Asymmetry Effects on Nuclear Fragmentation

We show the possibility of extracting important information on the symmetry term of the Equation of State ($EOS$) directly from multifragmentation reactions using stable isotopes with different charge asymmetries. We study n-rich and n-poor $Sn + Sn$ collisions at $50AMeV$ using a new stochastic transport approach with all isospin effects suitably accounted for. For central collisions a chemical component in the spinodal instabilities is clearly seen. This effect is reduced in the neck fragmentation observed for semiperipheral collisions, pointing to a different nature of the instability. In spite of the low asymmetry tested with stable isotopes the results are showing an interesting and promising dependence on the stiffness of the symmetry term, with an indication towards an increase of the repulsion above normal density.Comment: 8 pages (Latex), 7 Postscript figures, CRIS2000 Conference, Acicastello, Italy, May 22-26, (2000), Nucl. Phys. A (in press

Symmetry energy dependence of light fragment production in heavy-ion collisions

The pre-equilibrium light cluster emission in low to intermediate energy heavy ion collisions is a way to obtain information about the density and momentum dependence of the nuclear symmetry potential, i.e. about the stiffness of the symmetry energy and the neutron-proton effective mass splitting. We study the n/p and t/3He ratios as a function of the energy of the emitted particles and find that these allow to disentangle these two aspects of the symmetry energy. The t/3He ratios are found to carry similar information as the n/p ratios, making this a promising option for experimental investigations. More n-rich systems enhance the sensitivity to the symmetry energy, while double ratios between n-rich and n-poor systems tend to reduce it

Investigation of Low-Density Symmetry Energy via Nucleon and Fragment Observables

With stochastic transport simulations we study in detail central and peripheral collisions at Fermi energies and suggest new observables, sensitive to the symmetry energy below normal density. As such we identify on one hand the isospin imbalance ratio, i.e. the relative amount of isospin equilibration in binary, peripheral reactions of nuclei with different isospin, as a function of the energy loss, which is sensitive to isospin diffusion; on the other hand the isospin asymmetry of an intermediate mass fragment (IMF) in symmetric collisions in ternary reactions, or more particularly, the ratio of the IMF to the residue asymmetry, which is sensitive to isospin migration.Comment: 6 pages, 6 figures; Contrib. to Int. Symp. on Exotic States of Nuclear Matter (EXOCT2007), Catania, Italy, June 2007, World Scientifc styl

Isospin Dynamics in Heavy Ion Collisions: from Coulomb Barrier to Quark Gluon Plasma

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this report we present a selection of new reaction observables in dissipative collisions particularly sensitive to the symmetry term of the nuclear Equation of State (Iso-EoS). We will first discuss the Isospin Equilibration Dynamics. At low energies this manifests via the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation with the symmetry term acting as a restoring force. At higher beam energies Iso-EoS effects will be seen in Imbalance Ratio Measurements, in particular from the correlations with the total kinetic energy loss. For fragmentation reactions in central events we suggest to look at the coupling between isospin distillation and radial flow. In Neck Fragmentation reactions important $Iso-EoS$ information can be obtained from the correlation between isospin content and alignement. The high density symmetry term can be probed from isospin effects on heavy ion reactions at relativistic energies (few AGeV range). Rather isospin sensitive observables are proposed from nucleon/cluster emissions, collective flows and meson production. The possibility to shed light on the controversial neutron/proton effective mass splitting in asymmetric matter is also suggested. A large symmetry repulsion at high baryon density will also lead to an "earlier" hadron-deconfinement transition in n-rich matter. A suitable treatment of the isovector interaction in the partonic EoS appears very relevant.Comment: 18 pages, 12 figures, lecture at the 2008 Erice School on Nuclear Physics, to appear in Progress in Particle and Nuclear Physic

Constraining the Symmetry Energy: A Journey in the Isospin Physics from Coulomb Barrier to Deconfinement

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this work we present a selection of reaction observables in dissipative collisions particularly sensitive to the isovector part of the interaction, i.e. to the symmetry term of the nuclear Equation of State (EoS). At low energies the behavior of the symmetry energy around saturation influences dissipation and fragment production mechanisms. We will first discuss the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation during the charge equilibration in fusion and deep-inelastic collisions. Important Iso-EOS effects are stressed. Reactions induced by unstable 132Sn beams appear to be very promising tools to test the sub-saturation Isovector EoS. New Isospin sensitive observables are also presented for deep-inelastic, fragmentation collisions and Isospin equilibration measurements (Imbalance Ratios). The high density symmetry term can be derived from isospin effects on heavy ion reactions at relativistic energies (few AGeV range), that can even allow a ``direct'' study of the covariant structure of the isovector interaction in the hadron medium. Rather sensitive observables are proposed from collective flows and from pion/kaon production. The possibility of the transition to a mixed hadron-quark phase, at high baryon and isospin density, is finally suggested. Some signatures could come from an expected ``neutron trapping'' effect. The importance of studying violent collisions with radioactive beams from low to relativistic energies is finally stressed.Comment: 15 pages, 5 figures, Int.Workshop on Nuclear Dynamics in Heavy Ion Reactions and Neutron Stars, Beijing Normal Univ. July 07, to appear in Int.Journ.Modern Physics E (2008

Isospin Dynamics in Peripheral Heavy Ion Collisions at Fermi Energies

We present a detailed study of isospin dynamics in peripheral collisions at Fermi energies. We consider symmetric and mixed collisions of (124,112)Sn isotopes at 35 and 50 AMeV to study the isospin transport between the different reaction components (residues, gas and possibly intermediate mass fragments) and, in particular, the charge equilibration in the mixed system. We evaluate the effects of drift terms due to asymmetry and density gradients, which are directly related to the poorly known value and slope of the symmetry energy below saturation density. We verify the importance of an isoscalar momentum dependence of the mean field, which is found to influence the isospin transport since it changes the reaction times. We finally suggest two observables particularly sensitive to the isovector part of the nuclear equation-of-state: the correlation between isospin equilibration and kinetic energy loss for binary events, and the isospin content of the produced mid-rapidity fragments for neck fragmentation events.Comment: 34 pages, 15 figures, Nucl.Phys. A, in pres

Transverse collective flow and midrapidity emission of isotopically identified light charged particles

The transverse flow and relative midrapidity yield of isotopically identified light charged particles (LCPs) has been examined for the 35 MeV/nucleon ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$, ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$, and ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ systems. A large enhancement of the midrapidity yield of the LCPs was observed relative to the yield near the projectile rapidity. In particular, this enhancement was increased for the more neutron-rich LCPs demonstrating a preference for the production of neutron-rich fragments in the midrapidity region. Additionally, the transverse flow of the LCPs was extracted, which provides insight into the average movement of the particles in the midrapidity region. Isotopic and isobaric effects were observed in the transverse flow of the fragments. In both cases, the transverse flow was shown to decrease with an increasing neutron content in the fragments. A clear inverse relationship between the transverse flow and the relative midrapidity yield is shown. The increased relative midrapidity emission produces a decreased transverse flow. The stochastic mean-field model was used for comparison to the experimental data. The results showed that the model was able to reproduce the general isotopic and isobaric trends for the midrapidity emission and transverse flow. The sensitivity of these observables to the density dependence of the symmetry energy was explored. The results indicate that the transverse flow and midrapidity emission of the LCPs are sensitive to the denisty dependence of the symmetry energy

Sensitivity of intermediate mass fragment flows to the symmetry energy

The NIMROD-ISiS array was used to study the transverse flow of intermediate mass fragments in 35 MeV/nucleon ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$, ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$, and ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ reactions. The intermediate mass fragment flow was previously shown to be sensitive to the density dependence of the symmetry energy. To explore the model dependence of the results, the antisymmetrized molecular dynamics, constrained molecular dynamics, and stochastic mean-field models were each compared to the experimental results to extract information on the form of the symmetry energy. The results demonstrate that sensitivity of the models to the nuclear equation of state can vary significantly based on the treatment of the nuclear dynamics. Despite the differences in the sensitivity, improved agreement with the experimental data is observed for each model with a stiff density dependence of the symmetry energy