  The life-times due to Auger-electron emission for a hole on a deep electronic
shell of neutral and charged sodium clusters are studied for different sizes.
We consider spherical clusters and calculate the Auger-transition probabilities
using the energy levels and wave functions calculated in the
Local-Density-Approximation (LDA).
  We obtain that Auger emission processes are energetically not allowed for
neutral and positively charged sodium clusters. In general, the Auger
probabilities in small Na$_N^-$ clusters are remarkably different from the
atomic ones and exhibit a rich size dependence.
  The Auger decay times of most of the cluster sizes studied are orders of
magnitude larger than in atoms and might be comparable with typical
fragmentation times.

Atomic and Molecular Clusters