Superconductivity of small metallic particles. I

The ground state energy and orbital magnetic susceptibility of a small-particle superconductor are calculated with the use of perturbation theory, which is expected to give correct results in the limit of small particle size, i.e., when the average one-electron energy level spacing delta is much larger than the energy gap Δ of the bulk metal. The method is applicable up to particles of intermediate size for which Δ/delta=1/4-1/2 (e.g., aluminum particles of radius 25--30 A). The magnetic susceptibility does not undergo any drastic change in the region Δapprox.delta when the particle size is varied, and quantum size effects do not show up in the susceptibility