- 99-6 Andreas Knauf
- Qualitative Aspects of Classical Potential Scattering
Jan 7, 99
(auto. generated ps),
of related papers
Abstract. We derive criteria for the existence of trapped orbits (orbits which are
scattering in the past and bounded in the future). Such orbits exist if
the boundary of Hill's region is non-empty and not homeomorphic to a
For non-trapping energies we introduce a topological degree which
can be non-trivial for low energies, and for Coulombic and other
singular potentials. A sum of non-trapping potentials of disjoint
support is trapping iff at least two of them have non-trivial degree.
For $d\geq 2$ dimensions the potential vanishes if for any
energy above the non-trapping threshold the classical differential
cross section is a continuous function of the asymptotic directions.