arXiv subjects

M. Di Toro

Publications and source records attributed to M. Di Toro.

At least 73 records · Page 4Linked to original sources

arXiv2005

Effects of In-Medium NN Cross Sections on Particle Production

The in-medium modification of nucleon-nucleon (NN) cross sections is investigated by means of particle production in heavy ion collisions (HIC) at intermediate energies. In particular, the density dependence of the {\it inelastic} cross sections considerably affects the pion and kaon yields and their rapidity distributions. However, the $(π^{-}/π^{+})$- and $(K^{+}/K^{0})$-ratios depend only moderately on the in-medium behavior of the inelastic cross sections. It turns out that particle ratios seem to be robust observables in determining the nuclear equation of state (EoS) and, particularly, its isovector sector.

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arXiv2005

Aspects of particle production in isospin asymmetric matter

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 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 and the isospin dependent part of the Equation of State at high baryon densities.

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arXiv2005

Fast nucleon emission as a probe of the isospin momentum dependence

In this article we investigate the structure of the non-local part of the symmetry term, that leads to a splitting of the effective masses of protons and neutrons in asymmetric matter. Based on microscopic transport simulations we suggest some rather sensitive observables in collisions of neutron-rich (unstable) ions at intermediate ($RIA$) energies. In particular we focus the attention on pre-equilibrium nucleon emissions. We discuss interesting correlations between the N/Z content of the fast emitted particles and their rapidity or transverse momentum, that show a nice dependence on the prescription used for the effective mass splitting.

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arXiv2005

IMF isotopic properties in semi-peripheral collisions at Fermi energies

We study the neutron and proton dynamical behavior along the fragmentation path in semi-peripheral collisions: 58Fe+58Fe (charge asymmetric, N/Z = 1.23) and 58Ni+58Ni (charge symmetric, N/Z = 1.07), at 47 AMeV. We observe that isospin dynamics processes take place also in the charge-symmetric system 58Ni+58Ni, that may produce more asymmetric fragments. A neutron enrichment of the neck fragments is observed, resulting from the interplay between pre-equilibrium emission and the phenomenon of "isospin-migration". Both effects depend on the EoS (Equation of State) symmetry term. This point is illustrated by comparing the results obtained with two different choices of the symmetry energy density dependence. New correlation observables are suggested, to study the reaction mechanism and the isospin dynamics.

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arXiv2005

Relativistic Transport Approach to Collective Nuclear Dynamics

The isoscalar giant monopole resonance (ISGMR) and isovector giant dipole resonance (IVGDR) in finite nuclei are studied in the framework of a relativistic transport approach. The kinetic equations are derived within an effective nucleon-meson field theory in the Relativistic Mean Field (RMF) scheme, even extended to density dependent vertices. Small amplitude oscillations are analysed using the Relativistic Vlasov (RV) approach, i.e. neglecting nucleon collision terms. The time evolution of the isoscalar monopole moment and isovector dipole moment and the corresponding Fourier power spectra are discussed. In the case of ^{208}Pb we study in detail the dependence of the monopole response on the effective mass and symmetry energy at saturation given by the used covariant effective interaction. We show that a reduced m^* and a larger a_4 can compensate the effect on the ISGMR energy centroid of a much larger compressibility modulus K_{nm}. This result is important in order to overcome the conflicting determination of the nuclear compressibility between non-relativistic and relativistic effective interactions. For the symmetry energy dynamical effects, we carefully analyze the influence of the inclusion of an effective isovector scalar channel, δ-meson field, with constant and density dependent couplings. We show the relevance of the $slope$ (or pressure) of the symmetry energy at saturation on the ISGMR and IVGDR modes for neutron-rich systems. Density dependent vertices are not much affecting our conclusions. Following as a guidance some extended dispersion relations in nuclear matter, we see two main reasons for that, the smoothness of the density dependences around saturation and the presence of compensation effects coming from rearrangement terms.

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arXiv2005

Isospin Transport at Fermi Energies

In this paper we investigate isospin transport mechanisms in semi-peripheral collisions at Fermi energies. The effects of the formation of a low density region (neck) between the two reaction partners and of pre-equilibrium emission on the dynamics of isospin equilibration are carefully analyzed. We clearly identify two main contributions to the isospin transport: isospin diffusion due to the $N/Z$ ratio and isospin drift due to the density gradients. Both effects are sensitive to the symmetry part of the nuclear Equation of State (EOS), in particular to the value and slope around saturation density.

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arXiv2005

On the splitting of nucleon effective masses at high isospin density: reaction observables

We review the present status of the nucleon effective mass splitting $puzzle$ in asymmetric matter, with controversial predictions within both non-relativistic $and$ relativistic approaches to the effective in medium interactions. Based on microscopic transport simulations we suggest some rather sensitive observables in collisions of asymmetric (unstable) ions at intermediate ($RIA$) energies: i) Energy systematics of Lane Potentials; ii) Isospin content of fast emitted nucleons; iii) Differential Collective Flows. Similar measurements for light isobars (like $^3H-^3He$) could be also important.

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arXiv2005

Fragment Formation in Central Heavy Ion Collisions at Relativistic Energies

We perform a systematic study of the fragmentation path of excited nuclear matter in central heavy ion collisions at the intermediate energy of $0.4 AGeV$. The theoretical calculations are based on a Relativistic Boltzmann-Uehling-Uhlenbeck ($RBUU$) transport equation including stochastic effects. A Relativistic Mean Field ($RMF$) approach is used, based on a non-linear Lagrangian, with coupling constants tuned to reproduce the high density results of calculations with correlations. At variance with the case at Fermi energies, a new fast clusterization mechanism is revealed in the early compression stage of the reaction dynamics. Fragments appear directly produced from phase-space fluctuations due to two-body correlations. In-medium effects of the elastic nucleon-nucleon cross sections on the fragmentation dynamics are particularly discussed. The subsequent evolution of the primordial clusters is treated using a simple phenomenological phase space coalescence algorithm. The reliability of the approach, formation and recognition, is investigated in detail by comparing fragment momentum space distributions {\it and simultaneously} their yields with recent experimental data of the $FOPI$ collaboration by varying the system size of the colliding system, i.e. its compressional energy (pressure, radial flow). We find an excellent agreement between theory and experiment in almost all the cases and, on the other hand, some limitations of the simple coalescence model. Furthermore, the temporal evolution of the fragment structure is explored with a clear evidence of an earlier formation of the heavier clusters, that will appear as interesting $relics$ of the high density phase of the nuclear Equation of State ($EoS$).

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arXiv2005

Isospin in Reaction Dynamics. The Case of Dissipative Collisions at Fermi Energies

A key question in the physics of unstable nuclei is the knowledge of the $EOS$ for asymmetric nuclear matter ($ANM$) away from normal conditions. We recall that the symmetry energy at low densities has important effects on the neutron skin structure, while the knowledge in high densities region is crucial for supernovae dynamics and neutron star properties. The $only$ way to probe such region of the isovector $EOS$ in terrestrial laboratories is through very dissipative collisions of asymmetric (up to exotic) heavy ions from low to relativistic energies. A general introduction to the topic is firstly presented. We pass then to a detailed discussion on the $neck-fragmentation$ process as the main dissipative mechanism at the Fermi energies and to the related isospin dynamics. From Stochastic Mean Field simulations the isospin effects on all the phases of the reaction dynamics are thoroughly analysed, from the fast nucleon emission to the mid-rapidity fragment formation up to the dynamical fission of the $spectator$ residues. Simulations have been performed with an increasing stiffness of the symmetry term of the $EOS$. Some differences have been noticed, especially for the fragment charge asymmetry. New isospin effects have been revealed from the correlation of fragment asymmetry with dynamical quantities at the freeze-out time. A series of isospin sensitive observables to be further measured are finally listed.

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arXiv2005

Neutron stars with isovector scalar correlations

Neutron stars with the isovector scalar $δ$-field are studied in the framework of the relativistic mean field ($RMF$) approach in a pure nucleon plus lepton scheme. The $δ$-field leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses. Both features are influencing the stability conditions of the neutron stars. Two parametrizations for the effective nonlinear Lagrangian density are used to calculate the nuclear equation of state ($EOS$) and the neutron star properties, and compared to correlated Dirac-Brueckner results. We conclude that in order to reproduce reasonable nuclear structure and neutron star properties within a $RMF$ approach a density dependence of the coupling constants is required.

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arXiv2004

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 $δ$-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 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.

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arXiv2004

Stopping and Isospin Equilibration in Heavy Ion Collisions

We investigate the density behaviour of the symmetry energy with respect to isospin equilibration in the combined systems $Ru(Zr)+Zr(Ru)$ at relativistic energies of 0.4 and $1.528 AGeV$. The study is performed within a relativistic framework and the contribution of the iso-vector, scalar $δ$ field to the symmetry energy and the isospin dynamics is particularly explored. We find that the isospin mixing depends on the symmetry energy and a stiff behaviour leads to more transparency. The results are also nicely sensitive to the "fine structure" of the symmetry energy, i.e. to the covariant properties of the isovector meson fields. The isospin tracing appears much less dependent on the in-medium neutron-proton cross-sections ($σ_{np}$) and this makes such observable very peculiar for the study of the isovector part of the nuclear equation of state. Within such a framework, comparisons with experiments support the introduction of the $δ$ meson in the description of the iso-vector equation of state.

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arXiv2004

Fragmentation path of excited nuclear systems

We perform a study of the fragmentation path of excited nuclear sources, within the framework of a stochastic mean-field approach. We consider the reaction $^{129}$Xe + $^{119}$Sn at two beam energies: 32 and 50 MeV/A, for central collisions. It is observed that, after the compression phase the system expands towards a dilute configuration from which it may recontract or evolve into a bubble-like structure. Then fragments are formed through the development of volume and/or surface instabilities. The two possibilities co-exist at 32 MeV/A, leading to quite different fragment partitions, while at 50 MeV/A the hollow configuration is observed in all events. Large variances are recovered in a way fully consistent with the presence of spinodal decomposition remnants. Kinematical properties of fragments are discussed and suggested as observables very sensitive to the dominant fragment production mechanism. A larger radial collective flow is observed at 50 MeV/A, in agreement with experiments.

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arXiv2004

Isospin effects in intermediate energy heavy ion collisions

We investigate the density dependence of the symmetry energy in a relativistic description by decomposing the iso-vector mean field into contributions with different Lorentz properties. We find important effects of the iso-vector, scalar $δ$ channel on the density behavior of the symmetry energy. Finite nuclei studies show only moderate effects originating from the virtual $δ$ meson. In heavy ion collisions from Fermi to relativistic energies up to $1-2 AGeV$ one finds important contributions on the dynamics arising from the different treatment of the microscopic Lorentz structure of the symmetry energy. We discuss a variety of possible signals which could set constraints on the still unknown density dependence of the symmetry energy, when experimental data will be available. Examples of such observables are isospin collective flow, threshold production of pions and kaons, isospin equilibration and stopping in asymmetric systems like $Au+Au$, $Sn+Sn$ and $Ru(Zr)+Zr(Ru)$.

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arXiv2003

Neck fragmentation reaction mechanism

Based on a microscopic transport model, we study the origin of nonstatistical Intermediate Mass Fragment ($IMF$) production in semicentral heavy ion collisions at the Fermi energies. We show that a fast, dynamical $IMF$ formation process, the {\it neck fragmentation mechanism}, can explain the experimentally observed features: deviations from Viola systematics and anisotropic, narrow angular distributions. It may be regarded as the continuation of the multifragmentation mechanism towards intermediate impact parameters. Its relation to other dynamical mechanisms, the induced fission and the abrasion of the spectator zones, that can also contribute to mid-rapidity $IMF$ production, is discussed. The dependence on beam energy and centrality of the collision is carefully analysed. The competition between volume and surface instabilities makes this mechanism very sensitive to the in-medium nucleon-nucleon interactions, from the cross sections for hard collisions to the compressibility and other Equation of State ($EOS$) properties. For charge asymmetric collisions the sensitivity of various observables to the symmetry energy is investigated. Of particular interest appears the isospin diffusion dynamics with no signal of isospin equilibration. However, in spite of the short time scales and of the dynamical aspects, we notice isoscaling features of the neck mechanism. We observe that isospin enrichement of the neck zone as well as the isoscaling parameters are sensitive to the density dependence of asymmetry term of EOS around and below saturation value.

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arXiv2003

Transport properties of isospin effective mass splitting

We investigate in detail the momentum dependence ($MD$) of the effective in medium Nucleon-Nucleon ($NN$) interaction in the isovector channel. We focus the discussion on transport properties of the expected neutron-proton ($n/p$) effective mass splitting at high isospin density. We look at observable effects from collective flows in Heavy Ion Collisions ($HIC$) of charge asymmetric nuclei at intermediate energies. Using microscopic kinetic equation simulations nucleon transverse and elliptic collective flows in $Au+Au$ collisions are evaluated. In spite of the reduced charge asymmetry of the interacting system interesting $isospin-MD$ effects are revealed. Good observables, particularly sensitive to the $n/p$-mass splitting, appear to be the differences between neutron and proton flows. The importance of more exclusive measurements, with a selection of different bins of the transverse momenta ($p_t$) of the emitted particles, is stressed. In more inclusive data a compensation can be expected from different $p_t$-contributions, due to the microscopic $isospin-MD$ structure of the nuclear mean field in asymmetric matter.

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arXiv2003

On the Lorentz structure of the symmetry energy

We investigate in detail the density dependence of the symmetry energy in a relativistic description by decomposing the iso-vector mean field into contributions with different Lorentz covariant properties. We find important effects of the iso-vector, 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 iso-vector $δ$ 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.

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arXiv2003

Relativistic effects in the search for high density symmetry energy

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.

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