Relativistic transport theory of N, Δand N^{*}(1440) interacting through $σ$, $ω$ and $π$ mesons

Details Relativistic transport theory of N, Δand N^{*}(1440) interacting through $σ$, $ω$ and $π$ mesons Relativistic transport theory of N, Δand N^{*}(1440) interacting through $σ$, $ω$ and $π$ mesons

1997-09-24

arxiv.org/abs/nucl-th/9709047v1

Phys.Rev.C57:1938-1961,1998

Physics

Nuclear Physics

Nuclear Theory

64 pages, Latex, 13 PostScript figures included

Scientific paper

10.1103/PhysRevC.57.1938

A self-consistent relativistic integral-differential equation of the Boltzmann-Uehling-Uhlenbeck-type for the $N^{*}$(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 $N^{*}$(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 $N^{*}$(1440) distribution functions. All the $N^{*}$(1440)-relevant in-medium two-body scattering cross sections within the $N$, $\Delta$ and $N^{*}$(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 $pp \to pp^{*}(1440)$ cross section is in good agreement with the experimental data. We calculate the in-medium $N + N \to N + N^{*}$, $N^{*} + N \to N + N$ and $N^{*} + N \to N^{*} + N$ cross sections in cold nuclear matter up to twice the nuclear matter density. The influence of different choices of the $N^{*}N^{*}$ 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 $N^{*}N^{*}$ coupling strengths used. An evident density dependence will appear when a large scalar coupling strength of $g_{N^{*}N^{*}}^{\sigma}$ is assumed.

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