A dynamically consistent, gauge invariant model for πN bremsstrahlung is developed. The πN dynamics are described through an isobar model fit to the experimental phase shifts. The charge and current operators are constructed in a gauge invariant fashion and include contributions from interaction currents at the πNΔ vertices and from the bare Δ electromagnetic moments. The meaning of such moments for an unstable particle is discussed in detail. From a fit to the ${\pi }^{+}$p bremsstrahlung data, we extract a dipole moment for the bare ${\Delta }^{++}$ in the range &/${\mathrm{\mu }}_{\mathrm{p}\mathrm{\approxeq }2.5}$ to 3.5; if the contributions from internal pion and nucleon currents are included, this ratio is somewhat smaller. The ${\pi }^{\mathrm{-}}$p bremsstrahlung data are consistent &, including &=0. The Δ quadrupole moment cannot be extracted meaningfully from the data. We discuss the sensitivity of the extracted values of ${\mu }_{\Delta }$ to the off-shell extension of the πN scattering amplitude. The polarization asymmetry is found to be sensitive to ${\mu }_{\Delta }$ while being less sensitive to off-shell scattering.

• Received 25 July 1986

DOI:https://doi.org/10.1103/PhysRevC.35.718