Experimental reconstruction of primary hot isotopes and characteristic properties of the fragmenting source in the heavy ion reactions near the Fermi energy

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.

A novel determination of density, temperature and symmetry energy for nuclear multi-fragmentation through primary fragment yield reconstruction

For the first time primary hot isotope distributions are experimentally reconstructed in intermediate heavy ion collisions and used with antisymmetrized molecular dynamics (AMD) calculations to determine density, temperature and symmetry energy coefficient in a self-consistent manner. A kinematical focusing method is employed to reconstruct the primary hot fragment yield distributions for multifragmentation events observed in the reaction system $^{64}$Zn + $^{112}$Sn at 40 MeV/nucleon. The reconstructed yield distributions are in good agreement with the primary isotope distributions of AMD simulations. The experimentally extracted values of the symmetry energy coefficient relative to the temperature, $a_{sym}/T$, are compared with those of the AMD simulations with different density dependence of the symmetry energy term. The calculated $a_{sym}/T$ values changes according to the different interactions. By comparison of the experimental values of $a_{sym}/T$ with those of calculations, the density of the source at fragment formation was determined to be $rho /rho_{0} = (0.63 pm 0.03 )$. Using this density, the symmetry energy coefficient and the temperature are determined in a self-consistent manner as $a_{sym} = (24.7 pm 1.9) MeV$ and $T=(4.9 pm 0.2)$ MeV