Consistent calculation of boundary effects in thin superconducting films

A simple model is proposed to treat the quantum size effect in thin superconducting films so as to account for screening of the surface charge, and to thereby provide consistency with the Friedel sum rule for metal surfaces and the constancy of the Fermi level. The original Thompson and Blatt calculation is followed with the additional feature that the overlap integrals for the electron-phonon interaction are only evaluated over the geometrical thickness, which defines the extent of the ion cores even though the electron gas extends beyond the cores. This procedure provides a factor which lowers Tc that is of the order measured in experiments.