Step wise destruction of the pair correlations in micro clusters by a magnetic field

The response of $nm$-size spherical superconducting clusters to a magnetic field is studied for the canonical ensemble of electrons in a single degenerate shell. For temperatures close to zero, the discreteness of the electronic states causes a step like destruction of the pair correlations with increasing field strength, which shows up as peaks in the susceptibility and heat capacity. At higher temperatures the transition becomes smoothed out and extends to field strengths where the pair correlations are destroyed at zero temperature.