Direct Photons in Nuclear Collisions at FAIR Energies

Using the extrapolation of existing data estimations of prompt photon production at FAIR energies have been made. At $y=y_{c.m.}$ the rapidity density of prompt photons with $p_{t}>$ 1.5 GeV/c per central Au+Au event at 25 AGeV is estimated as $\sim 10^{-4}$ . With the planed beam intensity $10^{9}$ per second and 1% interaction probability, for 10% of most central events one can expect the prompt photon rate $\sim 10^{2}$ photons per second. Direct photons from the hadron scenario of ion collisions generated by the Hadron-String-Dynamics (HSD) transport approach with implemented meson scatterings $\pi\rho\to\pi\gamma, \pi\pi\to\rho\gamma$ have been analyzed. Photons from short-living resonances (e.g. $\omega \to \pi^{0} \gamma$) decaying during the dense phase of the collision should be considered as direct photons. They contribute significantly in the direct photon spectrum at $p_{t}=0.5 - 1$ GeV/c. At the FAIR energy 25 AGeV in Au+Au central collisions the HSD generator predicts, as a lower estimate, $\gamma_{direct}/\gamma_{\pi^{0}} \simeq$ 0.5% in the region $p_{t}=0.5 - 1$ GeV/c. At $p_{t}=1.5 - 2$ GeV/c $\gamma_{prompt}/\gamma_{\pi^{0}} \simeq$ 2%. Thermal direct photons have been evaluated with the Bjorken Hydro-Dynamics (BHD) model. The BHD spectra differ strongly from the HSD predictions. The direct photon spectrum is very sensitive to the initial temperature parameter $T_{0}$ of the model. The 10 MeV increase in the $T_{0}$ value leads to $\sim$ 2 times higher photon yield.Comment: 9 pages, 5 figures, Talk at the session of Russian Academy of Sciences, ITEP, Moscow, 26 - 30 November 200

Influence of the in-medium pion dispersion relation in heavy ion collisions

We investigate the influence of medium corrections to the pion dispersion relation on the pion dynamics in intermediate energy heavy ion collisions. To do so a pion potential is extracted from the in-medium dispersion relation and used in QMD calculations and thus we take care of both, real and imaginary part of the pion optical potential. The potentials are determined from different sources, i.e. from the $\Delta$--hole model and from phenomenological approaches. Depending on the strength of the potential a reduction of the anti-correlation of pion and nucleon flow in non-central collisions is observed as well as an enhancement of the high energetic yield in transverse pion spectra. A comparison to experiments, in particular to $p_t$-spectra for the reaction Ca+Ca at 1 GeV/nucleon and the pion in-plane flow in Ne+Pb collisions at 800 MeV/nucleon, generally favours a weak potential.Comment: 25 pages, using REVTeX, 6 postscript figures; replaced by published versio

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.

Resonance Model of πΔ→YK\pi \Delta \rightarrow Y K for Kaon Production in Heavy Ion Collisions

The elementary production cross sections $\pi \Delta \rightarrow Y K$ $(Y=\Sigma,\,\, \Lambda)$ and $\pi N \rightarrow Y K$ are needed to describe kaon production in heavy ion collisions. The $\pi N \rightarrow Y K$ reactions were studied previously by a resonance model. The model can explain the experimental data quite well \cite{tsu}. In this article, the total cross sections $\pi \Delta \rightarrow Y K$ at intermediate energies (from the kaon production threshold to3 GeV of $\pi \Delta$ center-of-mass energy) are calculated for the first time using the same resonance model. The resonances, $N(1710)\,I(J^P) = \frac{1}{2}(\frac{1}{2}^+)$ and $N(1720)\, \frac{1}{2} (\frac{3}{2}^+)$ for the $\pi \Delta \rightarrow \Sigma K$ reactions, and $N(1650)\, \frac{1}{2} (\frac{1}{2}^-)$, $N(1710)\, \frac{1}{2} (\frac{1}{2}^+)$ and $N(1720)\, \frac{1}{2} (\frac{3}{2}^+)$ for the $\pi \Delta \rightarrow \Lambda K$ reactions are taken into account coherently as the intermediate states in the calculations. Also t-channel $K^*(892) \frac{1}{2}(1^-)$ vector meson exchange is included. The results show that $K^*(892)$ exchange is neglegible for the $\pi \Delta \rightarrow \Sigma K$ reactions, whereas this meson does not contribute to the $\pi \Delta \rightarrow \Lambda K$ reactions. Furthemore, the $\pi \Delta \rightarrow Y K$ contributions to kaon production in heavy ion collisions are not only non-neglegible but also very different from the $\pi N \rightarrow Y K$ reactions. An argument valid for $\pi N \rightarrow Y K$ cannot be extended to $\pi \Delta \rightarrow Y K$ reactions. Therefore, cross sections for $\pi \Delta \rightarrow Y K$ including correctly the different isospins must beComment: ( Replaced with corrections of printing errors in the Table. ) 15 pages, Latex file with 4 figures, 1 figure is included in the text. A compressed uuencode file for 3 figures is appended. (A figure file format was changed.) Also available upon reques

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.

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

e^+e^- Pair Production from γ\gamma A Reactions

We present a calculation of e^+e^- production in $\gamma A$ reactions at MAMI and TJNAF energies within a semi-classical BUU transport model. Dilepton invariant mass spectra for $\gamma$C, $\gamma$Ca and $\gamma$Pb are calculated at 0.8, 1.5 and 2.2 GeV. We focus on observable effects of medium modifications of the $\rho$ and $\omega$ mesons. The in-medium widths of these mesons are taken into account in a dynamical, consistent way. We discuss the transport theoretical treatment of broad resonances.Comment: 42 pages including 16 figure

Role of isospin dependent mean field in pion production in heavy ion reactions

The importance of a isospin dependent nuclear mean field (IDMF) in regard to the pion production mechanism is studied for the reaction $Au+Au$ at 1 GeV/nucleon using the Quantum Molecular Dynamics (QMD) model. In particular, the effect of the IDMF on pion spectra and the charged pion ratio are analyzed. It is found that the inclusion of a IDMF considerably suppresses the low$-p_t$ pions, thus, leading to a better agreement with the data on pion spectra. Moreover, the rapidity distribution of the charged pion ratio appears to be sensitive to the isospin dependence of the nuclear mean field.Comment: 16 pages, using RevTex, 6 PS-Figure