[en] Based on the developed method for solving the multi-channel equation, which had been applied to the calculations of several kinds of ions including only open-open interactions, closed channels and their interactions with open channels have been studied. The wave functions of the closed channels are also expressed in terms of their homogeneous solutions which is just the same as for open channels. The homogeneous solutions are described and solved in WKB form, therefore the regular and irregular solutions as well as the quantum defect numbers can be obtained simultaneously. Excitations of Mg ⁺, Cd ⁺ ions impact by electrons are calculated for energies close to the thresholds. The results are compared with those of the experimental observations and previous theoretical calculations. The effect of including the closed channels, especially when the energy passes through the resonance energies, has been discussed according to the deduced formulae and the calculated results. (paper)