Pion-nucleon form factor in the Chew-Low theory

Abstract

We find a solution to the static Chew-Low theory of pion-nucleon scattering, avoiding the one-meson approximation. Our basic equation is crossing symmetric and may be solved for phase shifts $\ensuremath{\delta}(p)$ by standard numerical techniques, upon specifying a form factor $\ensuremath{\nu}(p)$ and a set of inelasticities. With $\ensuremath{\nu}(p)=\mathrm{exp}(\frac{\ensuremath{-}{p}^{2}}{30})$ we reproduce experimental $\ensuremath{\delta}(p)$ for ${p}_{L}\ensuremath{\le}1.2 \frac{\mathrm{GeV}}{c}$ in the (3,3) state; in the (1,3) states and (3,1) states $\ensuremath{\delta}(p)$ compare well on the average but in the (1,1) state $\ensuremath{\delta}(p)$ have opposite signs. We show the importance of crossing symmetry and the coupling to inelastic channels, and we discuss the possibility of determining $\ensuremath{\nu}(p)$ directly from elastic scattering by an inverse scattering formula.[NUCLEAR REACTIONS Pion-nucleon elastic scattering; Chew-Low theory, pion nucleon form factor, crossing symmetry, coupling to inelastic channels, inverse scattering problem.]