Relativistic transport approach for nucleus-nucleus collisions based on a NJL lagrangian

We formulate a covariant transport approach for high energy nucleus-nucleus collisions where the real part of the hadron selfenergies is evaluated on the basis of a NJL-type Lagrangian for the quark degrees of freedom. The parameters of the model Lagrangian are fixed by the Gell-Mann, Oakes and Renner relation, the pion-nucleon \Sigma-term, the nucleon energy as well as the nuclear binding energy at saturation density \rho_0. We find the resulting scalar and vector selfenergies for nucleons to be well in line with either Dirac-Brueckner results or those from the phenomenological optical potential when accounting for a swelling of the nucleon at finite nuclear matter density. The imaginary part of the hadron selfenergies is determined by a string fragmentation model which accounts for the in-medium mass of hadrons in line with the chiral dynamics employed. The applicability of the 'chiral' transport approach is demonstrated in comparison with experimental data from SIS to SPS energies. The enhancement of the K^+/\pi^+ ratio in A + A collisions compared to p + A reactions at AGS energies is reproduced within the 'chiral' dynamics. Furthermore, detailed predictions for the stopping in Pb + Pb collisions at 153 GeV/A are presented

Thermodynamics of resonances and blurred particles

Exact and approximate expressions for thermodynamic characteristics of heated matter, which consists of particles with finite mass-widths, are constructed. They are expressed in terms of Fermi/Bose distributions and spectral functions, rather than in terms of more complicated combinations between real and imaginary parts of the self-energies of different particle species. Therefore thermodynamically consistent approximate treatment of systems of particles with finite mass-widths can be performed, provided spectral functions of particle species are known. Approximation of the free resonance gas at low densities is studied. Simple ansatz for the energy dependence of the spectral function is suggested that allows to fulfill thermodynamical consistency conditions. On examples it is shown that a simple description of dense systems of interacting particle species can be constructed, provided some species can be treated in the quasiparticle approximation and others as particles with widths. The interaction affects quasiparticle contributions, whereas particles with widths can be treated as free. Example is considered of a hot gas of heavy fermions strongly interacting with light bosons, both species with zero chemical potentials. The density of blurred fermions is dramatically increased for high temperatures compared to the standard Boltzmann value. The system consists of boson quasiparticles (with effective masses) interacting with fermion -- antifermion blurs. In thermodynamical values interaction terms partially compensate each other. Thereby, in case of a very strong coupling between species thermodynamical quantities of the system, like the energy, pressure and entropy, prove to be such as for the quasi-ideal gas mixture of quasi-free fermion blurs and quasi-free bosons.Comment: 35 page

Treatment of Pionic Modes at the Nuclear Surface for Transport Descriptions

Dispersion relations and amplitudes of collective pionic modes are derived in a pi + nucleon-hole + delta-hole model for use in transport descriptions by means of a local density approximation. It is discussed how pionic modes can be converted to real particles when penetrating the nuclear surface and how earlier treatments can be improved. When the surface is stationary only free pions emerge. The time-dependent situation is also addressed, as is the conversion of non-physical (i.e. unperturbed delta-hole) modes to real particles when the nuclear density vanishes. A simplified one-dimensional scenario is used to investigate the reflection and transmission of pionic modes at the nuclear surface. It is found that reflection of pionic modes is rather unlikely, but the process can be incorporated into transport descriptions by the use of approximate local transmission coefficients.Comment: LaTeX 24 pages, 12 postscript figures in accompanying uuencoded fil

Effects of Spin-Isospin Modes in Transport Simulations

In-medium properties derived for nuclear matter in a microscopic pi + nucleon-hole + delta-hole model are incorporated into transport simulations of nuclear collisions by means of a local-density approximation and by utilizing a local medium frame. Certain features of the transport results differ from those based on the corresponding vacuum properties. Comparisons of the pi and delta production rates, as well as pion energy spectra, are discussed in particular.Comment: 11 pages total, Latex with psfig, and embedded 4 eps figure

Dileptons from the strongly-interacting Quark-Gluon Plasma within the Parton-Hadron-String-Dynamics (PHSD) approach

Dilepton production in In+In collisions at 158 AGeV is studied within the microscopic Parton-Hadron-Strings Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model (DQPM) matched to reproduce lattice QCD results in thermodynamic equilibrium. A comparison to the data of the NA60 Collaboration shows that the low mass dilepton spectra are well described by including a collisional broadening of vector mesons, while the spectra in the intermediate mass range are dominated by off-shell quark-antiquark annihilation in the nonperturbative QGP. In particular, the observed softening of the mT spectra at intermediate masses is reproduced.Comment: talk given at the 21st International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter 2009), to be published in Nucl.Phys.A, 4 pages, 3 figures, elsarticle styl

Reanalysis of antiproton production in proton-nucleus and nucleus-nucleus reactions at subthreshold energies

We reanalyse the production of $p\bar{p}$ pairs in proton-nucleus and nucleus-nucleus collisions employing novel elementary cross sections for baryon-baryon and pion-baryon production channels based on a boson-exchange model. In contrast to previous transport studies performed in the literature the secondary pion induced channel is found to be most important in both p+A and A+A collisions at subthreshold energies. A detailed comparison with the experimental data available indicates that sizeable attractive $\bar{p}$ potentials in the order of - 100 to - 150 MeV at normal nuclear matter density are needed to reproduce the size and shape of the experimental spectra.Comment: 25 pages, latex, including 15 ps-figures, UGI-97-21, submitted to Nucl. Phys.

Kaon versus Antikaon Production at SIS Energies

We analyse the production and propagation of kaons and antikaons in Ni + Ni reactions from 0.8--1.85 GeV/u within a coupled channel transport approach including the channels $BB \to K^+YN, \pi B\to K^+Y, BB \to NN K \bar{K}, \pi B\to N K\bar{K}, K^+B\to K^+B, \bar{K} B\to \bar{K}B, Y N\to \bar{K} NN, \pi \pi\to K \bar{K}$ as well as $\pi Y\to \bar{K}N$ and $\bar{K} N\to \pi Y$ for the antikaon absorption. Whereas the experimental $K^+$ spectra can be reproduced without introducing any selfenergies for the mesons in Ni + Ni collisions from 0.8 to 1.8 GeV/u, the $K^-$ yield is underestimated by a factor of 5--7 at 1.66 and 1.85 GeV/u. However, introducing density dependent antikaon masses as proposed by Kaplan and Nelson, the antikaon spectra can be reasonably well described.Comment: 16 pages, LaTeX, plus 12 postscript figures, submitted to Nucl. Phys.

Low-mass dileptons and dropping rho meson mass

Using the transport model, we have studied dilepton production from heavy-ion collisions at Bevalac energies. It is found that the enhanced production of low-mass dileptons observed in the experiment by the DLS collaboration cannot be explained by the dropping of hadron masses, in particular the $\rho$-meson mass, in dense matter.Comment: 9 pages, LaTeX, including 1 postscript figure, to appear in Phys. Lett.

Semiclassical transport of particles with dynamical spectral functions

The conventional transport of particles in the on-shell quasiparticle limit is extended to particles of finite life time by means of a spectral function A(X,\vec{P},M^2) for a particle moving in an area of complex self-energy \Sigma^{ret}_X = Re \Sigma^{ret}_X -i \Gamma_X/2. Starting from the Kadanoff-Baym equations we derive in first order gradient expansion equations of motion for testparticles with respect to their time evolution in \vec{X}, \vec{P} and M^2. The off-shell propagation is demonstrated for a couple of model cases that simulate hadron-nucleus collisions. In case of nucleus-nucleus collisions the imaginary part of the hadron self-energy \Gamma_X is determined by the local space-time dependent collision rate dynamically. A first application is presented for A + A reactions up to 95 A MeV, where the effects from the off-shell propagation of nucleons are discussed with respect to high energy proton spectra, high energy photon production as well as kaon yields in comparison to the available data from GANIL.Comment: 34 pages, LaTeX, 11-eps figures, submitted to Nucl. Phys. A, in prin

Equilibration within a semiclassical off-shell transport approach

Equilibration times for nuclear matter configurations -- modelling intermediate and high energy nucleus-nucleus collisions -- are evaluated within the semiclassical off-shell transport approach developed recently. The transport equations are solved for a finite box in coordinate space employing periodic boundary conditions. The off-shell transport model is shown to give proper off-shell equilibrium distributions in the limit $t \to \infty$ for the nucleon and $\Delta$-resonance spectral functions. We find that equilibration times within the off-shell approach are only slightly enhanced as compared to the on-shell limit for the momentum configurations considered.Comment: 19 pages, LaTeX, including 4 postscript figures, submitted to Nucl. Phys.