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It is shown both analytically and numerically for a number of examples that both radial and rotational nonadiabatic couplings within the standard adiabatic approach depend on the origin of the light-particle coordinates and the ambiguity in the nonadiabatic couplings does not lead to ambiguity in the coupled channel equations. The examples considered are the nH, nD, np Ϫ quasimolecules, for which the nonadiabatic couplings can be calculated analytically, and the HeH molecule, for which ab initio calculations are carried out. Analytical formulas for couplings calculated with the shifted origin are derived. The coupled equations take their simplest form in Jacobi coordinates for which many nonadiabatic couplings are nonzero, even for such noninteracting systems as nH, nD, and np Ϫ . These couplings are a fundamental feature of the adiabatic approach.

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It is pointed out that certain faults in the customary formulation describing electron capture in slow collisions arise from the defective character of the electronic eigenfunctions used in the standard expansion. These eigenfunctions satisfy the appropriate equation for all internuclear separations if the velocity of relative motion is zero ; but they do not as they should, satisfy it for all velocities of relative motion when the internuclear separation is infinite. When suitably modified eigenfunctions are adopted the faults mentioned disappear. The equivalence of the impact parameter and wave treatments is verified both for non­-resonance and for resonance capture.