## Smoothness of $$N$$-body scattering amplitudes.(English)Zbl 0781.35047

The author establishes the smoothness of the 2-cluster – 2-cluster and 2-cluster – $$N$$-cluster scattering amplitudes under some general short range conditions on the potential and under a discreteness assumption on the channel energies. The proofs are based on strong bounds on the resolvent by using so called “channel localization operators”.

### MSC:

 35P25 Scattering theory for PDEs 81U10 $$n$$-body potential quantum scattering theory
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