Multistep photon absorption has been used to measure the collective excitation of free lithium clusters having up to 1500 atoms. The blueshift of the Mie resonance energy, as cluster size increases, probes the surface effects. Its absolute value is consistent with the dielectric constants of the bulk down to a 100 atom cluster. The comparison with calculations in random-phase approximation in the local approximation demonstrates that the jellium model is no longer valid for lithium clusters. PACS numbers: 78.20.Dj, 61.46.+w The optical response of small metal particles as a function of size offers the possibility to follow the development of collective effects in metallic systems. Of these, alkali clusters, and in particular sodium and potassium, are regarded as a prototype of simple metallic particles. Their dipole absorption spectra are consistent with the optical excitation predicted by the classical Mie theory treatment of collective dipole oscillation in spherical or ellipsoidal distorted metallic droplets [1][2][3][4]. A more elaborate approach was obtained from time-dependent density-functional-theory calculations to quantitatively interpret the experimental data on sodium and potassium clusters having less than 40 atoms [5]. However, it was of fundamental interest to explore large cluster sizes to bridge the gap between the free small particles and the bulk in order to know to what extent the macroscopic dielectric function describes the optical response of metallic clusters.We have developed recently an experimental procedure for extending optical absorption measurements [6] to large masses, i.e., a few thousand atoms. For large potassium clusters we have shown that the experimental value of the resonance energy evolves toward the infinite limit h(DM deduced either from the experimental volume plasmon energy hcop [7] or from the surface plasmon energy hcos [8]: hwp^=^ h(OM^^^ hcDs^.Those values are close to the free-electron values. The small difference, less than 5%, which still remains between experimental values and free-electron values is greatly reduced when core polarization and effective mass are included [7,9].Lithium metal differs from the other alkali metals. The measured volume plasmon energy is greatly shifted down from the free-electron value and its linewidth is very broad as compared to other alkali metals [10]. The deviation of the experimental plasmon-peak position from the free-electron value was mainly interpreted in terms of optical effective mass and is due to intraband transitions as pointed out by Paasch [ll]. The volume plasmon linewidth in lithium was interpreted as a plasmon decay via interband transitions [10,12]. So the question arises as to whether such a deviation still exists for clusters. The measurement of the plasmon resonance of lithium clusters is a real challenge to know to what extent the dielectric constants of the bulk are pertinent parameters to interpret the collective excitation of lithium clusters. If so, the microscopic calculation of the dynamic response o...
The absorption cross-section profile of large charged clusters is measured by a new procedure based on multistep photoabsorption experiments. Comparison is done with the predictions of classical and quantum treatments. In light of these results, size trends in the optical properties of alkali clusters are discussed. PACS numbers: 78.20.-e, 36.40.+d Recent measurements of the visible photoabsorption spectra of small alkali-metal clusters [1-6] have been done to probe the electronic structure of those particles. Theoretical investigations [7][8][9][10][11][12] have followed the same progression as experimental studies did. One interesting question is how many atoms are required to make a cluster exhibiting collective effects. Two size domains may be distinguished: the very small sizes, smaller than the heptamer, for which ab initio molecular orbital calculations including electron configuration interaction completely reproduce the absorption features [11], and the larger sizes, for which the valence electrons are numerous enough to induce collective effects such as the well-known surface plasma resonance. For this last case the random phase approximation (RPA) in the local density approximation (LDA) [12] is a common theoretical baseline which can be used to interpret the experimental data. Up to now experiments have been performed on free clusters containing less than 40 atoms [1][2][3]. This size domain is too limited to probe the behavior toward the bulk and to correctly test the hypothesis of RPA-LDA treatments.In this Letter we present the collective resonance cross section of large potassium cluster ions K" + containing 500 and 900 atoms. For such sizes the single-photon depletion technique used for photoabsorption measurements for small sizes is hopeless [13]. So we developed a new procedure based on multistep photon absorption followed by evaporation. Our results provide evidence of the plasma resonance energy of potassium cluster blueshifted as cluster size increases and converging very slowly toward the bulk value. Such an evolution is discussed in light of the different theoretical models.The experimental procedure is based on the concept of photoinduced evaporation [14]. Adiabatic expansion of potassium generates a cluster distribution centered around 600-atom clusters. The distribution is photoionized by a pulsed UV laser . The accelerated cluster ion bunches first enter a field-free tube where they spatially resolve into separated ion packets within a mass resolution larger than 200. After size selection, a given cluster ion bunch enters a decelerating-accelerating region where it interacts with a second pulsed laser. The ion products from photointeraction are mass analyzed by a second time-of-flight spectrometer.It is well known that for metal clusters the electronic excitation resulting from the visible photon absorption re-laxes very rapidly among the numerous vibrational modes providing unimolecular evaporative cooling in the ground state [15]. For small cluster sizes the detection of the fragment...
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