We calculate the unpolarized differential cross section in magnetic dipole field, electric dipole field and uniform electrostatic and magnetostatic fields, respectively,by the Feynman perturbation technique. It is found that in electric dipole field, the differential cross section vanishes in both the same and the opposite propagating directions of the photon flux. In the magnetic dipole field the differential cross section generally has non-vanishing values in both directions,but when the propagating direction of photon flux is parallel to the magnetic dipole vector, the differential cross section is equal to zero. In the uniform electrostatic and magnetostatic fields, non-vanishing differential cross sections occur in the same and opposite propagating directions of the photon flux, but in the latter case it is weaker than in the former. When the mass of axion approaches to zero,the above process shows similar characters as the conversion of the photons to the gravitons.