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Register a new userReconstructed primary fragments and symmetry energy, temperature and density of the fragmenting source in $^{64}$Zn + $^{112}$Sn at 40 MeV/nucleon
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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 (AMD) 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.
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Simultaneous measurement of both neutrons and charged particles emitted in the reaction $^{64}$Zn + $^{64}$Zn at 45 MeV/nucleon allows comparison of the neutron to proton ratio at midrapidity with that at projectile rapidity. The evolution of N/Z in both rapidity regimes with increasing centrality is examined. For the completely re-constructed midrapidity material one finds that the neutron-to-proton ratio is above that of the overall $^{64}$Zn + $^{64}$Zn system. In contrast, the re-constructed ratio for the quasiprojectile is below that of the overall system. This difference provides the most complete evidence to date of neutron enrichment of midrapidity nuclear matter at the expense of the quasiprojectile.
We present a new experimental method to correlate the isotopic composition of intermediate mass fragments (IMF) emitted at mid-rapidity in semi-peripheral collisions with the emission timescale: IMFs emitted in the early stage of the reaction show larger values of $<$N/Z$>$ isospin asymmetry, stronger angular anisotropies and reduced odd-even staggering effects in neutron to proton ratio $<$N/Z$>$ distributions than those produced in sequential statistical emission. All these effects support the concept of isospin migration, that is sensitive to the density gradient between participant and quasi-spectator nuclear matter, in the so called neck fragmentation mechanism. By comparing the data to a Stochastic Mean Field (SMF) simulation we show that this method gives valuable constraints on the symmetry energy term of nuclear equation of state at subsaturation densities. An indication emerges for a linear density dependence of the symmetry energy.
We measured fragmentation cross sections produced using the primary beam of $^{86}$Kr at 64 MeV/nucleon on $^9$Be and $^{181}$Ta targets. The cross sections were obtained by integrating the momentum distributions of isotopes with 25<Z<36 measured using the RIPS fragment separator at RIKEN. The cross-section ratios obtained with the $^{181}$Ta and $^{9}$Be targets depend on the fragment masses, contrary to the simple geometrical models. We compared the extracted cross sections to EPAX; an empirical parameterization of fragmentation cross sections. Predictions from current EPAX parameterization severely overestimate the production cross sections of very neutron-rich isotopes. Attempts to obtain another set of EPAX parameters specific to the reaction studied here, to extrapolate the neutron-rich nuclei more accurately have not been very successful, suggesting that accurate predictions of production cross sections of nuclei far from the valley of stability require information of nuclear properties which are not present in EPAX.
We analyze the production cross sections and isotopic distributions of projectile-like residues in the reactions $^{112}$Sn + $^{112}$Sn and $^{124}$Sn + $^{124}$Sn at an incident beam energy of 1 GeV/nucleon measured with the FRS fragment separator at the GSI laboratory. Calculations within the statistical multifragmentation model (SMM) for an ensemble of excited sources were performed with ensemble parameters determined previously for similar reactions at 600 MeV/nucleon. The obtained good agreement with the experiment establishes the universal properties of the excited spectator systems produced during the dynamical stage of the reaction. It is furthermore confirmed that a significant reduction of the symmetry-energy term at the freeze-out stage of reduced density and high temperature is necessary to reproduce the experimental isotope distributions. A trend of decreasing symmetry energy for large neutron-rich fragments of low excitation energy is interpreted as a nuclear-structure effect.
In the past two decades, pions created in the high density regions of heavy ion collisions have been predicted to be sensitive at high densities to the symmetry energy term in the nuclear equation of state, a property that is key to our understanding of neutron stars. In a new experiment designed to study the symmetry energy, the multiplicities of negatively and positively charged pions have been measured with high accuracy for central $^{132}$Sn+$^{124}$Sn, $^{112}$Sn+$^{124}$Sn, and $^{108}$Sn+$^{112}$Sn collisions at $E/A=270~mathrm{MeV}$ with the S$pi$RIT Time Projection Chamber. While the uncertainties of individual pion multiplicities are measured to 4%, those of the charged pion multiplicity ratios are measured to 2%. We compare these data to predictions from seven major transport models. The calculations reproduce qualitatively the dependence of the multiplicities and their ratios on the total neutron to proton number in the colliding systems. However, the predictions of the transport models from different codes differ too much to allow extraction of reliable constraints on the symmetry energy from the data. This finding may explain previous contradictory conclusions on symmetry energy constraints obtained from pion data in Au+Au system. These new results call for better understanding of the differences among transport codes, and new observables that are more sensitive to the density dependence of the symmetry energy.
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