Formation of the interaction matrix in pion–nucleon scattering in optimal conditions and amplitude determination at 471, 547, and 625 MeV c⁻¹

Abstract

The most recent measurements of the polarization parameters were used to determine the magnitudes and relative phase of spin amplitudes in charged pion – proton scattering at 471, 547, and 625 MeV c−1. In addition to optimal conditions, invariance laws were imposed to reduce the number of independent amplitudes to two. In the transverse frame we obtained two amplitudes both being nonflip. In the helicity frame also we obtained two amplitudes, one spin flip and the other being spin nonflip. The magnitudes of the transverse amplitudes were also determined at 2.39 GeV c−1 in terms of square momentum transfer. In all the calculations, the differential cross section is normalized to unity.