Low-energy theorems for virtual nucleon-nucleon bremssrahlung; formalism and results

We present results for cross sections and response functions in virtual bremsstrahlung induced by nucleon-nucleon collisions NN → NN + e⁺e⁻, based on two different low-energy theorems. The first low-energy theorem is a generalization of Low's theorem for real-photon bremsstrahlung. The second low-energy theorem was derived by Liou et al. for real photons, and is generalized here to the case of virtual photons. The two low-energy theorems are compared by calculating the cross section and response functions in the kinematical region of possible future experiments. We find that for most observables the amplitude up to leading order only in the photon energy does not provide a reliable description, and that the next order term is very important. The differences between the two low-energy theorems turn out to be sizeable for pp, but quite small for pn virtual bremsstrahlung. We also pay attention to the correct implementation of the generalized Pauli principle and crossing symmetry which the reaction amplitude must obey.