  A substantial enhancement of the superconducting gap was recently reported in
clean, large ~30nm, and close to hemispherical Sn grains. A satisfactory
explanation of this behaviour is still missing as shell effects caused by
fluctuations of the spectral density or surface phonons are negligible in this
region. Here we show that this enhancement is caused by spatial inhomogeneities
of the Cooper's pairs density of probability. In the mean field approach that
we employ these inhomogeneities are closely related to the eigenstates of the
one-body problem, namely, a particle in a hemispherical shaped potential. The
parameter free theoretical prediction agrees well with the experimental
results. A similar enhancement is predicted for other weakly coupled
superconductors.
