Open Access

Guangjun Mao, Ludwig Neise, Horst Stöcker, Walter Greiner

• We derive the relativistic quantum transport equation for the pion distribution function based on an effective Lagrangian of the QHD-II model. The closed-time-path Green s function technique and the semiclassical, quasiparticle, and Born approximations are employed in the derivation. Both the mean field and collision term are derived from the same Lagrangian and presented analytically. The dynamical equation for the pions is consistent with that for the nucleons and Delta's which we developed before. Thus, we obtain a relativistic transport model which describes the hadronic matter with N,Delta, and pi degrees of freedom simultaneously. Within this approach, we investigate the medium effects on the pion dispersion relation as well as the pion absorption and pion production channels in cold nuclear matter. In contrast to the results of the nonrelativistic model, the pion dispersion relation becomes harder at low momenta and softer at high momenta as compared to the free one, which is mainly caused by the relativistic kinetics. The theoretically predicted free piN->Delta cross section is in agreement with the experimental data. Medium effects on the piN->Delta cross section and momentum-dependent Delta-decay width are shown to be substantial. PACS-numbers: 24.10.Jv, 13.75.Cs, 21.65.1f, 25.75.2q