Nonadiabatic, momentum-dependent, and energy-dependent corrections in the effective-potential description for low-energy scattering of spinless systems - Their relations and validity

In the effective-potential description for low-energy scattering involving a spinless complex (a body with internal structure), the nonadiabatic corrections are sometimes disguised in momentum-dependent terms. These are distinct from energy-dependent corrections. A general procedure is given here by which all the momentum-dependent corrections can be converted into nonadiabatic corrections in truly local form. Circumstances under which an expansion of the effective potential, in terms of the adiabatic term plus nonadiabatic and energy-dependent corrections is allowed and forbidden, are discussed. An example for the latter is in the case of near degeneracy in the spectrum of the complex or in the extrapolation of the effective potential to short-distance behavior. This indicates that certain claims of 'saturation effect' at short distances in low-energy electron-atom scattering are invalid.