PHASE CONTOURS OF SCATTERING AMPLITUDES .I. PHASE CONTOURS ZEROS AND HIGH-ENERGY BEHAVIOR

We define phase contours as curves along which the phase of an invariant scattering amplitude is a constant. These curves are sections of a complex surface, which we take either in the real (s,t) plane or in the complex plane of one of the variables. The relation between phase contours, zeros of the amplitude, and high-energy behavior is discussed. Characteristic features of phase contours are investigated in a variety of special models, and it is seen that basic assumptions about high-energy behavior can readily be expressed in terms of the topology of the phase contours. Specific illustrations of phase contours are given for pionnucleon scattering based on phase-shift solutions at low and medium energies and on an extrapolation from Regge solutions at high energies. © 1968 The American Physical Society.