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By enhancing electron position fluctuations, equilibrium electromagneticradiation modifies the potential for an electron in a Hydrogen atom. This canhave significant effects for weakly bound states and especially at finitetemperature. This implies a 2% correction to Bethe's value for 2S-2P Lamb shiftfor weak fluctuations, but the effect is an order of magnitude larger forstrong fluctuations where it provides direct measure of the proton diameter.

Brownian motion of the electron and the Lamb shift at finite temperature