Latest Advances in Atomic Cluster Collisions

The following sections are included:

• Preface

• CONTENTS

This article is the introduction to the volume of proceedings of the "International Symposium Atomic Cluster Collisions: fission, fusion, electron, ion and photon impact" (a Europhysics Conference) held in St. Petersburg, Russia, July 18-21, 2003 (ISACC 2003) as a satellite meeting of the XXIII International Conference on Photonic, Electronic, and Atomic Collisions (ICPEAC 2003, Stockholm, Sweden, July 23-29, 2003). A brief introduction to atomic cluster physics, the interdisciplinary field, which developed rather successfully during recent years, is presented. A review of recent achievements in the detailed ab initio description of structure and properties of atomic clusters and complex molecules as well as the methods of their study is given. The main trends of development in the field are discussed and some of its new focuses are outlined.

A general review of the subject of Confined Atoms is presented. This subject has a long history, extending back almost to the origins of Quantum Mechanics, but has remained fairly quiescent until recent times, because suitable experimental examples of confinement did not exist. Today, with the advent of cluster physics, the discovery of endohedral metallofullerenes and the fabrication of quantum dots, examples in fact abound, and the theory of confined atoms is undergoing a revival. The confined atom is, in some sense, the first rung of a ladder which leads up from the free atom to nanoscale physics. Indeed, it can be seen as the smallest device available in nanoscience. Endohedral atoms are very topical today: they have been proposed as suitable building blocks for the register of a quantum computer because a spherical cage can have the effect of isolating the spin of an atom confined at the center from the outside world. Atoms under extreme pressure also provide examples of quantum confinement, and have practical applications, for example in the diagnosis of metal fatigue in the walls of a nuclear reactor. Thus, quantum confinement is of general interest not only to atomic physicists, but also to a wide range of scientists from many different disciplines.

We have used classical and ab initio molecular dynamics to study the melting of sodium clusters in order to see the effects of the geometric and electronic magic numbers on the melting temperature as a function of the cluster size. It seems that classical many-atom interactions can not explain the experimentally observed size-dependence of the melting temperature. For selected cluster sizes we have used ab initio molecular dynamics to study the effects of the electronic structure on the melting and on the ionization potential. The results reveal no correlation between the vertical ionization potential and the degree of surface disorder, melting, or the total energy of the cluster.

The self consistent version of the density functional theory is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems. An exact functional equation for the effective interaction, from which one can construct the action functional, density functional, the response functions, and excitation spectra of the considered systems, is outlined. In the context of the density functional theory we consider the single particle excitation spectra of electron systems and relate the single particle spectrum to the eigenvalues of the corresponding Kohn-Sham equations. We find that the single particle spectrum coincides neither with the eigenvalues of the Kohn-Sham equations nor with those of the Hartree-Fock equations.

The optimized structure and electronic properties of small sodium and magnesium clusters have been investigated using ab initio theoretical methods based on density-functional theory and post-Hartree-Fock many-body perturbation theory accounting for all electrons in the system A new theoretical framework for modelling the fusion process of noble gas clusters is presented We report the striking correspondence of the peaks in the experimentally measured abundance mass spectra with the peaks in the size-dependence of the second derivative of the binding energy per atom calculated for the chain of the noble gas clusters up to 150 atoms.

Specific properties of electric (E1, E2, E3) and orbital magnetic (scissors M1 and twist M2) modes in metal clusters are reviewed. The analysis is performed within the Kohn-Sham LDA RPA method. Possible routes for an experimental observation of the modes are discussed.

In this paper, it is demonstrated that the electric dipole of complex molecules or clusters can be measured by beam deviation in an inhomogeneous electric field. This measurement, associated to appropriate theoretical calculations and simulations, allows us to determine the geometry of these systems and their dynamical behavior as a function of temperature. Selected examples for mixed clusters (metal-fullerene and metal-benzene) and biomolecules (hydrogen bound amino acids and glycine based polypeptides) are discussed.

Ion trapping is a versatile tool for cluster research. This article reviews various measurements of metal clusters stored in a Penning trap. The studies include technical aspects of ion trapping as well as properties of the clusters. Most notably the trapping of clusters allows us to investigate them over extended durations and provides the possibility for a sequence of many preparatory steps before the actual experiments. These may include the selection of cluster ensembles of a given cluster size, the adsorption of molecules and changes in charge state.

The characteristic oscillations in the partial photoionization cross sections of C₆₀ are analyzed in terms of the geometrical properties of both, the cage structure and the distribution of the delocalized electron cloud of the highest occupied molecular orbitals. The analysis is based on the Fourier transform of the cross section oscillations, the results are corroborated by different theoretical models. In contrast to this good overall agreement between theory and experiment there is striking disagreement with respect to discrete resonance structure in the partial cross sections. Possible reasons for this behavior are discussed.

A simple approach has been developed for the description of photoionization processes involving fullerenes. We consider the fullerenes as approximately spherical shells and use the jellium model. The local density approximation has been used for calculating initial state wave functions. The cross sections for photodetachment processes have been calculated within the self-consistent many-body theory approach including local-density (LDA) and random phase (RPA) approximations.

We predict a strong enhancement in the photoabsorption of small Mg clusters in the region of 4-5 eV due to the resonant excitation of the plasmon oscillations of cluster electrons. The photoabsorption spectra for neutral Mg clusters consisting of up to N = 11 atoms have been calculated using ab initio framework based on the time dependent density functional theory (TDDFT). The nature of predicted resonances has been elucidated by comparison of the results of the ab initio calculations with the results of the classical Mie theory. The splitting of the plasmon resonances caused by the cluster deformation is analysed. The reliability of the used calculation scheme has been proved by performing the test calculation for a number of sodium clusters and the comparison of the results obtained with the results of other methods and experiment.

We present a theoretical framework for the multiphoton excitation of plasmons. We show that, in addition to dipole plasmon excitations, multipole plasmons (quadrupole, octupole, etc.) are excited in a metallic cluster by multiphoton absorption processes, resulting in a significant difference between plasmon resonance profiles in multiphoton and single-photon absorption. The method is quite general, and applies to any system with delocalised electrons, of which the simplest are spherical metallic clusters.

The extension of the periodic system into various new areas is investigated. Experiments for the synthesis of superheavy elements and the predictions of magic numbers with modern meson field theories are reviewed. Further on, different channels of nuclear decay are discussed including cluster radioactivity, cold fission and cold multifragmentation. A perspective for future research is given.

The structural properties and the energetics of some of the smaller He_nH^-, Ne_nH^-, and clusters are examined both with classical and quantum treatments. The results of the calculations, the physical reliability of the employed interaction modeling, and the comparison with previous results are discussed. The emerging picture shows very different features when comparing the positively ionized pure rare gas clusters with respect to those in which the negative impurity H^- is present.

Fission of doubly charged sodium clusters is studied using the open-shell two-center deformed jellium model approximation and ab initio molecular dynamic approach accounting for all electrons in the system. Results of calculations of fission reactions and are presented. Dependence of the fission barriers on isomer structure of the parent cluster is analyzed. Importance of rearrangement of the cluster structure during the fission process is elucidated. This rearrangement may include transition to another isomer state of the parent cluster before actual separation on the daughter fragments begins and/or forming a "neck" between the separating fragments.

Nuclear collisions at intermediate, relativistic, and ultra-relativistic energies offer unique opportunities to study in detail manifold fragmentation and clustering phenomena in dense nuclear matter. At intermediate energies, the well known processes of nuclear multifragmentation – the disintegration of bulk nuclear matter in clusters of a wide range of sizes and masses – allow the study of the critical point of the equation of state of nuclear matter. At very high energies, ultra-relativistic heavy-ion collisions offer a glimpse at the substructure of hadronic matter by crossing the phase boundary to the quark-gluon plasma. The hadronization of the quark-gluon plasma created in the fireball of a ultra-relativistic heavy-ion collision can be considered, again, as a clustering process. We will present two models which allow the simulation of nuclear multifragmentation and the hadronization via the formation of clusters in an interacting gas of quarks, and will discuss the importance of clustering to our understanding of hadronization in ultra-relativistic heavy-ion collisions.

The dynamics of multiple evaporation in the mixed Lennard-Jones atomic cluster Ar₆Ne₇ has been studied from classical molecular dynamics simulations. A relationship between the liquid to gas like phase transition and pertinent observables has been explored. In particular the mean kinetic energy of the atomic fragments and the ratio between successive times of evaporation have been carefully analyzed as a function of energy to find such a link between thermodynamics and multi-evaporation dynamics.

We review experimental data on electron attachment to CO₂ and N₂O clusters showing very narrow vibrational Feshbach resonances of the type [(XY)_N-1·XY(ν ≥ 1)]^- which occur at energies below those of neutral cluster [(XY)_N-I·XY(ν ≥ 1)]. These resonances appear due to the stabilization of the cluster anion by the polarization interaction between the electron and the cluster. Based on this result, we develop an R-matrix model describing nondissociative electron attachment to CO₂ clusters. The results of calculations describe major features in electron attachment: very narrow vibrational Feshbach resonances and the weak dependence of their widths on the cluster size.

This paper gives a survey of physical phenomena manifesting themselves in electron scattering on atomic clusters. The main emphasis is made on electron scattering on fullerenes and metal clusters, however some results are applicable to other types of clusters as well. This work is addressed to theoretical aspects of electron-cluster scattering; however some experimental results are also discussed. It is demonstrated that the electron diffraction plays an important role in the formation of both elastic and inelastic electron scattering cross sections. The essential role of the multipole surface and volume plasmon excitations is elucidated in the formation of electron energy loss spectra on clusters (differential and total, above and below ionization potential) as well as the total inelastic scattering cross sections. Particular attention is paid to the elucidation of the role of the polarization interaction in low energy electron-cluster collisions. This problem is considered for electron attachment to metallic clusters and the plasmon enhanced photon emission. Finally, mechanisms of electron excitation widths formation and relaxation of electron excitations in metal clusters and fullerenes are discussed.

We investigate the photoionization behavior of nanoscale alkali particles in a beam. Photoionization yield curves have been measured as a function of temperature. Near the ionization threshold, they can be fitted very well by finite-temperature Fowler plots, originally derived for bulk surfaces. The T → 0 thresholds match the best literature work function values, and the temperature shifts of the work functions are in agreement with the predictions of recent theoretical models. The accuracy of the measurement demonstrates that the study of free nanoclusters offers an accurate, and economical, complement to traditional surface spectroscopy. At heights above the threshold, the yield functions begin to decline; the origin of this behavior is unclear at the moment, but is suggestive of inelastic scattering involving surface plasmon excitation. Furthermore, we demonstrate that the Fowler photoemission curves work very well even for smaller clusters (as tested on the available data for K_30–101). Both the ionization potentials and the internal cluster temperatures can be successfully extracted from such a fit. The results raise questions about the limits of applicability of bulk-derived models and highlights the need for the development of a comprehensive theory of metal cluster photoionization.

We investigate the diffusion of a spin polarized projectile on a ferromagnetic linear cluster. The interaction between the projectile and the target is described with a Heisenberg Hamiltonian which excludes the charge degree of freedom during the process. Our calculation is based on a real time description of the spins of the two interacting systems. The spin excitations induced by the spin of a projectile-atom are investigated versus the cluster size, the trajectory parameters (projectile velocity, impact parameter). Nonadiabatic behaviour during the collision has been characterized by the spin temperature at the end of the collision process. The effects of the phonons on the spin excitations will be discussed.

Collision and laser induced dynamics in atomic many-body systems are investigated within a common microscopic framework, the so-called Nonadiabatic Quantum Molecular Dynamics (NA-QMD). It is shown that the collision induced electronic and vibrational excitation mechanism depends crucially on the projectile mass in ion-fullerene collisions. In addition, its velocity-dependence is qualitatively different from that in metal-cluster collisions. In first fully three-dimensional calculations of molecules in a laser field, dramatic differences in the alignment of fragmenting and H₂ are obtained.

Phenomena associated with the electronic excitation, relaxation and ionization of clusters can span a wide range of time scales. In the case of weakly bound systems with high ionization potentials, processes in the femtosecond time scale dominate, while in the case of strongly bound clusters with low ionization potentials, delayed ionization extending to microseconds and beyond can be operative. Additionally, electron excitation in clusters arising from short laser pulses can contribute to the formation of highly charged species. Examples of each of these potentially important processes will be discussed, with attention focused on quantifying the cluster properties and laser excitation responsible for their dominance.

In particular, three classes of systems will be discussed. Firstly the influence of laser fluence, wavelength, and pulse duration will be presented for the case of van der Waals clusters, showing the effects on the formation of high charge states. The possibility of using ensuing coulomb explosion as a way of arresting intermediates in fast reactions will be discussed. Secondly the formation of ion-pairs and concomitant rearrangement of solvent molecules around the ions will be presented for the case of acid solvation phenomena and thirdly Met-Cars, unique early transition metal-carbon clusters of composition M₈C₁₂, displaying both fast excitiation and relaxation dynamics and operative competitive delayed ionization that depends on the laser excitation characteristics.

We have investigated the interaction of short, intense laser pulses with rare gas clusters in two different frequency regimes. At optical frequencies, we find for small clusters an enhancement of energy absorption which can be explained by the enhanced ionization mechanism for small clusters. For larger clusters the dynamics of quasi-free electrons, held back by the clusters space charge, determines the cluster ionization. At X-ray frequencies, however, the energy absorption turns out to be much less efficient than in the purely atomic case, due to the space charge of the cluster in combination with a small quiver amplitude and delocalization of electrons in the cluster.

We have performed multi-photon ionization experiments on small alkali clusters in order to probe their wave packet dynamics. The observed processes were highly dependent on the irradiated pulse parameters such as wavelength range or its phase and amplitude, emphasing the importance of employing a feedback control system for generating the optimum pulse shapes. Their spectral and temporal behavior reflects interesting properties about the investigated system and the irradiated photo-chemical process.

The controllability of three-photon ionization pathways is investigated on the model-like system NaK. A closed learning loop for adaptive feedback control is applied to find the optimal fs pulse shape. We examined the frequency dependent closed loop optimization of fs pulse shapes for the NaK dimer. The obtained ion yield depending on the employed central laser frequency shows a maximum in the range of 770-780 nm. By investigating the modifications of the optimal pulse shapes for different wavelengths we could gain information about the associated ionization path during the control process. Characteristic motions of the involved wave packets are proposed as an attempt to explain the optimized dynamical processes. Moreover, sinusoidal parameterizations of the spectral phase modulation are applied with regard to the obtained optimal field. By reducing the number of parameters and thereby the complexity of the phase modulation, optimal pulse shapes can be generated that carry fingerprints of the molecule's dynamical properties. This enables us to find "understandable" optimal pulse forms and offers the possibility to gain insight into the photo-induced control process.

Collisional reactions of isolated metal cluster ions (Cu and Cr) were studied at collision energies less than 2 eV by use of a tandem-type mass spectrometer. In the reaction of Cu_n⁺ with a methanol molecule, dominant reactions were methanol chemisorption, demethanation, and H(OH) formation on the cluster ions. The absolute cross sections of each reaction were measured, and found to change drastically with the cluster size; the demethanation proceeds efficiently on Cu_6–8⁺, H(OH) formation on Cu_4,5⁺, and the chemisorption on Cu_n⁺ (n ≥ 9). Structures of the reaction intermediates were calculated by use of the density functional method, and the origin of the size-specific reactivity was examined. In the reaction of Cr_n⁺ and Cr_nO⁺ (n ≥ 2) with an ethylene molecule, the abstraction of one Cr atom from the cluster by the ethylene molecule was found to proceed dominantly through ethylene chemisorption on Cr_n⁺. On the other hand, it was found that one ethylene molecule chemisorbs on CrO⁺ and CrOH⁺ under a single collision condition, and one more ethylene molecule chemisorbs further under a multiple collision condition. The density functional calculation and the measured threshold energy for the elimination of the chemisorbed ethylene molecules indicate that the chemisorbed ethylene molecules polymerize on CrOH⁺ and CrO⁺.

The stability and the fragmentation of highly charged fullerene clusters has been studied with high-resolution mass spectrometry. Fullerene clusters which are produced in a cluster aggregation source are multiply charged in slow collisions with highly charged ions (Xe^20+,30+). The observed appearance sizes are as small as 5, 10, 21 and 33 for charge states ranging from 2 to 5, respectively. The correlation measured between different fragment ions indicates that the charge is mobile within the cluster, i.e. the van der Waals cluster of fullerenes becomes conducting as soon as it is multiply charged. This is in contrast to recent results for Ar clusters, where charge localization effects have been observed.

An overview is given of experiments used to probe the dynamics of excited fullerenes. The reaction channels observed in collisions between fullerene ions and fullerenes are discussed with emphasis on the molecular fusion reaction. In a second example, experiments in which the energy dissipation in C₆₀ is studied using fs lasers are described and the production of excited Rydberg states is discussed.

A short overview of recent experimental and theoretical results on multiple ionization and fragmentation of C₆₀ in collisions with singly and multiply charged ions is presented. Experimentally, the produced electrons and positively charged ions have been detected and mass analyzed using a time- and position-sensitive multi-particle detector. The projectile ions ranged from H₊ to Ar^z+ (z = 1-3) with velocities of about 1 a.u. Cross sections of multiple ionization, evaporation rates of C₂ fragments, asymmetric fission, and multi-fragmentation patterns are discussed.

Employing the crossed-beams technique, we have studied the interaction of fullerene ions both with electrons and He²⁺-ions. Electron-impact ionization cross sections for have been measured at electron energies up to 1000 eV. Unusual features in shape and charge state dependence have been found, which are not observed for atomic ions. The evaporative loss of neutral C₂ fragments in collisions with electrons indicates the presence of two different mechanisms. In a first-ever ion-ion crossed-beams experiment involving fullerene ions, absolute cross sections for charge transfer in the collision systems and have been obtained.

Photoionization, electron scattering and excitation of silver and copper have been studied by a set of electron spectroscopy methods. Regularities of changes of electronic properties of matter in the conversion "supported atom – supported cluster of increasing size – solids" have been revealed. Evidence has been obtained that the shell electron structure of flat supported clusters is formed according to the same magic numbers as that of the spherical free clusters. The "cluster – solid" transition has been studied for fullerenes C₆₀ when these carbon clusters condense into crystal and when condensed fullerenes decay under electron or synchrotron radiation and are transformed into amorphous carbon. Photo- and electron- induced fission and transformation of fullerenes into amorphous carbon is accompanied by a decrease in electron binding energies and radical increase in the relaxation energy as well as in the case of metal clusters.

We investigated individual size-selected platinum clusters deposited on a silicon(111)-7 × 7 surface by means of a scanning-tunneling microscope (STM). The sample was prepared by collision of size-selected platinum cluster cations on the surface at a collision energy of 0.5-3 eV per platinum atom. It was found that the clusters were deposited firmly on the surface without dissociation nor aggregation. The real diameters of the clusters were estimated by considering the radius of the STM tip used for the measurement and the tunneling distance between the cluster and the tip.

We demonstrate the silicon cluster lattice system (CLS) assembling on an amorphous carbon film by using a well-defined supersonic neutral silicon cluster beam generated in a newly exploited spatiotemporal confined cluster source (SCCS). The SCCS has successfully achieved a characteristically narrow size distribution of a silicon cluster beam with ΔN/N < 5%. Neutral Si_N clusters collided with the substrate target at an energy of 1.1eV/Si atom, which is several times smaller than the cohesive energy at 4.0-4.2eV of silicon clusters. Images of the silicon clusters of 2-3nm in diameter taken by the high angle annular dark field (HAADF) method of a scanning transmission electron microscope (STEM) show a good contrast with a carbon background of the substrate. A unit cluster monolayer (CML) covers fully the substrate surface with silicon clusters of 2.3nm in diameter in the density of 1.0 × 10¹³cm^-2. The CLS formed on the substrate surface was developed spontaneously as the deposition density increases. The silicon clusters made pairs randomly oriented at 0.20CML. In progress of the deposition density around 0.67CML, silicon clusters had a tendency to form partially hexagonal closed packed structures. In further progress up to 1.0CML, the silicon clusters lined up spontaneously to form a tetragonal structure with a lattice constant of 4.0nm. The ultra high resolution transmission electron microscope (UHRTEM) imaged clearly a crystallographic atomic lattice structure of the individual silicon clusters. It was proved that the third power of the inter-cluster distance R_C and the product of the HAADF diffraction intensities I_i*I_j of all isolated cluster pairs had a linear relation. The correlation shows a possible conclusion that the induced dipole potential between silicon clusters coming close to each other dominantly makes them ordered spontaneously to form a silicon CLS.

The following sections are included:

• LIST OF PARTICIPANTS