From the LSZ reduction formula, it is clear that only the connected Feynman diagrams that contribute to a scattering amplitude. However, connected diagrams are of two types: 1PR and 1PI. 1PR diagrams can be constructed out of 1PI graphs as the building blocks. Therefore, while considering the divergences of a theory it suffices to regularize and renormalize the 1PI diagrams. But what about scattering?
1. Can one forget about the contribution of 1PR diagrams to a scattering? My understanding is that we cannot neglect 1PR diagrams while computing scattering amplitudes and they have to be taken into account in addition to the 1PI diagrams. But I'm not quite sure.
2. What is the utility of the classification of connected diagrams into 1PR and 1PI classes?