  The role that occupied $d$ bands play in the inelastic lifetime of bulk and
surface states in Ag is investigated from the knowledge of the quasiparticle
self-energy. In the case of bulk electrons, $sp$ bands are taken to be
free-electron like. For surface states, the surface band structure of $sp$
states is described with the use of a realistic one-dimensional hamiltonian.
The presence of occupied $d$ states is considered in both cases by introducing
a polarizable background. We obtain inelastic lifetimes of bulk electrons that
are in good agreement with first-principles band-structure calculations. Our
surface-state lifetime calculations indicate that the agreement with measured
lifetimes of both crystal-induced and image-potential induced surface states on
Ag(100) and Ag(111) is considerably improved when the screening of $d$
electrons is taken into account.
