Consider two free electrons passing close to each other. They start in a product state, independent and not entangled. Then they might have an event which emits a photon and fall into a entangled triplet state or a single state, each of which have lower energy than the product state. Is the probability of such an event something that we can write analytical QM expressions to calculate, or is it part of the standard model's coupling coefficients that are determined experimentally? If analytical, what is a good source for me to study? Am I correct in saying that the probability of such an event is a function of the distance between the electrons? Might the probability be a function of the relative velocities, or other factors too?