That seems like ridiculously strong screening, but that's what the jellium calculation gives, and I don't know a better calculation. Penetration depth is a measure of how deep light or any electromagnetic radiation can penetrate into a material. Igor-- yes and not exponential in form. Here, you assume that the potential enters a self-consistent jellium, which is a uniform positive charge density plus almost free Fermi gas. If a jellium metal has a potential V imposed on it, the number density of the electrons at any point can be calculated semiclassically with no significant error, as follows. In this regime, the assumptions used to derive the self-consistent jellium break down.
Penetration length is few atomic layers?
In either case the penetration depth is found directly from the imaginary part of the material's refractive index as is detailed above. Depending on the nature of the material, the electromagnetic field might travel very far into the material, or may die out very quickly. This means that the surface electrons are essentially confined to the first atomic layer, with some field entering into the next few layers, and the details of the atomic orbitals and the electron electron interactions are necessary for working out exactly how the electric field goes away. For a given material, penetration depth will generally be a function of wavelength. Sign up using Facebook. The result is less than an Angstrom, and is therefore unphysical. The potential shifts the energy levels of the electrons, and you take this into account by filling the levels in the potential.