Classical and quantum scattering by a gravitational center

The corrections to the leading term of the small-angle deflection of a classical particle by the Schwarzschild field and its linear approximation were found. The corresponding cross sections were obtained. The comparison with known in Born approximation cross sections for quantum massless particles of spins 0, 1, and 2 shows that only the leading term in all cases is the same. As the conditions for classical treatment are well fulfilled, this means that the classical results are much more accurate than the quantum one in Born approximation. The fact that the photon cross section is always smaller than that of massless scalar particle (both in Born approximation) suggests that with small probability (at least of order of the difference of these cross sections) the photon can fly by the Sun without deflection. The deflection of light, observable at a final distance from the Sun, is also considered and it is shown that measurements at the distances of several Sun's radii will decide which coordinate system is the privileged one.