Hydrogen atoms interacting with a quantised radiation mode

A model consisting of a hydrogen atom coupled to a single quantised radiation mode in the long-wavelength approximation is studied mathematically. It is shown that the Hamiltonian H for this model is dilatation analytic. This result makes it possible to describe various resonance phenomena associated with atoms in radiation fields by means of analytic continuation techniques. Furthermore, it is shown that H possesses an infinite number of bound states with negative energy. Nevertheless the photoionisation probability tends to one with increasing field strength.

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