Conserving quasiparticle calculations for small metal clusters

A novel approach for GW-based calculations of quasiparticle properties for finite systems is presented, in which the screened interaction is obtained directly from a linear response calculation of the density-density correlation function. The conserving nature of our results is shown by explicit evaluation of the $f$-sum rule. As an application, energy renormalizations and level broadenings are calculated for the closed-shell Na$_9^+$ and Na$_{21}^+$ clusters, as well as for Na$_4$. Pronounced improvements of conserving approximations to RPA-level results are obtained.