Rayleigh Scattering at Atoms with Dynamical Nuclei |
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Authors: | J Fröhlich M Griesemer B Schlein |
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Institution: | 1.Theoretical Physics,ETH-H?nggerberg,Zürich,Switzerland;2.Fachbereich Mathematik,Universit?t Stuttgart,Stuttgart,Germany;3.Department of Mathematics,Harvard University,Cambridge,USA |
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Abstract: | Scattering of photons at an atom with a dynamical nucleus is studied on the subspace of states of the system with a total energy below the threshold for ionization of the
atom (Rayleigh scattering). The kinematics of the electron and the nucleus is chosen to be non-relativistic, and their spins are neglected. In a simplified
model of a hydrogen atom or a one-electron ion interacting with the quantized radiation field in which the helicity of photons
is neglected and the interactions between photons and the electron and nucleus are turned off at very high photon energies
and at photon energies below an arbitrarily small, but fixed energy (infrared cutoff), asymptotic completeness of Rayleigh scattering is established rigorously. On the way towards proving this result, it is shown that, after coupling the electron and the
nucleus to the photons, the atom still has a stable ground state, provided its center of mass velocity is smaller than the
velocity of light; but its excited states are turned into resonances. The proof of asymptotic completeness then follows from
extensions of a positive commutator method and of propagation estimates for the atom and the photons developed in previous
papers.
The methods developed in this paper can be extended to more realistic models. It is, however, not known, at present, how to
remove the infrared cutoff.
Activities supported, in part, by a grant from the Swiss National Foundation.
Work partially supported by U.S. National Science Foundation grant DMS 01-00160.
Supported by a NSF postdoctoral fellowship. |
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