Symmetry energy, temperature and density at the time of the intermediate mass fragment formation are determined in a self-consistent manner, using the experimentally reconstructed primary hot isotope yields and anti-symmetrized molecular dynamics (AM
D) simulations. The yields of primary hot fragments are experimentally reconstructed for multifragmentation events in the reaction system $^{64}$Zn + $^{112}$Sn 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 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.
Subbarrier fusion of the 7Li + 12C reaction is studied using an antisymmetrized molecular dynamics model (AMD) with an after burner, GEMINI. In AMD, 7Li shows an alpha + t structure at its ground state and it is significantly deformed. Simulations ar
e made near the Coulomb barrier energies, i.e., E_{cm} = 3 - 8 MeV. The total fusion cross section of the AMD + GEMINI calculations as a function of incident energy is compared to the experimental results and both are in good agreement at E_{cm} > 3 MeV. The cross section for the different residue channels of the AMD + GEMINI at E_{cm} = 5 MeV is also compared to the experimental results.
In medium binding energies and Mott points for $d$, $t$, $^3$He and $alpha$ clusters in low density nuclear matter have been determined at specific combinations of temperature and density in low density nuclear matter produced in collisions of 47$A$
MeV $^{40}$Ar and $^{64}$Zn projectiles with $^{112}$Sn and $^{124}$Sn target nuclei. The experimentally derived values of the in medium modified binding energies are in good agreement with recent theoretical predictions based upon the implementation of Pauli blocking effects in a quantum statistical approach.
Clustering in low density nuclear matter has been investigated using the NIMROD multi-detector at Texas A&M University. Thermal coalescence modes were employed to extract densities, $rho$, and temperatures, $T$, for evolving systems formed in collisi
ons of 47 $A$ MeV $^{40}$Ar + $^{112}$Sn,$^{124}$Sn and $^{64}$Zn + $^{112}$Sn, $^{124}$Sn. The yields of $d$, $t$, $^{3}$He, and $^{4}$He have been determined at $rho$ = 0.002 to 0.032 nucleons/fm$^{3}$ and $T$= 5 to 10 MeV. The experimentally derived equilibrium constants for $alpha$ particle production are compared with those predicted by a number of astrophysical equations of state. The data provide important new constraints on the model calculations.
Measurements of the density dependence of the free symmetry energy in low density clustered matter have been extended using the NIMROD multi-detector at Texas A&M University. Thermal coalescence models were employed to extract densities, $rho$, and t
emperatures, $T$, for evolving systems formed in collisions of 47 $A$ MeV $^{40}$Ar + $^{112}$Sn,$^{124}$Sn and $^{64}$Zn + $^{112}$Sn, $^{124}$Sn. Densities of $0.03 leq rho/rho_0 leq 0.2$ and temperatures in the range 5 to 10 MeV have been sampled. The free symmetry energy coefficients are found to be in good agreement with values calculated using a quantum statistical model. Values of the corresponding symmetry energy coefficient are derived from the data using entropies derived from the model.
Isotope yields have been analyzed within the framework of a Modified Fisher Model to study the power law yield distribution of isotopes in the multifragmentation regime. Using the ratio of the mass dependent symmetry energy coefficient relative to th
e temperature, $a_{sym}/T$, extracted in previous work and that of the pairing term, $a_{p}/T$, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields have been corrected for these effects. For a given I = N - Z value, the corrected yields of isotopes relative to the yield of $^{12}C$ show a power law distribution, $Y(N,Z)/Y(^{12}C) sim A^{-tau}$, in the mass range of $1 le A le 30$ and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted $tau$ value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple de-excitation model, which the power law distribution of the primary isotopes is determined to $tau^{prim} = 2.4 pm 0.2$, suggesting that the disassembling system at the time of the fragment formation is indeed at or very near the critical point.
In their ground states, atomic nuclei are quantum Fermi liquids. At finite temperatures and low densities, these nuclei may undergo a phase change similar to, but substantially different from, a classical liquid gas phase transition. As in the classi
cal case, temperature is the control parameter while density and pressure are the conjugate variables. At variance with the classical case, in the nucleus the difference between the proton and neutron concentrations acts as an additional order parameter, for which the symmetry potential is the conjugate variable. Different ratios of the neutron to proton concentrations lead to different critical points for the phase transition. This is analogous to the phase transitions occurring in $^{4}$He-$^{3}$He liquid mixtures. We present experimental results which reveal the N/Z dependence of the phase transition and discuss possible implications of these observations in terms of the Landau Free Energy description of critical phenomena.
