A relativistic model for quasifree negative-pion photoproduction on nuclei

Abstract

A relativistic model for the negative-pion photoproduction reaction (γ,π −p) on a nucleus is discussed. The interaction of the photon with the target nucleon is comprised of the set of Born terms, arising from the pseudovector form of the pion-nucleon interaction lagrangian, as well as s- and u-channel diagrams involving delta propagation. The amplitude is calculated in a relativistic distorted wave framework. Both the bound- and continuum-state nucleons are described by solutions of the Dirac equation with appropriate vector and scalar potentials. The pion wave function is a solution of the Klein-Gordon equation, and the interaction of the pion with the residual nucleus is taken into account via an optical potential. The calculations are done in coordinate space and require the solution of eight-dimensional space-time integrals, which are simplified by making a local approximation to the propagators, allowing the integration at one vertex to be done trivially. As expected we find the contribution of the delta to be important in the resonance region, but in general the delta contribution is smaller than the contribution of the Born terms. The effects of changes in the binding and interaction potentials on the cross section and spin observables are studied and found to be small. We compare the results of the model with the few cross-section data sets available and find qualitative agreement in most cases.