  A theoretical many-body analysis is presented of the electron-electron
inelastic lifetimes of Shockley electrons and holes at the (111) surface of Cu.
For a description of the decay of Shockley states both below and above the
Fermi level, single-particle wave functions have been obtained by solving the
Schr\"odinger equation with the use of an approximate one-dimensional
pseudopotential fitted to reproduce the correct bulk energy bands and
surface-state dispersion. A comparison with previous calculations and
experiment indicates that inelastic lifetimes are very sensitive to the actual
shape of the surface-state single-particle orbitals beyond the $\bar\Gamma$
(${\bf k}_\parallel=0$) point, which controls the coupling between the Shockley
electrons and holes.
