S-wave pion-nucleus dynamics in theσ+ωmodel

Abstract

The $\ensuremath{\sigma}+\ensuremath{\omega}$ model of nuclear forces has many desirable properties, including approximate chiral symmetry (partial conservation of axial vector current) and renormalizability, and it gives a good account of nuclear structure. It is therefore a useful framework within which to explore the modification of pion-nucleon dynamics in a nuclear medium, a problem which resists the usual soft-pion current-algebra cum analyticity techniques owing to the presence of anomalous thresholds (nuclear structure effects). It is found that through order ${G}^{4}$ (for pion elastic scattering) and ${G}^{3}$ (for pion absorption or emission) the chiral invariance ensures sufficient cancellations between otherwise large terms so as to produce little renormalization of free-particle dynamics. Moreover, the pseudoscalar-coupled $\ensuremath{\sigma}+\ensuremath{\omega}$ model is equivalent in pion emission or absorption, through $O({G}^{3})$, to a pseudovector-coupled phenomenological model (with no $\ensuremath{\pi}\ensuremath{-}\ensuremath{\sigma}$ interaction, but with a form of partially conserved axial vector current). Thus, the question of whether one can distinguish experimentally between pseudoscalar and pseudovector $\ensuremath{\pi}\mathrm{NN}$ coupling is probably meaningless.NUCLEAR REACTIONS $A(\ensuremath{\pi},\ensuremath{\pi})A$, $A(p,\ensuremath{\pi})B$, $A(\ensuremath{\pi},NN)C$. ${E}_{\ensuremath{\pi}}<50$ MeV. Wick-formalism treatment of field-theoretic $\ensuremath{\sigma}$-model Lagrangian with $\ensuremath{\omega}N$ coupling. Consequences of broken chiral symmetry for finite-mass pions in nuclei. Nonlinear effects.