Linear response and Friedel oscillations of the pion field in relativistic nuclear matter

Abstract

This paper is concerned with the study of the linear response and the screening effects on the pion field in nuclear matter. The linear response of a relativistic plasma of nucleons interacting through the exchange of scalar (σ) and vector-isoscalar (ω) mesons in the framework of a QHD model is analyzed. The pions are assumed to be coupled to nucleons through the usual isospin invariant lagrangian. For the sake of comparison, we consider also a lagrangian that predicts reasonable low-energy πN scattering amplitudes in vacuum. It is obtained by adding a non-linear σπ coupling term to the QHD lagrangian. The ω- and σ-nucleon coupling constants are fixed in such a way that saturation is attained in the Hartree approximation near the nuclear density, while the πN coupling constant is taken from scattering data. The linear response formalism is introduced, and the quasi-pion propagator is computed in a self-consistent one-loop approximation. From these results, we analyze the screening effects on an external perturbing field. In the case of an uniform perturbing field, we obtain the behaviour of the effective πN coupling constant as a function of the density. Also, we study the effective field in the plasma created by a point-like baryonic source at rest. In vacuum, this field is given by the usual Yukawa expression. However, inside the matter, the form of the field is strongly modified by screening effects. In the non-degenerate case, the field exhibits exponentially damped oscillations, while in the degenerate case it shows Friedel-type oscillations, damped as the third power of the distance. Nevertheless, in both cases the effective field is strongly reduced as compared to the vacuum case (in the degenerate case, at least up to distances ∼10 fm). As a consequence, the range of the hard-core of the interaction inside the plasma remains smaller than the mean interparticle distance in all the meaningful range of densities. This behaviour is dominated by the analytic structure of the polarization tensor, and is rather insensitive to the model for the πN interaction.