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- Title
Stationary Scattering Theory: The N-Body Long-Range Case.
- Authors
Skibsted, E.
- Abstract
Within the class of Dereziński–Enss pair-potentials which includes Coulomb potentials and for which asymptotic completeness is known (Dereziński in Ann Math 38:427–476, 1993), we show that all entries of the N-body quantum scattering matrix have a well-defined meaning at any given non-threshold energy. As a function of the energy parameter the scattering matrix is weakly continuous. This result generalizes a similar one obtained previously by Yafaev for systems of particles interacting by short-range potentials (Yafaev in Integr Equ Oper Theory 21:93–126, 1995). As for Yafaev's paper we do not make any assumption on the decay of channel bound states. The main part of the proof consists in establishing a number of Kato-smoothness bounds needed for justifying a new formula for the scattering matrix. Similarly we construct and show strong continuity of channel wave matrices for all non-threshold energies. Away from a set of measure zero we show that the scattering and channel wave matrices constitute a well-defined 'scattering theory', in particular at such energies the scattering matrix is unitary, strongly continuous and characterized by asymptotics of generalized eigenfunctions of minimal growth.
- Subjects
S-matrix theory; QUANTUM scattering; COULOMB potential; SCATTERING (Mathematics); ENERGY function; EIGENFUNCTIONS
- Publication
Communications in Mathematical Physics, 2023, Vol 401, Issue 2, p2193
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-023-04689-7