Partially Conserved Axial-Vector Current Restrictions on Pion Photoproduction and Electroproduction Amplitudes

We discuss numerically the restrictions imposed by the partially conserved axial-vector current (PCAC) on the pion photoproduction amplitude V₁⁽⁺⁾(0) and on the pion electroproduction amplitude V₆^(-)(0). We find that the magnetic-dipole dominance and the narrow-resonance approximations are unreliable. The nonresonant s waves make an important contribution to V₁⁽⁺⁾(0), and we find that the PCAC prediction for this amplitude is reasonably well satisfied. The electric and longitudinal multipoles appear to make a much bigger contribution to V₆^(-)(0) than does the magnetic dipole M₁₊, which is strongly suppressed by the kinematics.