  This is a proof that if the eikonal is, as usually assumed, additive in
strong and electro-magnetic interactions then the application of the Bethe
Ansatz for the full scattering amplitude leads to the strong interaction
scattering amplitude with the ratio ( real/imaginary) independent on the
transferred momentum $ t $. Moreover, the unitarity condition makes the strong
interaction amplitude vanishing. Thus, the Bethe form for the Coulomb-nuclear
scattering amplitude and the same amplitude based on the additive eikonal are
incompatible.
