Application of the real Weinberg states in potential scattering

This work is the first step in a systematic application of a resonant scattering theory due to Huby in which the real Weinberg state is the crucial feature. The scattering cross sections ofl=0,1, 2 partial waves in a square well potential are calculated with the aid of the real Weinberg states. Perfect agreement with the exact calculation is obtained. Approximate cross sections resulting from a schematic approximation in the formalism which, apart from other desirable features, display the Breit-Wigner energy factor in the phase shifts, are also found to agree perfectly with the exact calculation. Some simple approximations of the complex and real Weinberg states are investigated, but none is found to be satisfactory forl>0 partial waves in complete contrast to works of previous authors on thel=0 partial wave.