Pion condensation in neutron star matter: Equilibrium conditions and model calculations

Abstract

The equilibrium thermodynamic conditions obeyed by a pion condensed state of dense neutron or neutron star matter are derived. Then simple model calculations of negative pion condensation in neutron star matter are carried out. In the simplest of these models, consisting of a p-wave pion-nucleon interaction alone, we find a local minimum in the free energy corresponding to a pion condensed phase, but we also find at larger density that matter is unstable to the formation of an ever increasing pion condensate. This model is made more realistic by including other forces: s-wave pion-nucleon interactions, pi-pi interactions, and phenomenological form factors in these interactions. These modifications have little influence on the stability of the system. Finally, effects of repulsive nuclear forces on pion condensation are considered in a simple model, in which we retain only a simplified repulsive zero range nucleon-nucleon interaction proportional to σ · σ′ τ · τ′. The density for the pion threshold is very sensitive to the strength of this force. This model of the nuclear force greatly reduces the instability of the system, although it is too crude to restore stability completely. It also indicates the important role nuclear forces play in a correct description of the pion condensed phase.