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

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