Abstract :
In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms
there is a nucleus of infinite mass andchar ge Ze, Z>0, fixedat the origin andan electron of
mass m andchar ge e. This system forms a boundstate with binding energy Ebin =me4Z2/8 2
to leading order in e. We investigate the radiative corrections to the binding energy and prove
upper andlo wer bounds which imply that Ebin = me4Z2/8 2 + c0e6 + O(e7 ln e) with explicit
coefficient c0 and independent of the ultraviolet cutoff. c0 can be computedby perturbation
theory, which however is only formal since for the Nelson Hamiltonian the smallest eigenvalue
sits exactly at the bottom of the continuous spectrum
