I am curious to know this,its confusing me a lot.How does it differ,What is the interaction cross section for both the cases if an infrared photon incidents on it?.
A free electron in a metal is actually a Bloch electron interacting with the periodic potential of the lattice and all the other electrons which are there. It turns out that the electrons in a band near the Fermi surface can be approximated rather well as being isolated (they are “dressed” quasiparticles), but there’s an important difference. A real isolated free electron is subject to no additional interactions. A free electron in a metal is subject to many. These include electron-electron scattering, electron-phonon scattering, defect scattering, surface scattering, collective oscillations (plasmons), interband transitions, etc. In a simple case, say, Au with photon energies in the infrared range, the scattering can be lumped into a phenomenological parameter called the Drude scattering time (or momentum relaxation time). Condensed matter computations of the light scattering cross-section often focus on calculating these scattering rates, based on various assumptions about the metal, after computing the band structure. This is because the scattering adds the degree of freedom to allow for absorption/phase shift of light in interaction with the metal. Light interacting with a totally isolated electron cannot be absorbed or experience a phase shift because there’s no scattering of electrons to conserve energy and momentum.