  It is now well established that radiative decay of quantum emitters can be
strongly modified by their environment. In this paper we present an exact,
within the weak-coupling approximation, multipole expression to compute the
Lamb (frequency) shift induced by an arbitrary set of resonant scatterers on a
nearby quantum emitter, using multi-scattering theory. We also adopt a
Quasi-Normal Mode description to account for the line shape of the Lamb shift
spectrum in the near-field of a plasmonic nanosphere. It is then shown that the
Lamb shift resonance can be blue-shifted as the size of the nanoparticle
increases, suggesting that nanoparticles may be used to tune this resonant
interaction. Finally, a realistic calculation of the Lamb shift is made for a
dimer configuration.
