A dynamical model of pion photoproduction on the nucleon

Pion photoproduction on the nucleon is investigated using a model hamiltonian defined in the channel-space H = πN⊕γN⊕B with B = δ and N. The basic electromagnetic matrix elements are deduced from the low-order Feynman amplitudes calculated from a lagrangian describing interactions among γ-, π-, ρ-, ω-, N- and Δ-fields. The πN interaction is described by B↔πN vertices, and a two-body separable potential. A scattering formalism is introduced to assure that the constructed pion photoproduction amplitude is unitary and gauge invariant. The πN parameters are determined by fitting the phase-shift data up to 500 MeV incident pion energy. The remaining three free parameters of the model, cutoff Λ for the form factor which regularizes the Born (nonresonant) terms, g_m and G_E for the γN↔Δ vertex, are determined by fitting the M_{1+( 3 2)} and E₁₊( 3 2) multipole data. The resulting E2/M1 ratio of the γN↔Δ excitation is -3.1%. The model can to a large extent describe the existing cross-section and polarization data for γp → π⁺n, γp→π⁰p and γn → π^-p up to 400 MeV incident photon energy. The importance of unitary in extracting the basic parameters from the data is demonstrated explicitly. It is also shown, that within the present unitary model, the πN off-shell effects can account for up to 50% of the cross section. For the interpretation of experimental data, this indicates a significant difference between the present hamiltonian approach and those that use only the Watson theorem to impose unitarity. The model is consistent with the existing unitary πNN models, and hence can be directly applied to study pion photoproduction on the deuteron and heavier nuclei.