Temperature effects on the optical absorption of jellium clusters

Temperature broadening of the microscopically obtained optical absorption of open-shell clusters is studied with ${\mathrm{Na}}_{10}$ as an example. The method used is the time-dependent local-density approximation, combined with the coupling to the shape fluctuations of the cluster, both in the ground state and in the excited state. In sharp contrast to earlier studies by Pacheco and Broglia, the quantum nature of the fluctuations is fully taken into account. The obtained linewidth is in good agreement with recent experimental data of Knight and collaborators. The breakdown of the so-called plasmon-pole approximation is investigated in detail, and it is found that the reason for this is the fragmentation of the oscillator strength stored in the plasmon line, which is a genuine particle-hole effect both in closed-shell jellium clusters (${\mathrm{Na}}_{20}$) and in open-shell metal clusters (${\mathrm{Na}}_{10}$).