The influence of the anion vibrational temperature on the fs dynamics in a NeNePo experiment

A negative-neutral-positive (NeNePo) femtosecond charge-reversal experiment studying the temperature-dependent relaxation dynamics of linear Ag₃ is described. A wavepacket is prepared on the potential-energy surface of the electronic ground state of the neutral trimer by photodetachment from an anion ensemble held at different, well-defined temperatures between 20 K and 350 K. The wavepacket dynamics is probed by resonant two-photon ionization. The cooled octopole ion trap developed to prepare the cold anions is described. The relaxation dynamics of the initially linear Ag₃ from a saddle point of the potential-energy surface into the triangular equilibrium configuration shows a significant dependence on the anion temperature, which is rationalized in terms of a simple model. We demonstrate that a low anion vibrational temperature results in the generation of “narrower” wavepackets on the neutral potential-energy surface. This allows us to probe coherent effects more sensitively. Received: 10 January 2000 / Published online: 24 July 2000     

Theoretical description of ultrafast phenomena in clusters

A theoretical study of different ultrafast nonequilibrium processes taking place during and after ultrashort excitation of clusters is presented. We discuss similarities and differences for several processes involving nonequilibrium ultrafast motion of atoms and electrons. We study ultrashort relaxation of clusters in response to excitations produced by femtosecond laser pulses of different intensities. We show how different relaxation processes, such as bond breaking, melting, fragmentation, emission of atoms, or Coulomb explosion, can be induced, depending on the laser intensity and laser pulse duration. We also discuss processes involving nonequilibrium electron dynamics, such as intraband Auger decay in clusters and ultrafast electronic motion during collisions between clusters and surfaces. We show that this electron dynamics leads to Stückelberg-like oscillations of measurable quantities, such as the electron emission yield. Received: 4 April 2000 / Accepted: 6 November 2000 / Published online: 9 February 2001     

Energy dependence of the decay pathways of optically excited small gold clusters

The pathway competition between neutral monomer and neutral dimer evaporation from optically excited odd-size gold cluster ions Au⁺ _n, n=7–15, has been investigated as a function of cluster size and excitation energy. Gold cluster ions of these sizes are the only ones to show observable pathway competition while all other sizes exclusively evaporate either neutral monomers or neutral dimers. The investigation has been performed by photoexcitation of stored size-selected gold cluster ions with a single 10-ns laser pulse. Subsequent time-resolved observation of the delayed dissociation allows us to quantitatively determine the relative fragment yields of the respective decay channels as a function of excitation energy. Contrary to theoretical expectations, the dimer-to-monomer branching ratio of evaporated particles is found to decrease monotonously with increasing excitation energy for all cluster sizes under investigation. Possible explanations for this behaviour are discussed. Received: 9 July 2001 / Revised version: 24 September 2001 / Published online: 15 October 2001     

Charging dynamics of metal clusters in intense laser fields

Clusters of heavy metal atoms in strong femtosecond laser-light fields undergo multi-ionization with the loss of hundreds of electrons. The cross section largely exceeds that of corresponding isolated atoms, which leads in the case of Pb_N to a complete ionization of the 4f shell with a light intensity of 1.2×10¹⁵ W/cm². Experimental investigations on Pb and Pt clusters with variable pulse widths and, for the first time, with the pump&probe technique give insight into the dynamics of the coupling of electromagnetic radiation into the clusters. Both approaches support the picture according to which, after an initial charging, the clusters expand due to Coulomb forces. This expansion is accompanied by a reduction of the electron density and at the same time by an increase of the optical sensitivity. Once the plasmon energy of the diluted nanoplasma approaches the photon energy, the charging efficiency increases significantly. The experimental observations are confirmed by random-phase approximation (RPA) calculations of the optical response, including molecular-dynamics simulations of the expanding systems. Received: 11 November 1999 / Published online: 13 July 2000     

Thermal emission of electrons from highly excited sodium clusters

Positively charged sodium clusters can be easily ionized by a fs laser pulse of relatively low intensity (<10¹⁰ W/cm²), if the laser is in resonance with the plasmon excitation of the cluster. This ionization process was investigated in detail by measuring the kinetic energy distribution of electrons emitted from a size-selected Na₉₃ ⁺ as a function of the fs laser intensity. In all cases pure Boltzmann-like energy distributions were observed. A comparison with statistical theory shows that the emission is a purely thermal process. It is different to normal thermionic emission insofar as the electrons are emitted from a hot electron system which is only weakly coupled to a cold ionic background. The results demonstrate purely statistical behaviour of a small fermionic system even for very high excitation energy. Received: 25 May 2000 / Accepted: 6 November 2000 / Published online: 9 February 2001     

The electronic structure and the band gap of nano-sized Si particles: competition between quantum confinement and surface reconstruction

The electronic structure and especially the band gap of Si_n clusters (n=3–45 atoms) is studied by photoelectron spectroscopy. Contrary to expectations of quantum confinement, almost all clusters studied here have a band gap smaller than that of crystalline Si or even display a continuous (metallic) density of states. We attribute this to covalent bond formation analogous to the reconstructions observed on single-crystal surfaces. Additionally, for Si₃₀ and Si₃₃ a gap size of 0.6 eV (0.4 eV) is observed, supporting the prediction of stable, spherically symmetric structures of these particular clusters. Received: 18 November 1999 / Accepted: 24 November 1999 / Published online: 5 April 2000     

Probing solvation dynamics with femtosecond vibrational spectroscopy

We explain why solvent reorganization can induce both red- and blue-shifting of vibrational transitions of a particular probe molecule upon excitation to the S₁ electronic state. We observe with femtosecond vibrational spectroscopy, after hydrogen-bond cleavage dynamics, an additional blue shift of the carbonyl stretch of coumarin 102 of 7 cm^-1 when dissolved in chloroform. Received: 28 June 2000 / Published online: 7 August 2000     

Cohesive properties of mercury clusters in the ground and excited states

Optimized structures and cohesive energies of small mercury clusters (Hg_N; N = 3–7, 13, 19) are calculated with the spin-orbit diatomics-in-molecules method. The theory takes into account the effect of s-p mixing which tends to enhance the binding energies in the ground state. It is shown that excimer clusters have significantly short optimum bond lengths and their atomic geometries differ considerably from those in the ground state. Excitation energy gap depends sensitively on both cluster size and nearest-neighbor separation. Numerical results are compared with other theories and experiments.     

EICO measurements of inner-core excited mixed rare-gas clusters

The spectra of deep inner-core excited mixed rare-gas clusters were recorded by using electron ion coincidence (EICO) and multi-hit momentum imaging (MHMI) techniques. The EICO spectra for Ar₉₉Kr₁ clusters reveal that singly charged ions are emitted from the inner-core excited clusters in addition to the multiple charged ions. The dependence of the EICO spectra on photon energy and cluster size suggests that the holes created through vacancy cascade on the krypton atoms are transferred to the surrounding atoms, and that the singly charged ions are the primary product of the krypton photoabsorption. Charge localization is suggested for the inner-core excited mixed rare-gas clusters from the analysis of the EICO peak width. The MHMI measurements give us direct evidence for the strong charge migration from X-ray absorbing atoms to surrounding atoms. The photon energy dependence of the PSD image for fragment ions suggests that the momentum of the fragment ions depends on the number of charges generated by the vacancy cascade.     

Conditions for XUV amplification considering recombination in clusters

3 cm^-l for a wavelength of λ_R≈200 Å in a time ≲1 ps can be expected. The measurable gain G_real depends on the cluster density N_cl. For N_cl≈10¹⁶ cm^-3 we expect G_real≳20 cm^-1. Received: 30 October 1997     

The factorization approximation for the Master Equation

We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω₀, where ω₀ is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small.     

Simple and efficient photo-ionization loading of ions for precision ion-trapping experiments

We report a simple and efficient method to load a Paul trap with Ca⁺ ions. A beam of neutral atomic calcium is ionized in a two-step photo-ionization process using uv-diode lasers near 423 nm and 390 nm. Photo-ionization of a calcium beam for loading a Paul trap has first been demonstrated by Kjaergaard et al. The advantages of our method are the use of cheap and easily handled diode-laser systems and the large cross section for field ionization when exciting high-lying Rydberg states. Finally, we discuss the advantages of photo-ionization for ion generation compared to loading by electron bombardment. Received: 24 August 2001 / Revised version: 16 October 2001 / Published online: 23 November 2001     

Photoionization of argon, krypton and xenon clusters in the inner valence shell region

Photoionization of rare gas clusters in the innervalence shell region has been investigated using threshold photoelectron and photoion spectrometers and synchrotron radiation. Two classes of states are found to play an important role: (A) valence states, correlated to dissociation limits involving an ion with a hole in its innervalence ns shell, (B) Rydberg states correlated to dissociation limits involving an ion with a hole in its outervalence np shell plus an excited neutral atom. In dimers, class A states are “bright”, that is, accessible by photoionization, and serve as an entrance step to form the class B “dark” states; this character fades as the size of the cluster increases. In the dimer, the “Mulliken” valence state is found to present a shallow potential well housing a few vibrational levels; it is predissociated by the class B Rydberg states. During the predissociation a remarkable energy transfer process is observed from the excited ion that loses its innershell electron to its neutral partner. Received: 10 February 1998 / Revised: 17 July 1998 / Accepted: 31 July 1998     

Experimental and theoretical studies of instabilities of metal nanoparticles: a new kind of quasimelting

In this work we report experimental and theoretical studies of structural instabilities of gold nanoparticles supported on a carbon substrate using high-resolution transmission microscopy and molecular dynamics simulations. It is shown that particles undergo structural fluctuations in which a particle exhibits a change in orientation whilst maintaining the overall structure. These fluctuations are of a different kind than the ones reported in previous work, in which transitions between different structures or the appearance, movement or vanishing of twin boundaries are observed. Computer calculations were performed using a model that included both the particle and the substrate. It is found that during the fluctuations there is a collective displacement of the atoms at the interface between the gold and the carbon substrate that results in a larger contact area. Calculations of particle stability that include the interaction with the carbon substrate show that different orientations of the particle have similar energies. As a result, during the fluctuations the particle becomes trapped between different orientations of the same structure. This kind of phenomenon can be considered as a new kind of quasimelting. Received: 26 September 2000 / Accepted: 27 January 2001 / Published online: 23 May 2001     

Size-selected, supported clusters: the interaction of carbon monoxide with nickel clusters

We report on the size-dependent chemical reactivity of nickel clusters with up to 30 atoms. Monodispersed Ni₃₀ clusters show a higher reactivity for CO dissociation than Ni₁₁ and Ni₂₀. Under our experimental conditions the smallest nickel clusters (Ni_x, x<4) produce nickelcarbonyl complexes. These results demonstrate that such small clusters are unique for catalytic reactions not only due to their high surface-to-volume ratio but also essentially because of the distinctive properties of different cluster sizes. In addition thermal desorption spectroscopy of CO shows that on average four molecules are weakly adsorbed per Ni₁₁ at saturation coverage. Using an isotopic mixture of ¹²CO and ¹³CO, infrared spectroscopy reveals the existence of a vibrational coupling interaction between the four COs. A semi-classical model of interacting dipoles is applied to correlate the observed vibrational frequency shifts with the arrangement of the COs on the cluster. This simple analysis favors a three-dimensional structure for the deposited clusters. Received: 23 March 1998/Accepted: 25 August 1998     

Time-resolved photo-electron spectroscopy on mass-selected metal clusters using a regenerative femtosecond amplifier up to 100 Hz

A femtosecond photo-electron experiment is described which provides excellent conditions for measuring time-resolved photo-electron spectra of free, monodispersed cluster anions using repetition rates up to 100 Hz. Cluster anions are synthesized in an electric arc and subsequently cooled in a helium carrier gas. A time-of-flight spectrometer is used for mass separation of the negatively charged clusters. The kinetic energy of the photo-electrons is analyzed by a magnetic-bottle time-of-flight spectrometer, which guarantees a maximum collection efficiency. Femtosecond laser pulses are generated by a seeded regenerative Ti:Sa amplifier, which is externally pumped with the second harmonic of a diode-pumped solid-state Nd:YAG laser. A retroreflector mounted on a computer-controlled translation stage serves as a reproducible time delay of the probe pulse. The high energy output of the laser pulses (∼3 mJ) in combination with the variable repetition rate and the high stability of the amplified pulses provide excellent conditions for recording pump-probe photo-electron spectra of mass-separated cluster anions even at the fairly low ion density of pulsed plasma cluster sources. First results on the electron dynamics of the Pt₃ ^- cluster demonstrate the reliability of the whole system. Further experimental investigations will concentrate on electron-relaxation processes in transition- and noble-metal clusters as well as on the nuclear and transition-state dynamics of chemically reacted adsorbate clusters. Received: 7 January 2000 / Published online: 7 August 2000     

Intensity enhancement of the C5+ Balmer radiation excited by capillary discharge pumping

The intensity of the 18.2 nm Balmer α-transition in C⁵⁺ excited in a capillary discharge using alumina and polyacetal tubes was studied. For discharge currents of up to 80 kA in tubes filled with C₂H₂, intense radiation from the excitation of C⁵⁺ ions and from the recombination of C⁶⁺ ions was observed. With increasing length of the discharge, the intensity in the falling edge of the recombination pulse rises faster than proportional. In contrast to previous investigations, gain by stimulated emission is excluded. The enhancement is ascribed to an optical guiding of the XUV radiation in the dense plasma created by ablation from the tube walls. Received: 1 April 1999 / Revised version: 22 July 1999 / Published online: 30 November 1999     

Predictions of geometrical structures and ionization potentials for small barium clusters Ba

The geometrical structure of ground state Ba_n clusters (n =2-14) has been predicted from various types of calculations including two ab initio approaches used for the smaller sizes namely HF+MP2( n =2-6), DFT (LSDA)( n =2-6, 9) and one model approach HF+pairwise dispersion used for all sizes investigated here. The lowest energy configurations as well as some isomers have been investigated. The sizes n =4, 7 and 13 are predicted to be the relatively more stable ones and they correspond to the three compact structures: the tetrahedron, the pentagonal bipyramid and the icosahedron. The growth behavior from Ba₇ to Ba₁₃ appears to be characterized by the addition of atoms around a pentagonal bipyramid leading to the icosahedral structure of Ba₁₃ which is consistent with the observed size-distribution of barium clusters. Values for vertical ionization potentials calculated for n =2-5 at the CI level are seen to be in quite good agreement with recent measures. Received: 14 May 1997 / Received in final form: 2 February 1998 / Accepted: 27 February 1998     

Theory of atomic diffraction from evanescent waves

We review recent theoretical models and experiments dealing with the diffraction of neutral atoms by a reflection grating, formed by a standing evanescent wave. We analyze diffraction mechanisms proposed for normal and grazing incidence, point out their scopes and confront the theory with experiment. Received: 12 June 1999 / Published online: 8 September 1999     

Dynamics of Na clusters in picosecond laser pulses

We investigate the electronic and ionic dynamics of Na clusters under the influence of a laser pulse in the range 100 femtoseconds to picoseconds. The dynamics is described by means of the time-dependent local-density approximation coupled to ionic molecular dynamics (TDLDA-MD). Variation of pulse length allows us to explore the time scales of ionic motion in a manner similar to pump and probe experiments. Resonant enhancement of electron emission serves as a measure for the time scale of Coulomb explosion. Received: 3 July 2001 / Published online: 10 October 2001