Dispersion effects in elastic electron scattering from $^{208}$Pb

Dispersion corrections to elastic electron scattering from $^{208}$Pb at energies up to 150 MeV are estimated within the second-order Born approximation. All strong transient nuclear excited states with angular momentum up to $L=3$ and natural parity are taken into consideration. It is found that at small scattering angles the high-lying $L=1$ isovector states provide the dominant contribution to the dispersive change of the differential cross section and of the beam-normal spin asymmetry. At the backmost angles these changes are considerably smaller and are basically due to the isoscalar $L=2$ and, to a lesser extent, $L=3$ states. In comparison with the findings for $^{12}$C, the dispersive cross-section modifications for $^{208}$Pb are significantly larger, while the spin-asymmetry changes are much smaller at all angles. The latter originates from the destructive interference of the multipole contributions in $^{208}$Pb that switch sign when proceeding from $L$ to $L+1$. This mechanism might be the origin of the small beam-normal spin asymmetries recently measured in ${}^{208}$Pb at much larger energies.