Quadrupole amplitude in the γnΔ transition

The tensor part of the color hyperfine interaction between quarks leads to a small electric quadrupole amplitude in the γNΔ excitation. It is demonstrated that pion photoproduction data available previously have a low sensitivity to the (isospin 3/2) electric quadrupole amplitude, E1+(3/2). An additional difficulty is that there is an appreciable background contribution to the total E1+ amplitude. The consequent difficulties in extracting the resonant part of this small amplitude from experiment are discussed. It is shown that γp→π0p and γp→π+n cross sections near 0°and 180°, and also those near 90°with polarized γ rays, both with and without polarized targets, have the greatest sensitivity to the E1+(3/2) amplitude. Since the anticipated observable effects of the resonant E2 amplitude are expected to be ∼10% to 20% in magnitude, the required accuracy to extract a precise E2/M1 ratio is ∼1% for both experiment and theory.