Cross sections, spin observables, and helicity amplitudes of the reaction at the isobar resonance and below

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Abstract
We have calculated the reaction cross sections and spin observables from threshold to the resonance by considering three types of mechanisms; the impulse (absorption) mechanism, rescattering and s-wave rescattering. The effect of final-state interactions has also been included. While traditionally the first two mechanisms have been included within a sound theoretical basis, the s-wave rescattering generally has been treated phenomenologically using a coupling constant fitted to the low-energy pion - nucleon data. Herein, we treat the isovector component of such a pion rescattering process as being mediated by the -exchange. Also, in those absorption mechanisms where the pion enters directly without rescattering, we employ a phenomenological cut-off scaling governed by the nucleon coordinates, since at the pion - nucleon vertex the nucleon itself may be off mass shell. The energy dependence of the total cross section is well explained by the combined effects of the three mechanisms, but we find that this observable is not sensitive enough to give useful insight into fine details of the reaction. We calculated the spin observables of at a variety of energies spanning the resonance, finding such sensitivity to fine details of the calculation that we cannot obtain a complete agreement with the vast experimental data base. A better understanding of the importance of the various aspects of the reaction was obtained when the calculated helicity amplitudes were compared with those extracted via phase-shift analyses of the reaction data.

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