Frequency shifts near an interface: inadequacy of two-level atomic models

In atoms a distance z from a perfectly conducting plane, electric dipole frequencies omega suffer shifts of order (d 2 )/z 3 for small z, where d is the dipole operator. A totally different expression has been proposed recently, behaving like (d 2 ) omega 3 log( omega z); it can emerge from some calculations on a two-level atomic model. One reason is an unrepresentative cancellation, peculiar to the model, between leading terms in the shifts of the two levels. A deeper failure of the model is its inconsistency with basic quantum mechanics, in that the upper level cannot obey the Thomas-Reiche-Kuhn sum rule, allowing results to depend on just how the calculation is performed.