  We report extensive calculations of the imaginary part of the electron
self-energy in the vicinity of the (100) and (111) surfaces of Cu. The
quasiparticle self-energy is computed by going beyond a free-electron
description of the metal surface, either within the GW approximation of
many-body theory or with inclusion, within the GW$\Gamma$ approximation, of
short-range exchange-correlation effects. Calculations of the decay rate of the
first three image states on Cu(100) and the first image state on Cu(111) are
also reported, and the impact of both band structure and many-body effects on
the electron relaxation process is discussed.
