Meson-nucleus dynamics

Abstract

A diagrammatic perturbation theory for the interaction of a pion with a finite nucleus is developed. The theory allows us to identify the various pieces of the physics which are believed to be important and to put into a unifying language the understanding which is emerging from apparently diverse studies. The theory proposed here is arranged so that it maintains the use of the nearly free pion-nucleon T-matrix and contemporary nuclear structure work which utilizes a nucleon-nucleon Bethe-Goldstone g-matrix. Within this framework, we calculate in momentum space and without approximation the first-order optical potential. This potential includes: (1) an exact performance of the Fermi-averaging integral (delta propagation), (2) covariant kinematics including the recoil of the nuclear target, (3) the use of invariant amplitudes and invariant normalizations and phase space factors, (4) the inclusion of the delta-nucleus interaction through a mean-spectral approximation, and (5) a realistic off-shell extrapolation of the pion-nucleon amplitude. The elastic scattering cross sections predicted by this potential are remarkably close to the data. The higher-order effects are classified and their inter-relationships discussed. Three of the higher-order corrections, Pauli effects, pion true-absorption, and short range correlation effects, are calculated and the success of the first-order potential is found to be validated by a large cancellation between the Pauli and true-absorption corrections. A detailed discussion of and comparison to alternate approaches to investigating pion-nucleus dynamics is provided.