Erik Skibsted
Institut for  Matematiske
Aarhus Universitet, Munkegade  8000 Aarhus C, 
Denmark
email:skibsted@imf.au.dk


Two-body scattering at low energies

We give an account of various recent results obtained with Jan
Derezi'nski on low-energy scattering for a class of long-range
potentials containing the attractive Coulombic one. This includes
the construction of wave operators of Isozaki--Kitada type diagonalizing
the  whole  continuous part of the Hamiltonian. The corresponding S-matrix
is strongly continuous (although not differentiable) at zero energy. 
We derive a relationship to the analogous Dollard type constructions,
and show that the location of the singularities of the scattering kernel
S(lambda)(omega,omega') experiences an abrupt change at $lambda=0$.
Thus, for example, for the purely Coulombic case the set of singularities
jumps (as the energy goes down) from the set of coinciding outgoing
and incoming angles, omega= omega', to the set of oppositely oriented angles,
omega=-omega', reflecting the fact that the classical orbits at zero
energy in this case are parabolas.




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