Quadrupole Amplitude In The Gamma-N[--]Delta Transition

The tensor part of the color hyperfine interaction between quarks-leads to a small electric quadrupole amplitude in the gammaN<-- -->DELTA 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 gammap --> pi0p and gammap --> pi+n cross sections near 0-degrees and 180-degrees, and also those near 90-degrees with polarized gamma 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 approximately 10% to 20% in magnitude, the required accuracy to extract a precise E2/M1 ratio is approximately 1% for both experiment and theory.