Charged Pion Photoproduction on Light Nuclei.

A formalism was devised for calculating cross sections for the photoproduction of charged pions on complex nuclei leading to discrete final nuclear states. The formalism was based on the Distorted Wave Impulse Approximation and the factoring approximation, using information gained from pion scattering and pionic atom experiments to represent the final state interaction between the produced pions and the residual nuclei. The impact of the factoring approximation, which was estimated to be small to begin with, was minimized by choosing the initial nucleon momentum in an optimal way. Through the use of the Helm model it was possible to incorporate accurately and effectively the information describing the nuclear transitions as gained from high precision electron scattering data. Since the use of the Helm model here required the principle of isospin invariance to be valid, applications of the formalism are limited to light nuclei. The elementary photoproduction amplitude was obtained from the multipole amplitudes of Berends et al. Since these amplitudes were found to account insufficiently for the photoelectric term, a derivation of the missing partial waves was provided. The transformation from the pion nucleon barycentric system to the laboratory frame applied to the photoproduction amplitude is analogous to that commonly employed for the pion scattering amplitude. An approximation for the off -shell form of the amplitude in the form of a linear combination of two on-shell amplitudes was proposed. The pion momenta in the photoproduction operator were replaced by gradients operating on the pion wave function. Differential and total cross sections were calculated for production of positive and negative pions on ('12)C and ('16)O over an energy range reaching from threshold to the (3,3) resonance region. Agreement of the results with recent experimental data was found to be very good, generally to within the experimental error bars, indicating the essential correctness of the approach chosen.