Finite Size Corrections in the Two-Level BCS Model

Superconducting properties of small metallic grains modelled by highly degenerate two-level spectrum have been studied. We have solved numerically Richardson's exact equations for the system of 2N electrons in two levels. Characterising the size of the grain by the level degeneracy we study the finite size corrections to the thermodynamic limit of the ground and lowest excited state energy. The interparticle distance∝ N$\text{}^{-1}\text{}^{/}\text{}^{3}$ seems to be the expansion parameter. The obtained results have been compared with those of other authors.