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We study the electronic and muonic nuclear polarizations with the nuclear excitations constructed by two nuclear models: the relativistic and nonrelativistic random-phase approximations. The importance of the nuclear dynamics in the level shift of electronic and muonic states is discussed.

Charge conservation for nonrelativistic RPA theory of finite nuclei is investigated. Charge conservation of the RPA is proved with effective one-body operators by taking the angular momentum coupling into account. For LS-closed shell nuclei, it is proved that this charge conservation is valid also in truncated particle-hole spaces.

In light of the recent finding of the discrepancies between theory and experiment in the Δ2p and Δ3p fine-structure splitting energies of muonic 208Pb, we have studied the effect of the electromagnetic transverse interaction on the nuclear-polarization energy shifts of muonic 208Pb. The reasons for this study are that the electric transverse interaction interferes coherently with the Coulomb interaction giving rise to large nuclear-polarization energy shifts, and that the transverse interaction may give nuclear-polarization energies of different muon-spin dependences from those of the Coulomb interaction. The calculation is based on the transition charge and current densities constructed from the random-phase approximation with the density-dependent contact interaction of Migdal and with particle-hole excitations of nearly a full 3 h ω space. The real part of the Feynman propagator was employed in the electromagnetic transverse interaction. The transverse interaction is found to explain 111 eV of the Δ2p binding-energy anomaly, which is one third of the total discrepancy, while it reduces the Δ3p anomaly by 32 eV. Large portions ofthe discrepancies still remain in both cases.