Pi-nucleon scattering

In preparation for a field-theoretic treatment of $\pi$-nucleus scattering, the corresponding $\pi$-nucleon problem is examined. In order to include two-body input in the many-body problem it is useful to have a linear wave equation which describes $\pi$-nucleon scattering. It is shown that the nonlinear Low equation, in the one-meson, one-nucleon truncation, may be expressed as a linear wave equation with an energy-dependent driving term interpretable as a potential. This potential includes the usual driving term of the Low equation plus an infinite set of higher order terms which incorporate the effects of crossing. A discussion of these terms and an iterative prescription for calculating them is given. In the static limit, our solution is shown to be equivalent to that of Chew and Low.