Multiple pion exchange in a nonstatic theory of nucleon-nucleon scattering and isobar production

Abstract

Exchange of nonstatic pions between a nucleon and Δ(1231) isobar in the reactions NN → NN and NN → NΔ is studied near the pion- and Δ-production thresholds. The nonstatic nature of the exchange permits the repeated formation and decay of a nearly on-shell isobar as the pion shuttles back and forth on its mass shell. The mechanism modifies the analysis of NN elastic and Δ production processes at intermediate range ( ≈ 1 2 M π −1). We examine these effects in a relativistic theory, restricted to spinless particles, based on the covariant off-shell formalism of Blankenbecler and Sugar. Three versions of this theory are considered, involving intermediate nucleon-isobar propagation taken off the mass shell (i) symmetrically, (ii) nonsymmetrically, and (iii) in a quasiparticle formulation. For the mechanism considered here, a clear preference is found for the nonsymmetrical prescription. Our results indicate that the nonstatic multiple-pion-exchange mechanism should be included in quantitative analyses of NN → NN, NΔ in the threshold regions for pion and Δ production.