Relativistic transport theory of N, \Delta and N^{*}(1440) interacting through $\sigma$, $\omega$ and $\pi$ mesons

Abstract

A self-consistent relativistic integral-differential equation of the Boltzmann-Uehling-Uhlenbeck-type for the $N^{\ast }$(1440) resonance is developed based on an effective Lagrangian of baryons interacting through mesons. The closed time-path Green's function technique and semi-classical, quasi-particle and Born approximations are employed in the derivation. The non-equilibrium RBUU-type equation for the $N^{\ast }$(1440) is consistent with that of nucleon's and delta's which we derived before. Thus, we obtain a set of coupled equations for the $N$, $\Delta$ and $N^{\ast }$(1440) distribution functions. All the $N^{\ast }$(1440)-relevant in-medium two-body scattering cross sections within the $N$, $\Delta$ and $N^{\ast }$(1440) system are derived from the same effective Lagrangian in addition to the mean field and presented analytically, which can be directly used in the study of relativistic heavy-ion collisions. The theoretical prediction of the free $pp\to p{p}^{\ast }(1440)$ cross section is in good agreement with the experimental data. We calculate the in-medium $N+N\to N+N^{\ast }$, $N^{\ast }+N\to N+N$ and $N^{\ast }+N\to N^{\ast }+N$ cross sections in cold nuclear matter up to twice the nuclear matter density. The influence of different choices of the $N^{\ast }{N}^{\ast }$ coupling strengths, which can not be obtained through fitting certain experimental data, are discussed. The results show that the density dependence of predicted in-medium cross sections are sensitive to the $N^{\ast }{N}^{\ast }$ coupling strengths used. An evident density dependence will appear when a large scalar coupling strength of $g_{N^{\ast }{N}^{\ast }}^{\sigma }$ is assumed.

Comments: 64 pages, Latex, 13 PostScript figures included