  The Born approximation, one photon exchange, used for DIS is subject to
virtual radiative corrections which are related to the long-range Coulomb
forces. They may be sizeable for heavy nuclei since Z\alpha is not a small
parameter. So far these corrections are known only for two processes, elastic
scattering and bremsstrahlung on the Coulomb field of a point-like target.
While the former amplitude acquires only a phase, in the latter case the cross
section is modified also. Although the problem of Coulomb corrections for DIS
on nuclei is extremely difficult, it should be challenged rather than 'swept
under the carpet'. The importance of these radiative corrections is questioned
in present paper. We show that in the simplest case of a constant hadronic
current the Coulomb corrections provide a phase to the Born amplitude,
therefore the cross section remains the same. Inclusion of more realistic
hadronic dynamics changes this conclusion. The example of coherent production
of vector mesons off nuclei reveals large effects. So far a little progress has
been made deriving exact lepton wave functions in the Coulomb field of an
extended target. Employing available results based on the first-order
approximation in Z\alpha, we conclude that the Coulomb corrections are still
important for heavy nuclei. We also consider an alternative approach for
extended nuclear targets, the eikonal approximation, which we demonstrate to
reproduce the known exact results for Coulomb corrections. Calculating
electroproduction of vector mesons we again arrive at a large deviation from
the Born approximation. We conclude that one should accept with caution the
experimental results for nuclear effects in DIS based on analyses done in the
Born approximation.

High Energy Physics - Phenomenology;Nuclear Theory