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

Abstract

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.

66 pages, Latex, 12 PostScript figures included; replaced by the revised version, to appear in Phys. Rev. C

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Cited by in corpus (10)

• Transport-theoretical Description of Nuclear Reactions
• Hot and dense hadronic matter in an effective mean field approach
• Chemical and mechanical instability in warm and dense nuclear matter
• Collective flows of pions in Au+Au collisions at energies 1.0 and 1.5 GeV/nucleon
• Hadronic freeze-out in an effective relativistic mean field model
• The density- and isospin- dependent $\Delta$-formation cross section and its decay width
• Investigation of Zero-Sound Dispersion Equation in the Complex Plane of Frequency
• A study of the elastic $\pi N$ scattering at finite baryon density
• On relativistic approaches to the pion self-energy in nuclear matter
• In-medium pion dispersion relation and medium correction of $N\pi \leftrightarrow \Delta$ near the threshold energy of pion production