Size-Dependent Plasmon Lifetimes and Electron-Phonon Coupling Time Constants for Surface Bound Na Clusters

In this paper we show that time-resolved analysis of second harmonic generation via femtosecond pump-probe studies can be used to extract simultaneously mean cluster radii, decay times ${\tau }_{\mathrm{sp}}$ of localized surface plasmon excitations, and electron-phonon coupling time constants ${\tau }_{\mathrm{ep}}$ in large ${\mathrm{Na}}_n$ $\left(n\approx {10}^7\right)$ clusters, bound to insulator surfaces. From the dependence of plasmon lifetime on the mean cluster radius $\left(5\le r_0\le 55\mathrm{nm}\right)$ a maximum of ${\tau }_{\mathrm{sp}}=10\mathrm{}\mathrm{fs}$ at a mean radius of about 25 nm is observed. Additionally, for Na clusters with mean radii of 30 to 50 nm and bound to a lithium fluoride surface the electron-phonon coupling time constant is found to be ${\tau }_{\mathrm{ep}}\approx 1.1\mathrm{ps}$.