Single Line Width and Lifetime of the Resonance

There exists only one measurement of the lifetime for a free sodium cluster ion that gives for the lifetime of the collective resonance of Na93 a value of = 10 to 20 fs [56]. This would correspond to a lifetime broadening of only f = 33 to 66 meV. From this one can conclude that (1) the plasmon lifetime contribution to the width of one single peak is small, and (2) the near-Lorentzian shape of a single line is not due to the lifetime. 

The time range obtained for the plasmon lifetime of a free cluster is corroborated by two studies of the plasmon lifetime of large sodium clusters deposited on dielectric surfaces. One obtains a value between 10 and 15 fs, after correcting for inhomogeneous broadening due to the cluster-size distribution, which is unavoidable for deposited clusters [57]. The other experiment obtains a cluster-size-dependent lifetime of 2 to 10 fs, without performing this correction [58]. 

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