Gauge Invariant Evaluation of Nuclear Polarization with Collective Model
  The nuclear-polarization (NP) energies with the collective model commonly employed in the NP calculations for hydrogenlike heavy ions are found to have serious gauge violations when the ladder and cross diagrams only are taken into account. Using the equivalence of charge-current density with a schematic microscopic model, the NP energy shifts with the collective model are gauge invariantly evaluated for the $1s_{1/2}$ states in $^{208}_{~82}$Pb$^{81+}$ and $^{238}_{~92}$U$^{91+}$. 
Yataro Horikawa, Akihiro Haga