  We have investigated the role of the quantum size effects in the evaluation
of the force caused by electromagnetic vacuum fluctuations between ultra-thin
films, using the dielectric tensor derived from the particle in a box model.
Comparison with the results obtained by adopting a continuum dielectric model
shows that, for film thicknesses of 1-10 nm, the electron confinement causes
changes in the force intensity with respect to the isotropic plasma model which
range from 40% to few percent depending upon the film electron density and the
film separation. The calculated force shows quantum size oscillations, which
can be significant for film separation distances of several nanometers. The
role of electron confinement in reducing the large distance Casimir force is
discussed.
