Molecular scattering: Convergence of close-coupling expansions in the presence of many open channels

In low-energy atomic scattering theory it is well known that the accuracy of the familiar target eigenstate expansion or ''close coupling'' methods cannot be totally relied upon unless all open channels of the target system are included in the expansion. We show that the same methods, as applied to low-energy scattering by a molecular target, converge even though all open channels above a certain energy level may be truncated in the target eigenstate expansion. The result is applicable only in the energy regime where rotational channels are open but vibrationally and electronically excited state channels are closed