  The multichannel scattering problem in an adiabatic representation is
considered. The non-adiabatic coupling matrix is assumed to have a non-trivial
constant asymptotic behavior at large internuclear separations. The asymptotic
solutions at large internuclear distances are constructed. It is shown that
these solutions up to the first order of perturbation theory are identical to
the asymptotic solutions of the re-projection approach, which was proposed
earlier as a remedy for the electron translation problem in the context of the
Born-Oppenheimer treatment.
