Classical and quantum scattering by a Coulomb potential

For relativistic energies the small angle classical cross section for scattering on a Coulomb potential agrees with the first Born approximation for quantum cross section for scalar particle only in the leading term. The disagreement in other terms can be avoided if the sum of all corrections to the first Born approximation for large enough Coulomb charge contain the classical terms which are independent of that charge. A small part of the difference in classical and quantum cross sections may be attributed to the fact that the relativistic quantum particle can rush through the field without interaction. We expect that smaller impact parameters and spin facilitate this affect.