  We present an alternative approach to the calculation of the lifetime of a
single excited electron (hole) which interacts with the Fermi sea of electrons
in a metal. The metal is modelled on the level of a Hamilton operator
comprising a pertinent dispersion relation and scattering term. To determine
the full relaxation dynamics we employ an adequate implementation of the
time-convolutionless projection operator method (TCL). This yields an analytic
expression for the decay rate which allows for an intuitive interpretation in
terms of scattering events. It may furthermore be efficiently evaluated by
means of a Monte-Carlo integration scheme. As an example we investigate
aluminium using, just for simplicity, a jellium-type model. This way we obtain
data which are directly comparable to results from a self-energy formalism. Our
approach applies to arbitrary temperatures.
