Low-Energy Theorem for Nucleon-Nucleon Bremsstrahlung

The low-energy theorem is derived for nucleon-nucleon bremsstrahlung. We assume that the two nucleons interact through a potential which can be any model, nonlocal as well as local. For those potentials which depend explicitly upon momentum and/or angular momentum operators, the gauge terms arising from these operators are included in the derivation. These gauge terms are always important in the study of the off-energy-shell effects of the two-nucleon interaction, and for the $\mathrm{np}\gamma$ process they are essential in the derivation of the low-energy theorem. It is found that the gauge terms are canceled precisely by parts of the terms which represent the photons emitted by the internal nucleon lines.