This paper presents calculations of the electronic polarizabilities of very small metallic particles and of very thin metallic films. The theoretical model we employ for the metallic particle is simply that of $N$ free electrons trapped by an infinitely deep spherical potential well. The model used for the thin-film problem is that of a system of free electrons constrained to move in the volume enclosed by two infinite parallel planes. Linear-response theory and Poisson's equation are used to calculate the electronic polarizability in terms of the electronic density-density response function. The numerical results provide an idea of just how small, or how thin, a small metallic particle, or thin metallic film, has to be for it to begin to lose its bulk property of being able to screen an externally applied electric field.

• Received 22 January 1973

DOI:https://doi.org/10.1103/PhysRevB.8.474