M. Di Toro

Reaction dynamics with exotic nuclei

Abstract We review the new possibilities offered by the reaction dynamics of asymmetric heavy-ion collisions, using stable and unstable beams. We show that it represents a rather unique tool to probe regions of highly asymmetric nuclear matter (ANM) in compressed as well as dilute phases, and to test the in-medium isovector interaction for high-momentum nucleons. The focus is on a detailed study of the symmetry term of the nuclear equation of state (EOS) in regions far away from saturation conditions but always under laboratory controlled conditions. Thermodynamic properties of ANM are surveyed starting from non-relativistic and relativistic effective interactions. In the relativistic case, the role of the isovector–scalar δ -meson is stressed. The qualitative new features of the liquid–gas phase transition, “diffusive” instability and isospin distillation, are discussed. The results of ab initio simulations of n -rich, n -poor, heavy-ion collisions, using stochastic isospin-dependent transport equations, are analyzed as a function of beam energy and centrality. The isospin dynamics plays an important role in all steps of the reaction, from prompt nucleon emissions to the final fragments. The isospin diffusion is also of large interest, due to the interplay of asymmetry and density gradients. In relativistic collisions, the possibility of a direct study of the covariant structure of the effective nucleon interaction is shown. Results are discussed for particle production, collective flows and isotransparency. Perspectives of further developments of the field, in theory as well as in experiment, are presented.

Asymmetric nuclear matter: The role of the isovector scalar channel

We try to single out some qualitative effects of coupling to a \ensuremath{\delta}-isovector-scalar meson, introduced in a minimal way in a phenomenological hadronic field theory. Results for the equation of state (EOS) and the phase diagram of asymmetric nuclear matter (ANM) are discussed. We stress the consistency of the \ensuremath{\delta}-coupling introduction in a relativistic approach. Contributions to the slope and curvature of the symmetry energy and to the neutron-proton effective mass splitting appear particularly interesting. A more repulsive EOS for neutron matter at high baryon densities is expected. Effects on the critical properties of warm ANM, mixing mechanical and chemical instabilities and isospin distillation, are also presented. The \ensuremath{\delta} influence is mostly on the isovectorlike collective response. The results are largely analytical, and this makes the physical meaning quite transparent. Implications for nuclear structure properties of drip-line nuclei and for reaction dynamics with radioactive beams are finally pointed out.

On the Lorentz structure of the symmetry energy

Abstract We investigate in detail the density dependence of the symmetry energy in a relativistic description by decomposing the isovector mean field into contributions with different Lorentz covariant properties. We find important effects of the isovector, scalar channel (i.e., δ-meson like) on the high density behavior of the symmetry energy. Applications to static properties of finite nuclei and to dynamic situations of heavy ion collisions are explored and related to each other. The nuclear structure studies show only moderate effects originating from the virtual δ meson. At variance, in heavy ion collisions one finds important contributions on the reaction dynamics arising from the different Lorentz structure of the high density symmetry energy when a scalar isovector δ field is introduced. Particularly interesting is the related neutron/proton effective mass splitting for nucleon transport effects and for resonance and particle production around the threshold. We show that the δ-like channel turns out to be essential for the production of pions, when comparing with experimental data, in particular for high momentum selections.

SPINODAL DECOMPOSITION OF LOW-DENSITY ASYMMETRIC NUCLEAR MATTER

Abstract We investigate the dynamical properties of asymmetric nuclear matter at low density. The occurrence of new instabilities, that lead the system to a dynamical fragment formation, is illustrated, discussing in particular the charge symmetry dependence of the structure of the most important unstable modes. We observe that instabilities are reduced by charge asymmetry, leading to larger size and time scales in the fragmentation process. Configurations with less asymmetric fragments surrounded by a more asymmetric gas are favoured. Interesting variances with respect to a pure thermodynamical prediction are revealed, that can be checked experimentally. All these features are deeply related to the structure of the symmetry term in the nuclear Equation of State (EOS) and could be used to extract information on the low density part of the EOS.

Fluctuations and dynamical instabilities in heavy-ion reactions

Abstract We present a new method to implement fluctuations in the mean-field dynamics. Assuming local thermal equilibrium, we calculate the fluctuation amplitude according to the statistical value and we determine the associated density variance. The method can be applied to study the role of fluctuations in both stable and unstable dynamics. While in stable cases fluctuations are only responsible for the width of the distributions around mean values, their role become crucial in unstable situations, where bifurcations occur and different reaction exit channels are possible. We illustrate this point by describing the break-up of di-nuclear systems exhibiting neck instabilities.

Relativistic effects in the search for high density symmetry energy

Abstract Intermediate energy heavy ion collisions open the unique possibility to explore the equation of state (EOS) of nuclear matter far from saturation, in particular the density dependence of the symmetry energy. Within a relativistic transport model it is shown that the isovector–scalar δ meson, which affects the high density behavior of the symmetry energy density, influences the dynamics of heavy ion collisions in terms of isospin collective flows. The effect is largely enhanced by a relativistic mechanism related to the covariant nature of the fields contributing to the isovector channel. Results for reactions induced by 132 Sn radioactive beams are presented. The elliptic flows of nucleons and light isobars appear to be quite sensitive to microscopic structure of the symmetry term, in particular for particles with large transverse momenta, since they represent an earlier emission from a compressed source. Thus future, more exclusive, experiments with relativistic radioactive beams should be able to set stringent constraints on the density dependence of the symmetry energy far from ground state nuclear matter.

Zero-temperature relaxation time. A test for the collision integral☆

Abstract The collisional relaxation time of a momentum space deformation in nuclei, corresponding to an isoscalar giant mode, is evaluated solving numerically the collision integral with a procedure based on the concept of the mean free path. We apply this procedure to solve the collision integral for two case: (a) the momentum space distribution is divided in parallel ensembles; (b) no division of the momentum space distribution in parallel ensembles is made. The results are compared to an exact calculation, in a frozen Pauli blocking prescription. We show that method (b) is in good agreement to the exact calculation. The parallel ensembles simulation tends to the exact solution for very large atomic mass numbers.

Nuclear Fragmentation: Sampling the Instabilities of Binary Systems

We derive stability conditions of asymmetric nuclear matter (ANM) and discuss the relation to mechanical and chemical instabilities of general two-component systems. We show that the chemical instability may appear as an instability of the system against isoscalarlike rather than isovectorlike fluctuations if the interaction between the two constituent species has an attractive character as in the case of ANM. This leads to a new kind of liquid-gas phase transition, of interest for fragmentation experiments with radioactive beams.

Dissipative effects in projectile fragmentation

Abstract Reaction mechanisms in intermediate energy heavy ion collisions are studied. A two-step model is proposed. Dissipative stage and abrasion stage are considered with special emphasis on the phase space configuration of the participant region. Fragmentation and damped collisions are found with their relative importance. Results are given for main observables and are compared to existing experimental data. Comparisons with other models are also discussed.

Aspects of particle production in isospin-asymmetric matter

Abstract The production/absorption rate of particles in compressed and heated asymmetric matter is studied using a Relativistic Mean Field (RMF) transport model with an isospin-dependent collision term. Just from energy conservation in the elementary production/absorption processes we expect to see a strong dependence of the yields on the basic Lorentz structure of the isovector effective interaction, due to isospin effects on the scalar and vector self-energies of the hadrons. This will be particularly evident for the ratio of the rates of particles produced with different charges: results are shown for π + / π − , K + / K 0 yields. In order to simplify the analysis we perform RMF cascade simulations in a box with periodic boundary conditions. In this way we can better pin down all such fine relativistic effects in particle production, that could likely show up even in realistic heavy ion collisions. In fact, the box properties are tuned in order to reproduce the heated dense matter formed during a nucleus–nucleus collision in the few A GeV beam energy region. In particular, K + , 0 production is expected to be directly related to the high density behaviour of the symmetry energy, since kaons are produced very early during the high density stage of the collision and their mean free path is rather large. We show that the K + / K 0 ratio reflects important isospin contributions on the production rates just because of the large sensitivity around the threshold. The results are very promising for the possibility of a direct link between particle production data in exotic Heavy Ion Collisions (HIC) and the isospin-dependent part of the Equation of State (EoS) at high baryon densities.