Proton Polarization in the $p(\vec e,e'\vec p)\pi^0$ Reaction and the Measurement of Quadrupole Components in the N to $\Delta$ Transition

Abstract

The recoil proton polarization in the $\pi^0$ production off the proton with longitudinally polarized electron beam has been studied as a means to measure quadrupole components in the N to $\Delta$ transition. On top of the $\Delta$ resonance a high sensitivity to a possible Coulomb quadrupole excitation is found in parallel kinematics. The ratio of $S_{1+}/M_{1+}$ multipole amplitudes can be determined from the ratio of the two in-scattering-plane recoil proton polarization components. Avoiding the absolute measurement of the polarizations, such a ratio allows small experimental uncertainties. Furthermore, the electron helicity independent proton polarization component enables the characterization of resonant and non-resonant pieces.