Solutions of the Static Theory Integral Equations for Pion-Nucleon Scattering in the One-Meson Approximation

Numerical solutions of the one-meson approximation of the Low equations for elastic pion-nucleon scattering in the fixed-nucleon, extended-source theory are obtained with a Gaussian cutoff function. The validity of the method requires that the scattering amplitudes have no zeros in the complex plane other than at $z=\pm 1$. The functions obtained for the (3,3) and (1,1) states satisfy the Low equations within the accuracy of the method, but the (1,3) and (3,1) states are only approximately given. This difficulty with the (1,3) and (3,1) states is correlated with the development of a zero in the corresponding scattering amplitude well before physically interesting values of the parameters (coupling constant and cutoff) are reached.