  The characteristic properties of the hot nuclear matter existing at the time
of fragment formation in the multifragmentation events produced in the reaction
$^{64}$Zn + $^{112}$Sn at 40 MeV/nucleon are studied. A kinematical focusing
method is employed to determine the multiplicities of evaporated light
particles, associated with isotopically identified detected fragments. From
these data the primary isotopic yield distributions are reconstructed using a
Monte Carlo method. The reconstructed yield distributions are in good agreement
with the primary isotope distributions obtained from AMD transport model
simulations. Utilizing the reconstructed yields, power distribution, Landau
free energy, characteristic properties of the emitting source are examined. The
primary mass distributions exhibit a power law distribution with the critical
exponent, $A^{-2.3}$, for $A \geq 15$ isotopes, but significantly deviates from
that for the lighter isotopes. Landau free energy plots show no strong
signature of the first order phase transition. Based on the Modified Fisher
Model, the ratios of the Coulomb and symmetry energy coefficients relative to
the temperature, $a_{c}/T$ and $a_{sym}/T$, are extracted as a function of A.
The extracted $a_{sym}/T$ values are compared with results of the AMD
simulations using Gogny interactions with different density dependencies of the
symmetry energy term. The calculated $a_{sym}/T$ values show a close relation
to the symmetry energy at the density at the time of the fragment formation.
From this relation the density of the fragmenting source is determined to be
$\rho /\rho_{0} = (0.63 \pm 0.03 )$. Using this density, the symmetry energy
coefficient and the temperature of fragmenting source are determined in a
self-consistent manner as $a_{sym} = (24.7 \pm 3.4) MeV$ and $T=(4.9 \pm 0.2)$
MeV.
