Rare Gas Clusters Research Articles

Ionization heating in rare-gas clusters under intense XUV laser pulses

The interaction of intense extreme ultraviolet (XUV) laser pulses ($\ensuremath{\lambda}=32 \mathrm{nm}$, $I={10}^{11}--{10}^{14}$ W/cm${}^{2}$) with small rare-gas clusters (${\mathrm{Ar}}_{147}$) is studied by quasiclassical molecular dynamics simulations. Our analysis supports a very general picture of the charging and heating dynamics in finite samples under short-wavelength radiation that is of relevance for several applications of free-electron lasers. First, up to a certain photon flux, ionization proceeds as a series of direct photoemission events producing a jellium-like cluster potential and a characteristic plateau in the photoelectron spectrum as observed in Bostedt et al. [Phys. Rev. Lett. 100, 133401 (2008)]. Second, beyond the onset of photoelectron trapping, nanoplasma formation leads to evaporative electron emission with a characteristic thermal tail in the electron spectrum. A detailed analysis of this transition is presented. Third, in contrast to the behavior in the infrared or low vacuum ultraviolet range, the nanoplasma energy capture proceeds via ionization heating, i.e., inner photoionization of localized electrons, whereas collisional heating of conduction electrons is negligible up to high laser intensities. A direct consequence of the latter is a surprising evolution of the mean energy of emitted electrons as function of laser intensity.

Finite-temperature quantum simulations of mixed rare gas clusters

Finite-temperature quantum Monte Carlo simulations are presented for mixed neon/argon rare gas clusters containing up to n=10 atoms. For the smallest clusters (n=3) comparison with rigorous bound state calculations and experiments shows that the present approach is accurate to within fractions of wavenumbers for energies and to within a few percent or better for rotational constants. For larger cluster sizes, for which no rigorous quantum calculations are available, comparison with experiment becomes even more favorable. In all simulations accurate pair potentials for the rare gas-rare gas interactions are employed and comparison with high-level electronic structure calculations suggest that many-body interactions play a minor role. For the largest clusters investigated (Ne(4)Ar(6)) gradual melting of the neon phase is observed while the argon-phase remains structurally intact.

Investigation of the interaction of xenon cluster with intense EUV–FEL pulses using pulsed cluster beam source and momentum imaging spectrometer

We investigated the interaction of rare-gas clusters with intense EUV–FEL pulses in the 51–62-nm region by using the SPring-8 Compact SASE Source (SCSS) test facility in Japan. For this purpose, we developed a pulsed cluster source consisting of a solenoid-type pulsed valve and a liquid helium cryostat. The interaction of giant xenon clusters with intense FEL pulses was investigated by detecting photoions using a momentum imaging spectrometer. We observed the emission of energetic highly charged ions when xenon cluster beam (〈 N〉 ∼ 10,000) was irradiated by intense FEL pulses of wavelength 62 nm.

Frustration of direct photoionizations of rare gas clusters in intense extreme ultraviolet free-electron laser pulses

We performed a momentum imaging measurements of Ar clusters irradiated by extreme ultraviolet free electron laser pulses (61nm 1.3×1011W/cm2) for various cluster sizes. Dominant fragment ions were Ar+ and Ar2+ ions with significant kinetic energy (up to 40eV). This indicates that Ar clusters absorbed many photons, become highly ionized and finally dissociated into many fragments through Coulomb explosion. The size dependence of the ion kinetic energy distribution indicates that larger clusters significantly suffer from the frustration of direct photoelectron emissions and multiple ionizations.

Photoabsorption spectra of small cationic xenon clusters from time-dependent density functional theory

Upon ionization, rare-gas (like Ar and Xe) clusters shift their absorption spectrum from the ultraviolet to the visible. This happens as bonding becomes much stronger due to the removal of an electron from a strongly antibonding orbital. In this article, we study the absorption spectrum of small cationic xenon clusters (Xe(n) (+), with n=3,...,35) by means of time-dependent density functional theory. These calculations include relativistic effects through the use of relativistic j-dependent pseudopotentials in a two-spinor formulation of the Kohn-Sham equations. The peak positions in our calculated spectra are in fairly good agreement with experiment and confirm that absorption is mainly due to a charged linear core composed of 3, 4, or 5 Xe atoms where the positive charge is localized. However, we find large deviations concerning the oscillator strengths, which can be partially explained by the unsatisfactory treatment of exchange in common density functionals. Furthermore, we find that adequate ground-state geometries are necessary for the correct prediction of the qualitative features of the spectra.

Emission of electrons from rare gas clusters after irradiation with intense VUV pulses of wavelength 100 nm and 32 nm

Kinetic Boltzmann equations are used to describe electron emission spectra obtained after irradiation of noble-gas clusters with intense vacuum ultraviolet (VUV) radiation from a free-electron-laser (FEL). The experimental photoelectron spectra give a complementary and more detailed view of nonlinear processes within atoms and clusters in an intense laser field compared to mass spectroscopy data. Results from our model obtained in this study confirm the experimental and theoretical findings on the differing ionization scenarios at longer (100 nm) and shorter (32 nm) VUV radiation wavelengths. At the wavelength of 100 nm the thermoelectronic electron emission dominates the emission spectra. This indicates the plasma formation and the inverse bremsstrahlung (IB) heating of electrons inside the plasma. This effect is clearly visible for xenon (with the fitted temperature of 6–7 eV), and less visible for argon (with the fitted temperature of 2–3 eV). The two-photon-ionization rate for argon that initiates the cluster ionization, is much lower than the single-photoionization rate for xenon. Also, more of the photoelectrons created within an argon cluster are able to leave it, as they are more energetic than those released from a xenon cluster. Therefore, the IB heating of plasma electrons in argon is less efficient than in xenon, as the density of the electrons remaining within the cluster is lower.At a wavelength of 32 nm the dominant ionization mechanism identified from the electron spectra of argon clusters is the direct multistep ionization. The signature of the thermalization of electrons is also observed. However, as the heating of electrons due to the inverse bremsstrahlung process is weak at these radiation wavelengths and pulse fluences, the increase of the electron temperature with the pulse intensity is mainly due to the increasing photoionization rate within the irradiated sample.

Electronic excitation processes in rare gas clusters studied by electron energy loss spectroscopy

We present the electron energy loss spectra for Ar clusters as a function of incident electron energy and of cluster size. In spectra measured with 100 eV incident electron energy the bulk excitation peak becomes visible for a mean cluster size above 170 atoms per cluster. For 250 eV incident electron energy the bulk excitation peak is clearly observable even for a mean cluster size of 120 atoms per cluster. These experimental results are qualitatively reproduced by a simple calculation that accounts for the mean free path of electrons in Ar clusters; i.e., the penetration depth of incident electrons into the cluster.

Semiclassical description of vibrational quantum coherence in a three dimensional I2Arn (n≤6) cluster: A forward-backward initial value representation implementation

The semiclassical (SC) initial value representation (IVR) has been applied to describe true quantum coherence effects in a complex molecular system in full three dimensional space. The specific quantity considered is the time-dependent probability distribution of the I(2) vibrational coordinate following photoexcitation of I(2) in a rare gas cluster. The "forward-backward" version of the IVR method is shown to be capable of capturing detailed quantum coherence in this quantity, coherence that cannot be described by a classical Wigner model (which is equivalent to a linearized approximation to the more general SC-IVR). Solvent effects on this vibrational quantum coherence have also been investigated for a I(2)Ar(n) (n=1,6) cluster. A solvent cage consisting of six argon atoms reduces the fraction of iodine molecules that dissociate (an example of the "cage effect") and also diminishes, but does not entirely eliminate, quantum coherence in the vibrational motion of the molecules that remain undissociated.

Free clusters studied by core-level spectroscopies

In this review we describe the development and current status of free clusters studied using core-level spectroscopies. This topic ranges from simple model systems, such as rare gas clusters, to molecular clusters, and clusters of solids, held together by ionic, covalent and metallic bonding.

Angular distributions of inner-shell photoelectrons from rare-gas clusters

The photoionization of Ar, Kr, and Xe rare-gas clusters was investigated using angle-resolved time-of-flight photoelectron spectroscopy. Fine-structure-resolved photoelectron angular distributions were determined for the Ar $2p$, Kr $3d$, and Xe $4d$ core levels and the Ar $3s$ inner-valence level as a function of photon energy for two average cluster sizes. Overall, the angular distributions of inner-shell photoelectrons from the cluster and the free atom are found to be very similar, except for the first $10--15\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ above the respective photoionization thresholds, where the angular anisotropy of the atomic photoelectrons is high, while our measurements demonstrate considerably less anisotropy in the cluster photoelectron emission. The angular distribution of Ar $3s$ inner-valence photoelectrons from the cluster is substantially less anisotropic than for the atomic photoelectrons throughout the covered photon energy range, but the difference decreases for increasing photon energy.

Emergence of valence band structure in rare-gas clusters

The formation of electronic band structure by the valence-shell of Ar, Kr, and Xe clusters was studied for various cluster sizes using angle-resolved photoelectron spectroscopy. Different widths of the fine-structure components in the cluster spectra are attributed to a splitting of the outermost p 3 / 2 levels due to valence-orbital overlap between neighboring atoms. Photoelectron angular distributions from the cluster differ from the atomic cases and vary substantially for different bands. The evolution of the electronic structure with increasing cluster size emulates the changes of the valence band structure in the transition from a condensed-phase monolayer to the bulk.

Observation of site-specific decay processes in Ar–Kr mixed clusters following K-shell excitation of Kr

Multiple ion coincidence momentum imaging measurements have been performed for an Ar–Kr mixed rare-gas cluster with an average cluster size 〈 N〉 = 100 in the 1s threshold region of Kr. The signals resulting due to the photoabsorption by Kr have been extracted on the basis of the difference in the spectra between 14.08 and 14.50 keV, i.e., on both sides of the 1s threshold for Kr. The time-of-flight spectra for the clusters reveal that multiply charged cluster ions produced as a result of inner-core excitation emit many singly charged ions such as Kr +, Ar +, ArKr +, and Ar 2 +. The abundance of daughter ions suggests the transfer of positive charges from the X-ray absorbing atom to the surrounding atoms before the Coulomb explosion is suggested from. The momentum of daughter ions is deduced from the time-of-flight and position data, and the momentum distribution shows the characteristic size dependence of the ions on the number of coincidence signals N coin, i.e., the average momentum of the Ar + ions increases with N coin, while that of the Kr + ions decreases. The N coin dependence of momentum is interpreted according to the site-dependent decay processes.

On the Use of Different Potential Energy Functions in Rare-Gas Cluster Optimization by Genetic Algorithms: Application to Argon Clusters

We study the effect of the potential energy function on the global minimum structures of argon clusters arising in the optimization performed by genetic algorithms (GAs). We propose a robust and efficient GA which allows for the calculation of all of the putative global minima of Ar(N) (N = 3-78) clusters modeled with four different potentials. Both energetic and structural properties of such minima are compared among each other and with those previously obtained for the Lennard-Jones function. In addition, the possibility of obtaining global minima of one potential through local optimization over the corresponding cluster geometry given by other potentials was associated with some structural parameters. The influence of the contribution from the three-body (Axilrod-Teller-Muto) triple-dipole potential (including or not a damping function to describe its correct behavior at smaller interatomic distances) has also been analyzed.

Modified nanoplasma model for laser-cluster interaction

We present a modified nanoplasma model to describe the interaction of intense laser pulses with rare-gas clusters of nanometric size. Compared to previous models, the model relies on a better description of the collisional processes and allows one to obtain highly charged ion populations and associated x-ray spectra in accordance with experimental findings. We further study the x-ray emission dependence on pulse duration and cluster size and show that these parameters can be optimized to maximize $\text{He}\text{ }\ensuremath{\alpha}$ production.

Optimizing the ionization and energy absorption of laser-irradiated clusters

It is known that rare-gas or metal clusters absorb incident laser energy very efficiently. However, due to the intricate dependencies on all the laser and cluster parameters, it is difficult to predict under which circumstances ionization and energy absorption are optimal. With the help of three-dimensional particle-in-cell simulations of xenon clusters (up to 17256 atoms), it is shown that for a given laser pulse energy and cluster, an optimum wavelength exists that corresponds to the approximate wavelength of the transient, linear Mie-resonance of the ionizing cluster at an early stage of negligible expansion. In a single ultrashort laser pulse, the linear resonance at this optimum wavelength yields much higher absorption efficiency than in the conventional, dual-pulse pump-probe setup of linear resonance during cluster expansion.

Fragmentation channels of K-shell excited rare-gas clusters studied by multiple-ion coincidence momentum imaging

Multiple-ion coincidence momentum imaging experiments were carried out for K-shell (1s) excited Ar clusters containing about 130 atoms and Kr clusters containing about 30, 90, and 160 atoms. The time-of-flight spectra reveal that the major products of the Coulomb explosion are singly charged ions. With increasing the number of charges generated in clusters, the momentum of monomer ions such as Ar(+) and Kr(+) increases, while that of cluster ions such as Ar(3) (+), Kr(2) (+), and Kr(3) (+) decreases. This observation indicates the site-specific decay process that the heavier ions appear in the central part of clusters. We have also investigated the momentum distribution in various fragmentation channels and the branching ratio of each channel at the Coulomb explosion. When the number N(coin) of coincidently detected ions is four, for example, the most frequent channel from Kr clusters containing 30 atoms is to emit simply four Kr(+) ions, but Kr(2) (+) ions participate in the fragmentation from the larger Kr clusters. The fragmentation channel in which two Ar(2) (+) ions are emitted becomes dominant with increasing N(coin), and the average momentum of Ar(2) (+) ion in this channel is larger than that in the channels where only single Ar(2) (+) is emitted.

Tracing non-equilibrium plasma dynamics on the attosecond timescale in small clusters

It is shown by microscopic calculations that the energy absorption of a rare-gas cluster from a vacuum-ultraviolet (VUV) pulse can be traced with time-delayed extreme-ultraviolet (XUV) attosecond probe pulses by measuring the kinetic energy of the electrons detached by the probe pulse. By means of this scheme we demonstrate that, for pump pulses as short as one femtosecond, the charging of the cluster proceeds during the formation of an electronic nano-plasma inside the cluster. Using moderate harmonics for the VUV and high harmonics for the XUV pulse from the same near-infrared laser source, this scheme with well defined time delays between pump and probe pulses should be experimentally realizable. Going to even shorter pulse durations we predict that pump and probe pulses of about 250 attoseconds can induce and monitor non-equilibrium dynamics of the nano-plasma.

A comparison of interatomic potentials for rare gas nanoaggregates

Rare-gas clusters are usually modeled by Lennard–Jones pairwise potential energy functions. A more realistic representation of the rare-gas pair interaction is given by the benchmark Aziz HFD type potentials, of high computational cost for large scale molecular simulations. Here we compare Lennard–Jones and HFD potentials with that obtained from a generalization of the Lennard–Jones potential, recently presented by Pirani et al. Parameters are given for the two-body interaction for all dimers and structural properties of Ar 5 and Ar 6 are discussed through a comparison of the Pirani et al. potentials with those of Lennard–Jones.

Optical Spectroscopy of Potassium-Doped Argon Clusters. Experiments and Quantum-Chemistry Calculations

Rare-gas clusters produced in a supersonic expansion into vacuum are doped with alkali-metal atoms using the pickup technique. We give here a detailed description of our experimental apparatus, which is suitable for electronic spectroscopy of any desired gas clusters doped with low-temperature melting metals. Potassium-doped Ar clusters (average size N approximately 2000) are investigated by beam-depletion (BD) spectroscopy as well as laser-induced fluorescence (LIF) spectroscopy. The observed BD spectra are strong and exhibit several broad peaks within the scan range of the Ti:sapphire excitation laser; only one weak band is observed instead in LIF spectra. This situation resembles the one previously observed for K-doped H2 clusters [Callegari et al., J. Phys. Chem. A 1998, 102, 4952] where it was argued that fluorescence is either quenched or strongly red-shifted by the cluster. We investigate BD spectra as a function of the potassium vapor pressure in the pickup cell, and we perform an extensive analysis of the pickup process, necessary to separate the overlapping spectral contributions of different species. We tentatively assign parts of the spectra to the monomer, singlet dimer, and doublet trimer, of potassium residing on the surface of the cluster. To support our trimer assignment, we perform complete active space self-consistent field (CASSCF) calculations to determine the lowest 12 electronic spin-doublet states of free K3. We find several candidate transitions in the region of interest. Although a definite assignment is not possible because the energy shifts due to the perturbation by the Ar cluster are not known, our theoretical and experimental data compare favorably with existing spectra, and with simulations, of the closely related Na3-molecule, upon suitable scaling of its energy-level structure.

Attosecond Resolved Charging of Ions in a Rare-Gas Cluster

A scheme to probe dissipative multielectron motion in time is introduced. In this context attosecond probing enables one to obtain information which is lost at later times and cannot be retrieved by conventional methods in the energy domain due to the incoherent nature of the dynamics. As a specific example we will trace the transient charging of ions in a rare-gas cluster during a strong femtosecond vacuum-ultraviolet pulse by means of delayed attosecond pulses.