Laurent Amour, Jeremy Faupin
The confined hydrogenoid ion in non-relativistic quantum electrodynamics
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ABSTRACT.  We consider a system of a nucleus with an electron together with 
the quantized electromagnetic field. Instead of fixing the 
nucleus, the system is confined by its center of mass. This model 
is used in theoretical physics to explain the Lamb-Dicke and the 
M\"ossbauer effects (see [CTDRG]). When an ultraviolet cut-off is 
imposed we initiate the spectral analysis of the Hamiltonian 
describing the system and we derive the existence of a ground 
state. This is achieved without conditions on the fine structure 
constant. 
[CTDRG] C. Cohen-Tannoudji, J. Dupont-Roc and G. Grynberg. Processus d'interaction entre photons et atomes. Edition du CNRS, 2001.