu(p))/T scales linearly with delta(NN), where delta(NN) is the asymmetry parameter, (N-Z)/A, of the emitting source and (mu(n)-mu(p))/T = (11.1 +/- 1.4)delta(NN)-0.21 was derived. The experimentally extracted (mu(n)-mu(p))/T and the double ratio temperatures are compared with those from the QSM calculations. The temperatures, T, and densities, rho, extracted from the (mu(n)-mu(p))/T values agreed with those from the double ratio thermometer which used the yield ratios of d, t, h and alpha particles. However the two analyses of the differential chemical potential analysis and the initial temperature analysis end up almost identical relation between T and rho. T=5.25 +/- 0.75 MeV is evaluated from the (mu(n)-mu(p))/T analysis, but no density determination was possible. From the extracted T value, the symmetry energy coefficient E-sym=14.6+3.5 MeV is determined for the emitting source of T=5.25+0.75 MeV.