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Photoabsorption cross sections of small neutral sodium clusters composed of TV =2-40 sodium atoms are measured by longitudinal-beam-depletion spectroscopy at several wavelengths of visible light. Absorption occurs via coupling of photons to collective oscillations of the valence electrons. The cross section is strongly size and wavelength dependent. Good agreement is found with predictions based on an extended Clemenger-Nilsson shell model and the experimental static polarizabilities.PACS numbers: 36.40.+d, 33.20.Kf, 35.20.Wg Presently available data on optical spectra of metal microclusters are meager and primarily concern alkalimetal dimers and trimers.' Heretofore no values of cross sections, except for dimers, were available. Our results indicate that the optical spectrum for clusters larger than the tetramer is dominated by the collective resonances of the valence electrons. Neutral sodium clusters TV =2-40 are studied at several wavelengths between 450 and 600 nm. The results are analyzed in terms of an ellipsoidalshell model 2,3 which has proven to be very successful for the description of the properties of metal clusters. For example, it is well known that spherical-shell closings occur in alkali and other metal clusters for electron numbers TV =2,8,20,40, . . . , resulting in observed features in the abundances and ionization-potential curves. Enhanced polarizabilities for the open-shell clusters are also observed 4 and are known to be related to ellipsoidal shapes of the open-shell clusters. In this work the cluster shapes from the extended ellipsoidal-shell model are used to calculate the resonance frequencies and the photoabsorption cross sections. They are in good agreement with experiment. Since the resonance frequencies are uniquely related to the relative lengths of the ellipsoidal axes, measurement of the frequencies gives a direct measure of the cluster geometries.The experimental apparatus has been described elsewhere. 2 The clusters are produced in a supersonic expansion of a mixture of sodium vapor (50 Torr, 920 K) and argon (300 kPa) through a 0.0076-cm-diam nozzle into vacuum. A skimmer (0.04-cm-diam aperture) 0.6 cm downstream and a rectangular slit (0.1 x0.1 cm 2 ) 77 cm downstream from the nozzle collimate the molecular beam with an angular divergence of less than 1 mrad. The beam enters the detector via a 0.2-cm-widex0.3-cm slit, 2 m downstream from the nozzle, and the clusters are photoionized with filtered light from a uv arc lamp. Mass-sensitive detection is accomplished with a quadrupole mass analyzer in conjunction with a Daly ion detector. The detected signals are converted into digital pulses for storage and further processing by a microcomputer. A window in the detector chamber is installed so

Photoabsorption cross sections of small free neutral sodium clusters are measured in the wavelength range of 452 -604 nm. The results indicate that the photoabsorption spectra are dominated by surface plasma oscillations of the valence electrons. The measured photoabsorption cross sections are consistent with a sum-rule calculation based on an ellipsoidal shell model and the experimental static electric polarizabilities of Na clusters. The calculated photoabsorption spectra of closed-shell clusters contain a single surface-plasma-resonance peak, whereas those of open-shell clusters have double or triple peaks. The experimental magnitudes of the photoabsorption cross o 2 sections near resonance peaks are between 1 and 2 A per delocalized electron.

Absolute photoabsorption cross sections of free neutral sodium clusters containing from N =3 to 40 atoms are presented. Investigation of a wide continuous range of cluster sizes reveals the size development of the photoabsorption behavior. In the smallest clusters the absorption is moleculelike.A transition to collective electronic excitations (surface plasmons) occurs in the size range of N =3 to 5. For clusters with N=6 to 12 atoms the surface plasma resonances are particularly well defined, and their positions are consistent with the predictions of an ellipsoidal shell model. The cluster shapes can be deduced from the observed resonance positions; the data provide a sensitive measurement of the relative axis lengths of ellipsoidal clusters. For clusters containing N~3 atoms, the plasma resonances do not always coincide with the positions predicted by the ellipsoidal shell model. In addition to these resonances, which dominate the spectra, there are three distinct wavelength regions within which absorption occurs for all investigated clusters.

The cooling of objects is often described by a law, attributed to Newton, which states that the temperature difference of a cooling body with respect to the surroundings decreases exponentially with time. Such behaviour has been observed for many laboratory experiments, which led to a wide acceptance of this approach. However, the heat transfer from any object to its surrounding is not only due to conduction and convection but also due to radiation. The latter does not vary linearly with temperature difference, which leads to deviations from Newton's law. This paper presents a theoretical analysis of the cooling of objects with a small Biot number. It is shown that Newton's law of cooling, i.e. simple exponential behaviour, is mostly valid if temperature differences are below a certain threshold which depends on the experimental conditions. For any larger temperature differences appreciable deviations occur which need the complete nonlinear treatment. This is demonstrated by results of some laboratory experiments which use IR imaging to measure surface temperatures of solid cooling objects with temperature differences of up to 300 K.