  Motivated by recent experiments on Al nanoparticles, we have studied the
effects of fixed electron number and small size in nanoscale superconductors,
by applying the canonical BCS theory for the attractive Hubbard model in two
and three dimensions. A negative ``gap'' in particles with an odd number of
electrons as observed in the experiments is obtained in our canonical scheme.
For particles with an even number of electrons, the energy gap exhibits shell
structure as a function of electron density or system size in the weak-coupling
regime: the gap is particularly large for ``magic numbers'' of electrons for a
given system size or of atoms for a fixed electron density. The grand canonical
BCS method essentially misses this feature. Possible experimental methods for
observing such shell effects are discussed.
