  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.
