A relativistic quantum kinetic equation for nucleus-nucleus collisions

A relativistic quantum kinetic equation is derived corresponding to the non-equilibrium extension of the Dirac-Brueckner approach for nuclear matter. The equation is of the VUU-type with a self-consistent mean field and collision term

Two-body collisions and mean-field theory:The Brueckner-Boltzmann equation

Starting from the BBGKY hierarchy of density matrices, a quantum mechanical Boltzmann equation, including a mean field, is derived. Both the mean field, which is of the well-known Brueckner-Hartree-Fock form, as well as the collision term are expressed in terms of the self-consistent Brueckner G-matrix. The relation with the generalized Boltzmann equation of Kadanoff and Baym is discussed. It is shown that the usual quantum mechanical theories like TDHF and Uehling-Uhlenbeck appear as limiting case

Relativistic quantum transport theory of hadronic matter: the coupled nucleon, delta and pion system

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, the semi-classical, quasi-particle and Born approximation 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 deltas 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 non-relativistic 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 $\pi N \to \Delta$ cross section is in agreement with the experimental data. Medium effects on the $\pi N \to \Delta$ cross section and momentum-dependent $\Delta$-decay width are shown to be substantial.Comment: 66 pages, Latex, 12 PostScript figures included; replaced by the revised version, to appear in Phys. Rev.

Two-body collisions and mean-field theory:The Brueckner-Boltzmann equation

Starting from the BBGKY hierarchy of density matrices, a quantum mechanical Boltzmann equation, including a mean field, is derived. Both the mean field, which is of the well-known Brueckner-Hartree-Fock form, as well as the collision term are expressed in terms of the self-consistent Brueckner G-matrix. The relation with the generalized Boltzmann equation of Kadanoff and Baym is discussed. It is shown that the usual quantum mechanical theories like TDHF and Uehling-Uhlenbeck appear as limiting case