Mean-field instabilities and cluster formation in nuclear reactions

We review recent results on intermediate mass cluster production in heavy ion collisions at Fermi energy and in spallation reactions. Our studies are based on modern transport theories, employing effective interactions for the nuclear mean-field and incorporating two-body correlations and fluctuations. Namely we will consider the Stochastic Mean Field (SMF) approach and the recently developed Boltzmann-Langevin One Body (BLOB) model. We focus on cluster production emerging from the possible occurrence of low-density mean-field instabilities in heavy ion reactions. Within such a framework, the respective role of one and two-body effects, in the two models considered, will be carefully analysed. We will discuss, in particular, fragment production in central and semi-peripheral heavy ion collisions, which is the object of many recent experimental investigations. Moreover, in the context of spallation reactions, we will show how thermal expansion may trigger the development of mean-field instabilities, leading to a cluster formation process which competes with important re-aggregation effects

Probing the Nuclear Symmetry Energy with Heavy Ion Collisions

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 an Isospin Diffusion mechanism, via Imbalance Ratio Measurements, in particular from correlations to 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 fragment isospin content, velocity and alignement correlations. The high density symmetry term can be probed from isospin effects on heavy ion reactions at relativistic energies (few AGeV range), in particular for high transverse momentum selections of the reaction products. 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. The binodal transition line of the (T,\rho_B) diagram is lowered to a region accessible through heavy ion collisions in the energy range of the new planned facilities, e.g. the FAIR/NICA projects. Some observable effects of the formation of a Mixed Phase are suggested, in particular a Neutron Trapping mechanism. The dependence of the results on a suitable treatment of the isovector part of the interaction in effective QCD Lagrangian approaches is critically discussed. We stress the interest of this study in nuclear astrophysics, in particular for supernovae explosions and neutron star structure, where the knowledge of the Iso-EoS is important at low as well as at high baryon density.Comment: 52 pages, 28 figures, topical review submitted to J. Phys. G: Nucl. Phys (IOP Latex

Reaction Dynamics with Exotic Beams

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 nonrelativistic and relativistic effective interactions. In the relativistic case the role of the isovector scalar $\delta$-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 analysed 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 iso-transparency. Perspectives of further developments of the field, in theory as well as in experiment, are presented.Comment: 167+5 pages, 77 figures, general revie

Isospin in fragment production

Based on a general approach to binary systems we show that in the low density region asymmetric nuclear matter (ANM) is unstable only against isoscalarlike fluctuations. The physical meaning of the thermodynamical chemical and mechanical instabilities is related to the inequality relations verified by the strength of interaction among different components. Relevance of these results in bulk and neck fragmentation is discussed.Comment: 8 pages, 5 Postscript figures, talk at Cortona 2002 Conference, Oct.7-Oct.12, Italy, World Scientific (in press

Spinodal instability growth in new stochastic approaches

Are spinodal instabilities the leading mechanism in the fragmentation of a fermionic system? Numerous experimental indications suggest such a scenario and stimulated much effort in giving a suitable description, without being finalised in a dedicated transport model. On the one hand, the bulk character of spinodal behaviour requires an accurate treatment of the one-body dynamics, in presence of mechanical instabilities. On the other hand, pure mean-field implementations do not apply to situations where instabilities, bifurcations and chaos are present. The evolution of instabilities should be treated in a large-amplitude framework requiring fluctuations of Langevin type. We present new stochastic approaches constructed by requiring a thorough description of the mean-field response in presence of instabilities. Their particular relevance is an improved description of the spinodal fragmentation mechanism at the threshold, where the instability growth is frustrated by the mean-field resilience.Comment: Conf. proc. IWM2014-EC, Catania, 6-9 May 201

Isospin emission and flows at high baryon density: a test of the symmetry potential

High energy Heavy Ion Collisions (HIC) are studied in order to access nuclear matter properties at high density. Particular attention is paid to the selection of observables sensitive to the poorly known symmetry energy at high baryon density, of large fundamental interest, even for the astrophysics implications. Using fully consistent transport simulations built on effective theories we test isospin observables ranging from nucleon/cluster emissions to collective flows (in particular the elliptic, squeeze out, part). The effects of the competition between stiffness and momentum dependence of the Symmetry Potential on the reaction dynamics are thoroughly analyzed. In this way we try to shed light on the controversial neutron/proton effective mass splitting at high baryon and isospin densities. New, more exclusive, experiments are suggested.Comment: 10 pages, 16 figures, new figure added, accepted for publication in Phys.Rev.