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Working in the weak-field approximation, we study the scattering of quantum fields from a gravitational source. For definiteness, we consider the electromagnetic radiation field as well as a massive scalar field, both propagating in a slightly curved spacetime and employ the first-order Born approximation to deduce the scattering cross-sections of the process. We find that the (unpolarized) cross-section for the electromagnetic field coincides (at the tree level) with the classical value, predicted by general relativity; also our results fairly agree with those obtained by other authors in some previous works. On the other hand, our analysis of the massive scalar field leads to results which are quite different when compared with those presented, e.g., in the papers by Golowich et al (1990 Am. J. Phys. 58 688) and by Uno et al (1996 Phys. Lett . A 223 137). Actually, we find that the quantum behavior deviates from its classical counterpart, showing an enhancement in the cross-section as the massive field approaches the non-relativistic regime. We critically discuss and compare our results and those of the above references, attempting to give a possible physical justification of such a puzzling issue in terms of quantum non-locality.

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