Nuclear polarization in hydrogenlike ₈₂²⁰⁸Pb⁸¹⁺

We calculate nuclear-polarization energy shifts for the hydrogenlike ₈₂²⁰⁸Pb⁸¹⁺. The retarded transverse part as well as the longitudinal part is taken into account as the electromagnetic interaction between an electron and the nucleus. With a finite charge distribution for the nuclear ground state and the random-phase approximation to describe the nuclear excitations, we obtain nuclear-polarization energy of the 1s_1/2 state as -38.2 (-37.0) meV in the Feynman (Coulomb) gauge. For the 2s_1/2, 2p_1/2, and 2p_3/2 states, they are -6.7 (-6.4), -0.2 (-0.2), and +0.0 (+0.0) meV, respectively. The transverse contribution is small in comparison with the longitudinal nuclear-polarization correction. It is about 12% both for the 1s_1/2 and 2s_1/2 states. The seagull term in the two-photon exchange diagrams is also shown to be quite important to obtain the gauge-invariant nuclear-polarization energies.