 01124 J. Froehlich, M. Griesemer, B. Schlein
 Asymptotic Completeness for Rayleigh Scattering
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Mar 30, 01

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Abstract. It is expected that the state of an atom or molecule, initially
put into an excited state with an energy below the
ionization threshold, relaxes to a groundstate by spontaneous
emission of photons which propagate to spatial infinity. In this
paper, this picture is established for a large class of models of
nonrelativistic atoms and molecules coupled to the quantized
radiation field, but with the simplifying feature that an
(arbitrarily tiny, but positive) infrared cutoff is imposed on
the interaction Hamiltonian.
This result relies on a proof of asymptotic completeness
for Rayleigh scattering of light on an atom. We establish
asymptotic completeness of Rayleigh scattering for a class of
model Hamiltonians with the features that the atomic Hamiltonian
has point spectrum coexisting with absolutely continuous spectrum,
and that either an infrared cutoff is imposed on the interaction
Hamiltonian or photons are treated as massive particles.
We show that, for models of massless photons, the spectrum
of the Hamiltonian strictly below the ionization threshold is
purely continuous, except for the groundstate energy.
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