 996 Andreas Knauf
 Qualitative Aspects of Classical Potential Scattering
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Jan 7, 99

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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 nonempty and not homeomorphic to a
sphere.
For nontrapping energies we introduce a topological degree which
can be nontrivial for low energies, and for Coulombic and other
singular potentials. A sum of nontrapping potentials of disjoint
support is trapping iff at least two of them have nontrivial degree.
For $d\geq 2$ dimensions the potential vanishes if for any
energy above the nontrapping threshold the classical differential
cross section is a continuous function of the asymptotic directions.
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