The lifetime of electronic excitations in metal clusters

Density functional theory and the self-energy formalism are used to evaluate the lifetime of electronic excitations in metal clusters of nanometre size. The electronic structure of the cluster is obtained in the jellium model and spherical symmetry is assumed. Two effects that depend on the size of the clusters are discussed: the change in the number of final states to which the excitation can decay, and the modification in the screened interaction between electrons. For clusters with density parameter r(s) = 4 and diameter a few nanometres, a lifetime value of approximate to 5 fs is reached for electronic excitations of approximate to 1 eV. This value is of the same order of magnitude of that obtained in the bulk limit at the same level of approximation. For smaller clusters, a distinct non-monotonic behaviour of the lifetime as a function of the cluster size is found and the lifetime of excitations of approximate to 1 eV can vary between 4 and 30 fs.