Scattering of Mesons by a Fixed Scatterer

The meson-nucleon scattering equations of Chew and Low are generalized to the case of mesons and scatterers having arbitrary angular momenta. In consequence, the algebraic structure of the equations is made clearer. Two coupling schemes for the angular momenta are studied, the $J$-scheme in which momenta of meson and scatterer in the initial state are coupled, and the $N$-scheme in which the meson momenta in initial and final states are coupled. The condition of unitarity of the $S$-matrix is simple only in the $J$-scheme, the condition of causality is simple only in the $N$-scheme. The interlock between the two schemes gives rise to the peculiar linking of different $J$-values in the Chew-Low equations. The linkage coefficients are shown to be ordinary Racah coefficients.