Is it an accurate statement to say that free electrons in a metal experience NO restoring force when they interact with electromagnetic waves? I understand that the electrons exist in a space filled with ions, and doesn't the cumulative potential that is present due to the presence of the ions exert an electric field on the electrons. Even in the case of simple metals, where you can say that the nucleus is shielded by the valence electrons, so called Coulomb shielding, how significant is the shielding. Naively, it seems to me that because the charge in the nucleus is not balanced by the charge in the bound electrons, there should be some net potential that the free electron sees.
Answer
The free electron model is surprisingly good at predicting the properties of electrons in metals, and this implies that the electrons really are nearly free. However when you look more closely there is of course an interaction with the lattice. This is modelled using the (rather predictably named) nearly free electron model.
The conduction electrons are delocalised, so you shouldn't think of them as little balls bouncing off the ion cores. The spatial extent of their wavefunction is typically far greater than the lattice repeat, hence the relatively weak interactions. However interactions with the lattice are responsible for electrical resistance and thermal conductivity, and at very low temperatures for superconductivity. However note that these aren't interactions between a single electron and a single ion core, but rather interactions between electron waves and lattice waves (phonons).
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