Pair Correlations and Magnetic Susceptibility of Small Al-Grains

Pair correlations and the magnetic susceptibility of electrons in a spherical cavity are studied both for grand canonical and the canonical ensemble. The coupling constant of the BCS Hamiltonian is adjusted to experimental values of the gap parameter. The gap parameter is found to increase for small grains as a consequence of the pronounced shell structure in the spectrum of the spherical cavity. The sharp phase transition at Tc is smeared out for the canonical ensemble. The strong paramagnetic susceptibility of the normal electrons in the cavity is reduced by the superconductivity, but it remains positive.