Pion condensation and realistic nucleon-nucleon interactions

Abstract

The general ideas behind Pion Condensation are discussed and the Pion p-wave selfenergy is calculated in nuclear matter taking into account the effects of the nucleon particle-hole and Δ-isobar nucleon-hole states. The residual particle-hole interaction is derived from the Brueckner reaction-matrix using a realistic nucleon-nucleon interaction. This reaction matrix depends on starting energy, nuclear matter density and three momentum variables. The transition potentials between NN⁻¹-ΔN⁻¹ states and the ΔN⁻¹-ΔN⁻¹ states are described by the exchange of π and ϱ mesons with the correlations between the nucleons properly included. The resulting selfenergies are analized within the commonly used model of constant interaction strengths. This analysis yields effective interaction strengths weakly depending on the momentum of the Pion field and on the nuclear density. The particle-hole interaction described by the Brueckner reaction matrix, including the Δ-isobars yields pion condensation at twice the empirical nuclear matter density. The inclusion of the higher order terms in the particle-hole interaction (induced ph-interaction), however, shifts this density up to about 6 times the empirical nuclear matter density. Finally, the influence of the Δ-isobars and the transition potential with the π and ϱ mesons exchange is studied on pion condensation in ¹⁶O. Although the calculation in finite nuclei with realistic forces is yet to be done the results of the model calculation show that it is essential to include Δ-isobars and ϱ-meson exchange. In the model presented here these two effects shift down the critical density for pion condensation from 8ϱ_O to 3ϱ_O.