A study of meson dynamics in relativistic models of nuclear matter

Abstract

We analyze the dynamics of mesons in nuclear matter, as resulting from two relativistic models for the meson-nucleon interaction (σ and Walecka model). The covariant Wigner function techniques are used in order to describe a plasma of nucleons in thermodynamical equilibrium, and to analyze the quasi-meson spectra in the medium. The models are solved in the mean-field and Hartree approximations, as first-order approximations to the solution of a hierarchy of kinetic equations describing the collective behaviour of the plasma. The small perturbations around both ground states give, in every case, the dispersion relations for the mesons. A numerical study of the different branches and the evolution of the quasi-meson masses with density is performed. This analysis shows that the mean-field ground state is unstable in some density ranges and should evolve towards a new spatially-structured state. We also show that vacuum polarization effects eliminate such instabilities, although they introduce a new instability related to “tachyonic modes”, arising at large momenta. For such momenta, the structural properties of the nucleon should be taken into account. We show that the “tachyonic instability” disappears with the introduction of a simple monopolar form factor for the nucleon. Finally, we study the linear response of the plasma and analyze the screening effects on the interaction.