Primary Isotope Yields and Characteristic Properties of the Fragmenting Source in Heavy-ion Reactions near the Fermi Energies

For central collisions of $^{40}$Ca $+ ^{40}$Ca at 35 MeV/nucleon, the density and temperature of a fragmenting source have been evaluated in a self-consistent manner using the ratio of the symmetry energy coefficient relative to the temperature, $a_{sym}/T$, extracted from the yields of primary isotopes produced in antisymmetrized molecular dynamics (AMD) simulations. The $a_{sym}/T$ values are extracted from all isotope yields using an improved method based on the Modified Fisher Model (MFM). The values of $a_{sym}/T$ obtained, using different interactions with different density dependencies of the symmetry energy term, are correlated with the values of the symmetry energies at the density of fragment formation. Using this correlation, the fragment formation density is found to be $\rho/\rho_0 = 0.67 \pm 0.02$. Using the input symmetry energy value for each interaction temperature values are extracted as a function of isotope mass $A$. The extracted temperature values are compared with those evaluated from the fluctuation thermometer with a radial flow correction.