Effect of. pi pi. interactions in. pi. N scattering

The standard cloudy bag model description of ..pi..N scattering is extended to include contributions at the two-pion level. The ..pi pi.. scattering amplitudes are parametrized in phenomenological, separable forms consistent with the known ..pi pi.. S-italic- and P-italic-wave phase shifts. These amplitudes are embedded in the ..pi..N description to account for scattering of the incident pion from the nucleon's virtual pion cloud. A self-consistent analysis of the coupled ..pi..N, ..pi delta.., and ..pi..N/sup */ (1470) systems results in excellent reproduction of the phase shifts in the ..pi..N P-italic/sub 33/ channel to energies above the pion production threshold. In the P-italic/sub 11/ channel, without two-pion intermediate states, no acceptable fit to the data is possible for any values of the bag parameters. It is shown that the additional attraction provided by ..pi pi.. scattering is essential to reproduce the low-energy phase shifts and fix the sign change at the correct energy.