PSEUDOSCALAR PION-NUCLEON INTERACTION WITH METHOD OF UNITARY PADE APPROXIMANTS OF S-MATRIX

The formalism for the application of the Padé method to the S-matrix of the pion-nucleon scattering with the pseudoscalar field theory is introduced. The results of the pseudoscalar pion-nucleon theory due to the first nontrivial approximant and without any phenomenological parameter are in satisfectory agreement with the experimental T=3/2 phase shifts (S 31, P31, D35, D33 and P 33, up to roughly 1500 MeV c.m. total energy), except for the width of the P 33, which seems related with more involved dynamics than the one considered here. An interesting consistency between the γππ→ππ term in the present problem and the one predicted from the pure boson-boson interaction is achieved. The situation changes in the isospin T=1/2 where the mechanism of absorption with coupled channels and more inelastic contributions (by using approximants of higher order and matrices in two-body channel space) seem necessary to reproduce the strongly absorbed phase shifts. © 1969 Società Italiana di Fisica.