Free size-selected $\mathrm{Na}_n^{+}$ ($n=16–250$) clusters have been studied by femtosecond pump-probe photoelectron and photofragmentation spectroscopy. Thermal electron emission from the hot electron gas was used to monitor the energy transfer from the electronic system to lattice vibrations. The electron-phonon coupling constants determined for the different sizes can be described by the radius dependent function $g(R)=(2.3+114{\AA }^2/R^2)\times {10}^{16}\mathrm{W}/{\mathrm{m}}^3\mathrm{K}$. No strong quantum size effect was observed even for the smallest cluster size.

• Received 8 October 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.117405