Abstract
The photon-proton scattering reactions , and are investigated in the framework of the three-dimensional time-ordered approach using different models of the on-shell Δ propagators. These Δ propagators are taken from the unitary separable models of the elastic-scattering amplitude and from the relativistic Breit-Wigner shape representation of the nonunitary amplitude in the tree approach. The numerical calculations are performed with the complete set of the one-particle (-meson, nucleon, and Δ) exchange diagrams. It is found that the numerical calculations of the above reactions in the Δ-resonance region are very sensitive to the model of the Δ propagator. This sensitivity is explained by the difference between the input elastic-scattering observables used for the construction of the Δ propagator. It is shown, that after additional approximation our calculations reproduce the tree-level model calculations with the Breit-Wigner shape Δ propagator. This model is in good agreement with the reaction and with the preliminary data for the reaction. Conversely, it is demonstrated, that the relativistic Breit-Wigner shape Δ propagators, obtained from the nonunitary amplitudes in the tree approximation, is inconsistent to apply for reproduction of the scattering observables because they do not describe the scattering data in the Δ resonance region. It is emphasized, that to extract the magnitude of the magnetic moment from the cross sections of the reaction it is necessary to fix the form of the Δ propagator based on the unified description of the two body basic channels together with the essential and reactions.
9 More- Received 9 December 2003
DOI:https://doi.org/10.1103/PhysRevC.72.024002
©2005 American Physical Society