Validity of the BCS model Hamiltonian in the limit of small sizes

Finite-size effects when the electronic level spacings become comparable to the bulk superconducting gap can suppress pairing correlations in small metallic particles. We examine an alternative mechanism for finite-size suppression of superconductivity: the role of the nonpair portion of the interaction, which could become important in small systems. We show that the crossover size at which the nonpair contribution becomes significant is typically already within the regime wherein finite level spacing suppresses the pairing correlations; however, the nonpair terms could become relevant in certain weak-coupled superconductors.