Pion condensation in neutron star matter: (II). Nuclear forces and stability

This paper presents several stable models of charged-pion condensed neutron star matter. The non-relativistic limit of the chirally symmetric Weinberg Lagrangian is used to describe interactions of the condensed pion field with the nucleons, as well as the pi-pi interactions of the condensed field. In the absence of nucleon-nucleon interactions, matter in this model is unstable, tending to ever-increasing baryon density and condensate wave vector. The connection of this model of condensation with the σ-model is shown.A general framework for including nuclear forces is then laid out. Results are given for a simple model in which the nuclear forces are assumed to produce an interaction energy V(ρ) dependent only on the total baryon density, independent of the degree of pion condensation, and also to produce a constant G-matrix element g in the nucleon-nucleon charge exchange channel. In the absence of condensation the equation of state reduces to that of interacting normal matter. We also consider effects of beta equilibrium and form factors in the p-wave pion-nucleon interaction. The condensed models are stable. Depending on the choice of parameters the models exhibit first- or second-order pion condensation phase transitions, or both.