 Two-centre scattering-length model

Two separated short-range scatterers are coupled because the outgoing wave from either centre supplies part of the regular incoming field at the other. Applying the Bethe-Peierls boundary condition at both centres gives the displayed two-by-two linear system, where $s_j$ is the incident plane-wave phase. matrix inversion sums repeated scattering between the centres. Near a small determinant, effective-range corrections may matter even if the nominal microscopic range is short.