Investigation of the nuclear equation of state and dielectron production in heavy ion collisions

Several investigations involving strongly interacting matter at high temperature and density are pursued. First concentrating on relativistic heavy ion collisions slightly below the GeV/nucleon range, we perform studies of the equation of state (EOS) for nuclear matter. The non-equilibrium aspects of such collisions are simulated by the Boltzmann-Uehling-Uhlenbeck transport model with a momentum-dependent nuclear mean field. The EOS effects on the collective flow observables and dielectron spectra have been systematically and quantitatively examined by comparing with the experimental data gathered by the DIOGENE, Streamer Chamber, Plastic Ball, EOS TPC, E848H and DLS collaborations. The importance of the precise functional dependence of the nuclear mean field on the particle momentum, and the compressibility coefficient K of the nuclear matter are addressed. Using a simple coalescence model, we show that a quantitative connection between the composite flow and K can be established. In such nucleus-nucleus collisions, we also consider and discuss lepton pair production mechanisms. These include nucleon-nucleon bremsstrahlung, $ Delta$ decay, $ eta$ decay, and pion-pion annihilation. We then turn to lepton pair production in ultrarelativistic heavy ion collisions. We concentrate on pion-pion virtual bremsstrahlung in the soft limit M $<$ 300 MeV, and we make a quantitative comparison of various soft-photon-approximation (SPA) formulae with a full one-boson-exchange (OBE) calculation