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### Description

Nuclear symmetry energy, temperature and density at the time of the intermediate mass fragment formation are determined using two novel methods, i.e., a self-consistent method and a chemical potential method.

(1) In a self-consistent manner, the yields of primary hot fragments are experimentally reconstructed for multifragmentation events in the reaction system ^64Zn + ^112Sn at 40 MeV/nucleon. Using the reconstructed hot isotope yields and an improved method, based on the modified Fisher model, symmetry energy values relative to the apparent temperature, a_sym/T, are extracted. The extracted values are compared with those of the anti-symmetrized molecular dynamics (AMD) simulations, extracted in the same way as that for the experiment, with the Gogny interaction with three different density-dependent symmetry energy terms. a_sym/T values change according to the density-dependent symmetry energy terms used. Using this relation, the density of the fragmenting system is extracted first. Then symmetry energy and apparent temperature are determined in a self consistent manner in the AMD model simulations. Comparing the calculated a_sym/T values and those of the experimental values from the reconstructed yields, \rho /\rho_0 = 0.65 \pm 0.02 , a_sym = 23.1 \pm 0.6 MeV and T= 5.0 \pm 0.4 MeV are evaluated for the fragmenting system experimentally observed in the reaction studied.

(2) In the chemical potential method, ratios of differential chemical potential values relative to the temperature, (\mu_n-\mu_p)/T, extracted from isotope yields of thirteen reaction systems at 40 MeV/nucleon are compared to those of a quantum statistical model to determine the temperature and symmetry energy values of the fragmenting system. The experimental (\mu_n-\mu_p)/T values are extracted based on the Modified Fisher Model. Using the density value of \rho/\rho_0=0.56 from the previous analysis, the temperature and symmetry energy values of T=4.6 \pm 0.4 MeV and a_sym=23.6 \pm 2.1 MeV are extracted in a frame work of a quantum statistical model. These values agree well with those of the previous work, in which a self-consistent method is utilized with AMD simulations.