The infinite multichannel-scattering process of the two-particle scattering of mesons of arbitrary isospin off an isospin-½ target, inelastic two-particle channels being admitted, is considered in the static limit. The restrictions on the S matrix arising from crossing under SU(2) and two-particle unitarity are expressed in terms of three equations alone in the limit of degenerate meson masses. These equations are solved by a perturbative technique, the expansion parameter being a measure of the strength of the inelastic scattering. The principal result of this paper is that the inelastic amplitudes are all related, so that if one is zero all must be zero. Comparisons are made with strong-coupling theory, which also requires an infinite number of channels.

Constraints on the solution of the unitarity equation for a two-channel scattering problem arising from the requirements of crossing for the inelastic amplitude are shown to imply the relations imposed by crossing under SU(2) for the elastic amplitudes in the limit of vanishing coupling to the inelastic channel. This result is extended to the three-channel case, where at least two distinct classes of internal symmetry crossing relations can exist: the unitarity equations alone simulate the SU(2) case, but not that associated with higher symmetry groups.