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Structures of S-matrices for three body Schrödinger operators. (English) Zbl 0748.35026
Summary: Structures of the $$S$$-matrix associated with the collision process from 2 clusters to 3 clusters are studied. This $$S$$-matrix is shown to have a continuous kernel except for 2-dimensional spheres on which 2-body subsystems have zero velocity. On these spheres, the $$S$$-matrix has, in general, singularities whose existence arises from the zero eigenvalues and the zero resonances of the 2-body subsystems.

##### MSC:
 35P25 Scattering theory for PDEs 81U20 $$S$$-matrix theory, etc. in quantum theory 35Q40 PDEs in connection with quantum mechanics 47A40 Scattering theory of linear operators 81U10 $$n$$-body potential quantum scattering theory
##### Keywords:
collision process; continuous kernel; singularities
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##### References:
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