Gy. Wolf

Dilepton production in heavy-ion collisions

Abstract The dynamical evolution of nucleus-nucleus collisions is described by a transport equation of the Uehling-Uhlenbeck type. Our model evolves phase-space distribution functions for nucleons, Δs, N ∗ (1440)-resonances and pions with their isospin degrees of freedom. The equations are solved by the test-particle simulation method. We apply this model to proton-nucleus and nucleus-nucleus collisions from 400 MeV/ A to 2.1 GeV/ A . Our approach is found to correctly describe the spectra of baryons and pions. Furthermore, we calculate the production of dileptons considering proton-neutron and pion bremsstrahlung, Δ and N ∗ decay and π + π − annihilation. The calculations reproduce the data for p+ 9 Be and for 40 Ca + 40 Ca at the bombarding energies of 1 GeV/ A and 2 GeV/ A except for small invariant masses ( M ⩽ 200 MeV) where the situation is not fully understood. Above 300 MeV dilepton invariant mass the relevant contributions arise from proton-neutron bremsstrahlung, the Δ Dalitz-decay and π + π − annihilation. At 2 GeV/ A for 40 Ca + 40 Ca, however, we find the bremsstrahlung contribution to be higher than that from pion annihilation.

Pion-production in heavy-ion collisions at SIS energies

We investigate the production of pions in heavyion collisions in the energy range of 1–2 GeV/A. The dynamics of the nucleus-nucleus collisions is described by a set of coupled transport equations of the Boltzmann-Uehling-Uhlenbeck type for baryons and mesons. Besides theN(938) and theΔ(1232) we also take into account nucleon resonances up to masses of 1.95 GeV/c2 as well asπ-,η- andρ-mesons. We study in detail the influence of the higher baryonic resonances and the 2π-production channels (NN→NNππ) on the pion spectra in comparison toπ− data fromAr+KCl collisions at 1.8 GeV/A andπ0-data forAu+Au at 1.0GeV/A. We, furthermore, present a detailed comparison of differential pion angular distributions with the BEVALAC data forAr+KCl at 1.8 GeV/A. The general agreement obtained indicates that the overall reaction dynamics is well described by our novel transport approach.

Transport theories for heavy-ion collisions in the 1 A GeV regime

We compare multiplicities as well as rapidity and transverse momentum distributions of protons, pions and kaons calculated within presently available transport approaches for heavy-ion collisions around 1 A GeV. For this purpose, three reactions have been selected: Au+Au at 1 and 1.48 A GeV and Ni+Ni at 1.93 A GeV.

Pion-nucleus reactions in a microscopic transport model

Abstract We analyse pion-nucleus reactions in a microscopic transport model of the BUU type, which propagates nucleons, pions, deltas and N(1440) resonances explicitly in space and time. In particular we examine pion absorption and inelastic-scattering cross sections for pion kinetic energies Tπ = 85–315 MeV and various target masses. In general, the mass dependence of the experimental data is well described for energies up to the Δ-resonance (≈ 160 MeV), while the absorption cross sections are somewhat overestimated for the higher energies. In addition we study the possible dynamical effects of delta and pion potentials in the medium on various observables as well as alternative models for the in-medium Δ-width.

Dilepton Decays of Baryon Resonances

Dalitz decay of baryon resonances is studied and expressions for the decay width are derived for resonances with arbitrary spin and parity. Contributions of the various terms in the transition matrix element are compared and relevance of spin-parity and the resonance mass is discussed. Explicit algebraic expressions are cited for spin ≤5/2 resonances. The results can be used in models of dielectron production in elementary reactions and heavy ion collisions.

Covariant kinetic equations and relaxation processes in relativistic heavy-ion collisions

We present a derivation of covariant kinetic equations for nucleons and deltas within a model of quantum hadrodynamics, which includes scalar, vector and pseudo-scalar mesons. By generalizing the Kadanoff-Baym equations to relativistic fields and using the gradient expansion as well as the quasi-particle approximation for the baryons, we find kinetic equations with covariant collision integrals of the Uehling-Uhlenbeck type. These relativistic LandauVlasov equations for nucleons and deltas are solved numerically for two counter-streaming nuclear-matter currents. Using the microscopic expressions we find — due to modifications of the baryon properties in nuclear matter — strong medium effects on relaxation processes in intermediate-energy heavy-ion collisions.

Baryonic contributions to the dilepton spectrum of nucleon-nucleon collisions

We study the production of dileptons in relativistic nucleon-nucleon collisions. Additionally to the traditional dilepton production channels (vector meson decays, meson and Delta(1232) Dalitz decays) we included in our model as new dilepton sources the Dalitz decay of higher unflavored baryon resonances with spin<=5/2 and mass<=2.25 GeV/c^2. The contributions of these new channels are estimated using experimental information about the Ngamma decays of the resonances and have large uncertainties. The obtained dilepton spectra are compared to the experimental data by the DLS collaboration. Predictions for the HADES detector (SIS, GSI) are also discussed. In spite of the large uncertainties of the higher resonance Dalitz decay contributions we are able to draw the conclusion that these contributions are negligible compared to the other dilepton sources and do not influence the detectability of the phi and omega vector meson peaks.

Single-particle resonant states in deformed potentials

It is shown that the approximation scheme to the Schrodinger equation with purely outgoing asymptotics based on the separable expansion of the potential (PSE method) can be extended into the wave-number region k = κ-iγ with 0 < γ < κ. This extended scheme is proved to be equivalent to the analytic continuation of the homogeneous Lippmann-Schwinger equation into the same region. Thus its solutions are the Gamow states. As the PSE method handles spherical and non-spherical potentials on an equal footing it is able to yield Gamow states in deformed potentials.

Probing nuclear expansion dynamics with π−/π+-spectra

We study the dynamics of charged pions in the nuclear medium via the ratio of differential π− - and π+-spectra in a coupled-channel BUU (CBUU) approach. The relative energy shift of the charged pions is found to correlate with the pion freeze-out time in nucleus-nucleus collisions as well as with the impact parameter of the heavy-ion reaction. Furthermore, the long-range Coulomb force provides valuable information on the expansion dynamics of the hot nuclear system. Detailed comparisons with experimental data for Au + Au at 1 AGeV and Ni + Ni at 2.0 AGeV are presented.

Dynamics of heavy-ion reactions and the nuclear equation of state

Abstract The description of heavy-ion collisions up to bombarding energies of a few GeV per nucleon is based on a relativistic transport equation for the baryon phase-space distribution as derived from time-dependent Dirac-Brueckner theory within semiclassical limits. It describes the selfconsistent mean-field dynamics with its momentum-dependent forces as well as the residual nucleon-nucleon collisional history. We analyze the sensitivity of flow observables to the scalar and vector part of the nucleon selfenergy and try to extract information on the nuclear equation of state (EOS) in comparison with experimental data. Furthermore, we provide predictions for K + spectra for 40 Ca + 40 Ca collisions from 0.6 GeV/u to 1.5 GeV/u which show a sensitivity to the nuclear equation of state. In the last part of this contribution we compare the theoretical predictions for e + e − spectra with the available data for p+Be and Ca+Ca at 1 and 2 GeV/u where we incorporate the incoherent on-shell nucleon-nucleon and pion-nucleon bremsstrahlung processes, the Dalitz decay of the Δ-particle and π + π − annihilation.