Determination of the Real Part of the Compton Amplitude at a Nucleon Resonance

The real part of the virtual Compton amplitude can be directly determined from measurements of electron (or muon) bremsstrahlung or pair photoproduction. In general, the interference of the Compton amplitude with the Bethe-Heitler amplitude for pair production or bremsstrahlung yields a contribution to the cross section which is antisymmetric when the leptons are interchanged. This interference contribution thus produces different cross sections for electron and positron bremsstrahlung at a given scattering energy and angle. Also, the counting rate for pair production will depend on which lepton has the greater momentum. The determination of the real part of the Compton amplitude would supply information on the isobar resonance shape, test the dispersion relation for the forward amplitude, and resolve uncertainties in the determination of the nucleon resonances. A simple estimate for the lepton asymmetry of the pair production cross sections due to the forward Compton amplitude is given, in addition to a complete calculation of the effect of the first nucleon resonance using the isobar model. The results are also discussed for nuclear targets. For the latter case, a broadening of the isobar decay width due to absorption in the nuclear medium must be taken into account.