= Two-centre scattering-length model
{title2=$(a_j^{-1}+ik)c_j+(e^{ikd}/d)c_{3-j}=-ks_j$}
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.
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