A Realistic Approach to Charged Pion Condensation in Neutron Matter

For a realistic approach to describe the equation of state and cooling of neutron stars in a consistent way, a new formalism for the charged pion (πc) condensed phase in neutron matter is developed within the framework of the SU (2) × SU (2) version of the SU (3) × SU (3) σ-model. The degree of freedom of the isobar Δ (1232) is described by using the SU (4) constituent quark model and a variational technique: Baryonic states are described in terms of quasi-proton and quasi-neutron states which are composed of nucleon and isobar ones. As a consequence of this procedure, the roles of the Δ-isobars in the πc condensed phase are clearly seen. Moreover the formalism has a straightforwardly applicable form to neutron star problems, especially the neutron star cooling. The effects of short-range baryon-baryon correlations and the form factors of the pion-baryon p-wave coupling vertex are also included. Numerical results on the properties of the ground state are discussed in detail.