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The absence of magic numbers in bosonic 4He clusters predicted by all theories since 1984 has been challenged by high-resolution matter-wave diffraction experiments. The observed magic numbers were explained in terms of enhanced growth rates of specific cluster sizes for which an additional excitation level calculated by diffusion Monte Carlo is stabilized. The present theoretical study provides an alternative explanation based on a simple independent particle model of the He clusters. Collisions between cluster atoms in excited states within the cluster lead to selective evaporation via an Auger process. The calculated magic numbers as well as the shape of the number distributions are in quite reasonable agreement with the experiments.

The theoretical methods currently in use for the calculation of surface phononsurface phonon dispersion curves and how they have evolved from the phenomenological force-constant models to the present day first principles theories are discussed. Aselection of paradigmatic examples for the different classes of crystal surfaces is presented with comparisons to the experimental data obtained from helium atom scattering or electron energy-loss spectroscopy.

The resonant interaction of the He atom with the bound states of the atom-surface potential can have a great influence on the elastic and inelastic intensities. Examples from experiment are used to illustrate how bound state resonances can be used to detect weakly coupled surface phonons by means of resonance enhancement. In addition there are a variety of focusing and surfing effects, arising from a coupling between the motion of the atomic projectile and that of the surface phonons. Several different focusing phenomena called critical kinematic effects are characterized by various tangency conditions among scan, resonance and phonon dispersion curves. Kinematical focusing, in particular, allows to determine envelopes of the surface phonon dispersion curves without resorting to time-of-flight measurements. Focused resonances provide a possible mechanism for an atom beam monochromator, while the surfing effect, allowing trapped atoms to ride a Rayleigh wave and leading to very sharp resonances, corresponds to a type of atomic polaron.

The phenomenological models and the quantum theoretical methods which are currently used to calculate the dispersion curves of surface phonons are reviewed for the various classes of solids.

The chapter starts with an overview of the history of the theory of surface phonons. Next the history of helium atom and electron inelastic scattering experiments are briefly reviewed. Present day helium atom scattering experiments are described next and some important related concepts are introduced. The chapter closes with a short history of the classical and quantum theory of inelastic surface scattering.

This chapter reviews some exemplary high resolution HAS experiments on surface phonon dispersion curves of adsorbate atoms and molecules either well dispersed or in layers on single crystal surfaces. Here also HAS provides unique information on the low energy vibrations with respect to the surface as well as within the layers. HAS experiments have also been used to follow the evolution of the phonon dynamics as the coverage is increased to produce one or more monolayers. These experiments are first illustrated for rare gases and simple molecules. The alkali metals show a number of new phenomena, including so-called organ-pipe modes which result from the confinement provided by the interface at the substrate. In the classical macroscopic realm the organ-pipe modes are known as Sezawa modes. The HAS dispersion curve measurements of thin films of the superconductor Pb on Cu(111) show a surprising plethora of modes. Recent DFPT and EAM calculations demonstrate that the dynamics throughout the entire film can only be understood by taking account of the strong electron-phonon coupling, which is discussed in detail in Sect. 8.4. Thus modes deep within the film and even modes localized at the interface, known as Stonely waves in the classical limit, make themselves noticed at the surface by a mechanism which is called the quantum sonar effect. HAS has also been used to study thin films of polyatomic organic molecules physisorbed on metals and also self-assembled chemisorbed monolayers. Interesting changes accompany the temperature induced transition from physisorption to chemisorption. The complex phonon dispersion curves of methyl radicals chemisorbed on silicon have recently been understood with the aid of DFPT calculations. The chapter closes with a brief review of HAS prospects for studying one-dimensional chains. Each section is meant as an introduction to the specific phenomena and issues characteristic to each of these different surface types, with special consideration to the questions solved and the new theoretical issues raised. This chapter is complemented by appendices which contain a comprehensive list (up to 2016) of the HAS experimental data on adsorbates on insulators and semiconductors (Appendix A.5), atomic adsorbates on metals (Appendix A.6), diatomic molecules on metals (Appendix A.7) and polyatomic molecules on metals (Appendix A.8).

The reflection coefficient determining the inelastic scattered intensity is defined and analysed theoretically. Various approximations including the Born approximation, the Distorted-Wave Born approximation (DWBA), the GR method and the eikonal approximation are discussed and illustrated with examples. From an expression for the DWBA inelastic reflection coefficient for n-phonon processes, factors determining the relative role of temperature for multiphonon processes and one-phonon scattering are analysed. Several approximate expressions for the Debye-Waller factor are derived and used to define experimental criteria favouring one-phonon scattering. Most of the examples dealt with are for insulator surfaces. Chapter 8 then describes the scattering theory for metal and semiconductor surfaces.

The forces that an He atom exerts on the atoms of a solid surface causing inelastic scattering have much in common with the interatomic forces that govern the dynamics of the lattice. The scattering theory, described in Chap. 7 based on two-body collisions, provides the correct interpretation of data for closed-shell surfaces, much as their lattice dynamics is well described by phenomenological interatomic potentials. The inelastic HAS experiments from metal surfaces, however, cannot be successfully described in the same way. In this Chapter the approaches developed for the lattice dynamics of metals, where the interatomic forces are mediated by free electrons, such as the Multipole Expansion (ME) and the Density Functional Perturbation Theory (DFPT) are introduced for the analysis of inelastic HAS intensities from metal surfaces. These theories have the important consequences that inelastic HAS intensities are directly proportional to the electron-phonon coupling strength for individual phonons and that HAS can detect deep sub-surface phonons. The propensity of HAS to excite certain phonons of conducting surfaces rather than others is found to depend on the electron-phonon interaction and the surface electron band structure.

The previous chapters have been devoted to summarizing the vast knowledge acquired about the single phonon vibrations of atoms in or near the surface and about atoms and molecules on the surface and their dispersion curves. This new knowledge was made possible largely thanks to the development of He atom scattering spectroscopy and the progress made in theoretical analysis. Single phonon inelastic scattering processes were implicit since only in this case is it possible to extract accurate phonon dispersion curves from the data. The high resolution of HAS spectroscopy, especially in its 3He-spin echo version also allows for the observation of dynamical phenomena far beyond the harmonic motion, like multiphonon processes involving low energy phonons or the diffusion of adsorbates on the surface. Moreover, the unique property of closed shell He atoms to exchange energy and momentum with the ion cores of the surface atoms via the virtual excitation of interposed electrons makes HAS also a valuable tool for investigating collective surface electron excitations in the THz domain. It therefore seems appropriate to discuss also some of these and other emerging areas of HAS research where new important insight can be expected in the future.

In this chapter the various models and approximations used for describing the static atom-surface potential are reviewed and analyzed. The potentials are of fundamental importance for the calculation of the elastic scattering of atoms from surfaces. These potentials also are the basis for the calculations of the inelastic scattering from surface phonons on insulator surfaces, discussed in detail in Chap. 7. In the case of metal and semiconductor surfaces the semi-empirical parameters used to describe the modifications of the potential resulting from the spill-out of the conduction electrons are discussed. The theory of inelastic surface phonon scattering from metals and semiconductors is the subject of Chap. 8.

The effect of the surface termination on the phonon dispersion curves is illustrated by comparison with the bulk dispersion curves. After a review of Rayleigh’s theory of surface waves in elastic media the atomistic Born-von Karman theory for bulk phonons is presented. How the surface affects the surface vibrations is illustrated by the Green’s function theory and slab calculations. The chapter closes with some illustrations of surface phonon dispersion curves and their classification.

In this chapter some exemplary high resolution HAS experiments on surface phonon dispersion curves of single crystal surfaces based largely on the TOF technique are reviewed. A selection is made of significant results for insulator, semiconductor and conducting surfaces, with special attention to the HAS results for metals, semimetals, and layered materials, where evidence is found for important effects of, for example, electron-phonon coupling and the related observation of Kohn anomalies, anomalous longitudinal branches and deep subsurface modes. Studies on complex surfaces with large-period unit cells due to reconstruction or high index orientation are also reviewed. Here also the comparatively high resolution of HAS permits to observe low energy dynamical excitations and their dispersion. Each section is meant as an introduction to the specific phenomena and issues characteristic to each of these different surface types, with special consideration to the questions solved and the new theoretical issues raised. This chapter is complemented by Appendix A, which contains a comprehensive list of the available HAS experimental data on phonon dispersion curves and of the theoretical studies for the different classes of materials, as of early 2018 which update previous reviews: [1, 2] (all systems), [3, 4] (layered compounds), [5, 6] (semiconductors), [7] (metals) and Landot-Bornstein Chapters [8, 9, 10, 484].

Surface elastic waves, discovered by Lord Rayleigh in the late 19th century in the realm of seismology, besides occurring in nature over a wide range of length scales, have found a broad spectrum of technological applications (Sect. 1.1). Surface acoustic waves (SAWs) on the nanometric scale and their quanta, surface phonons, while allowing for signal processing devices operating in the THz domain, hold information on the structure and the interatomic forces at solid surfaces, which generally differ from those of the solid bulk (Sect. 1.2). Inelastic He atom scattering, as compared to other surface phonon probes, offers convenient kinematical conditions for a high-resolution surface phonon spectroscopy over the complete momentum and energy spectral range (Sect. 1.3).

The Born-von Karman model introduced in the previous Chapter, is used to illustrate how the invariance properties of the total energy, the equilibrium conditions and the emergence of the surface stress affect the surface force constants in the surface region and the surface phonon dispersion curves. Then the effects of extended surface and interplanar force constant perturbations, which in the case of metals may involve several layers, are discussed.

A modified semi-empirical Tang-Toennies potential model is used to describe the a 3Σ+u potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth De, well location Re, and the harmonic vibrational frequency ωe of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na2, K2, Rb2, and Cs2, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li2 and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li2 less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.

The pulsed flow of solid $^{4}\mathrm{He}$ through a narrow capillary in a flow system which issues into vacuum is investigated at temperatures between 1.64 and 2.66 K and pressures between 54 and 104 bars. After each pulse three different capillary flow regimes are observed as the upstream pressure decreases: an oscillatory [mini-geyser (MG)] regime, a constant flow (CF) regime with a linearly decreasing pressure difference, and a nonresistant (NR) regime. A quantitative analysis of the three regimes suggests that the flow of solid $^{4}\mathrm{He}$ is driven by a counterflow of excess vacancies, which are injected downstream of the capillary at the solid/liquid interface near the micrometric orifice exposed to vacuum. The CF regime, where the flow velocity is found to be independent of the pressure difference, and the NR regime, where the solid flows as a Bernoulli fluid, suggest a new dynamic phase of solid helium induced by a steady influx of vacancies.

The spectrum of the band of the S1 ← S0 transition of tetracene molecules embedded in superfluid helium droplets is studied via laser induced fluorescence spectroscopy. Measurements are reported for droplets of different average sizes from about 103 to 107 helium atoms. In agreement with previous observations in small droplets the band shows two components designated as α and β peaks split by about 1 cm−1. In addition the higher energy β-peak shows some sharp superimposed peaks separated by about 0.05 cm−1. A very similar fine structure of the band is found in the tetracene–argon complex and in pentacene which challenges a simple explanation in terms of a free molecule Hamiltonian. Presumably the rotational-translational coupling of very anisotropic molecules, such as tetracene in superfluid helium has a noticeable affect on the spectra. In droplets larger than about = 106, obtained in supercritical expansions, the β peak has a broad feature shifted by 0.1 cm−1 towards higher energies from the maximum fo...

Wolfsohn's parameters for the frequency-dependent polarisability α(ω) of mercury are modified to fit the recent interferometric measurements of Goebel and Hohm [J. Phys. Chem. 100, 7710 (1996)]. The resulting α(ω) are extended to imaginary frequencies α(iω) and used to calculate the upper and lower bounds of the dipole dispersion coefficient in the long range dimer potential. The new value of C 6 = 392±4 a.u. is much greater than the generally accepted value. With the corresponding changes in the dipole–quadrupole and dipole–octopole interactions, new dispersion coefficients C 8 and C 10 are obtained. Together with the experimentally determined D e (well-depth) and R e (equilibrium distance), the Tang–Toennies model is used to predict the shape of the entire dimer potential energy curve. The new potential is found to be in excellent agreement with the ab initio calculations of Munro et al. [J. Chem. Phys. 114, 5545 (2001)] and the parameters ωe and χeωe agree with the spectroscopic measurements within the...

The growth of Pb ultrathin films on Cu(111) has been long studied in connection with electronic quantum-size effects and for the different temperature-dependent growth kinetics. At low temperature the formation of a wetting layer (1 monolayer (ML)), is followed by an instability of the 2 ML film and a regular layer-by-layer growth is then only observed for more than two monolayers. The 2 ML film was, however, shown to be stabilized by alloying Pb with 20% Tl. This work presents a theoretical study of the dynamics of the wetting layer as well as for 2 ML Pb0.8Tl0.2, 3 and 4 ML Pb on Cu(111) in the 4 × 4 commensurate phase, for which detailed inelastic Helium atom scattering (HAS) spectra have been measured. The present calculations based on the embedded atom method (EAM) include the dynamics of the substrate. Besides leading to a detailed interpretation of the HAS experimental data, the present results are compared with a previous density-functional perturbation theory (DFPT) study for 3 to 7 ML Pb on a rigid substrate. The comparison reveals the role played by the substrate dynamics at the smallest thicknesses, despite the large mass and stiffness differences between Pb and Cu. Also the different thermal expansion of the film with respect to the substrate is shown to cause appreciable anomalies in the temperature and thickness dependence of the phonon dispersion curves., The work was carried out at the financial support by a grant (8.1.05.2015) from The Tomsk State University Academic D. I. Mendeleev Fund Program, an RFBR grant (15-02-02717-a), and the Fundamental Research Program of the State Academies of Sciences for 2013–2020.

A new analysis of inelastic helium atom scattering (HAS) data for the (111) surface of Xe reveals a surprising similarity between the surface phonon dispersion curves of the solid noble gas xenon and of the noble metal copper, the only difference being an energy scale factor. Even more surprising is that the poorly understood X phonon branch observed in Xe(111) actually corresponds to the subsurface S2 phonon branch of Cu(111). A subsurface phonon in a closed-shell insulator surface should not be detectable by HAS, as is instead the case for free electron surfaces, where the electron−phonon interaction can couple the scattering He atoms to phonons several layers beneath the surface (quantum sonar effect). A density functional perturbation theory analysis shows that the large atomic polarizability of surface Xe atoms actually provides the electron−phonon coupling sufficient to explain the comparatively large HAS intensity from the S2 branch of Xe(111). It is concluded that the possibility of directly measuring the surface electron−phonon coupling constants from inelastic HAS intensities, originally demonstrated for conducting surfaces, can be extended to polarizable insulating surfaces, as well as oxides and heavier chalcogenides.

Diffraction of molecular beams of CH3F, CHF3, and metastable He* and Ne* from a 100-nm-period micro-fabricated transmission grating has been observed. Due to the finite velocity spread and the corresponding temporal coherence of the molecular beams, diffraction peaks of only the first few orders are resolved in total-intensity measurements, while higher order peaks are increasingly broadened and smeared-out. Combining time-of-flight (TOF) measurements with angular scans has allowed to observe TOF-resolved diffraction data which yield full resolution of all detected diffraction peaks. Here, this method has been applied to investigate atom/molecule-surface interactions. In general, it can be used to observe resolved diffraction patterns of a wide range of atomic and molecular beams whose broad velocity distributions prevent peak-resolution in conventional total-intensity measurements.

A pairwise sum model is used to derive the laterally averaged atom–surface potential using the Tang–Toennies potential for interactions between a free atom and the atoms in a solid. The atom–surface van der Waals attraction is shown to include all multipole terms with the proper damping. The analytical expressions for the damping functions have the same damping parameter as for the free atom–atom interactions.

The low-energy part of the surface vibrational spectrum of the Si(111)(7×7) surface has been measured along both symmetry directions using high-resolution helium atom scattering. The analysis of the experimental data with a simple model enables the identification of contributions arising from the geometrical back-folding of the Rayleigh wave and from vibrations of adatoms, in excellent agreement with recent ab initio results.

Recent inelastic helium atom scattering measurements of the phonon dispersion curves of epitaxial thin films (2{endash}30 ML) of four different types of systems are analyzed within the framework of a force constant model. Whereas Na/Cu(001) shows nearly flat dispersionless modes with frequencies at the {bar {Gamma}} point that follow the open standing wave sequence, the other systems Pb/Cu(111), Ar(Kr)/Ag(111), and KBr/NaCl(001) reveal a more complex behavior. These qualitative differences can be explained in terms of a simple linear chain model in which the behavior is determined by the strength of the force constant coupling of the thin films to the substrate relative to the force constant within the films. Detailed slab calculations for Na/Cu(001) confirm this model and indicate that the observed flat phonon dispersion curves are related to the strength of the interface interaction and bcc structure of the epitaxially grown Na thin films. {copyright} {ital 1996 The American Physical Society.}

Durch die Fortschritte der Mikrotechnologie ist es in den letzten Jahren gelungen, Lehrbuchexperimente der Optik auf Atom- und Molekulstrahlen zu ubertragen. Die optisch-wellentheoretische Beschreibung von Beugungsexperimenten am Doppelspalt und am Gitter stimmt qualitativ gut mit den Erwartungen uberein. Aber aus kleinen Abweichungen davon lassen sich durch prazise Messungen und raffinierte theoretische Methoden neue uberraschende Erkenntnisse uber Teilchengrosen und ihre Wechselwirkung mit Oberflachen gewinnen.

The forces governing the inelastic scattering of He atoms from the surface phonons of a metal surface have been obtained from first principles as functions of the surface ground-state properties. The large inelastic scattering intensities which have been observed in association with the anomalous longitudinal surface modes of noble and transition metals are interpreted in the light of the present new theory.

Absolute integral cross sections have been measured for n-H2-n-H2 at primary particle velocities between 1270 and 9650 m/sec with a 77 °K target. The number density of target particles was determined with an accuracy of 1% by the method of dynamic expansion. The velocity dependence of the integral cross section was also measured for the isotopic systems n-D2-n-H2 and n-D2-n-D2 at primary beam velocities between 280 and 1170 m/sec with a 15 °K target. All available integral cross section data are compared with literature potentials. A new potential is proposed, which exhibits one bound state for H2-H2.

The phonon dispersion curves of ultrathin films of Cs(110) on Pt(111) measured with inelastic helium atom scattering (HAS) are reported and compared with density-functional perturbation theory (DFPT) calculations. The combined HAS and DFPT analysis also sheds light on the bulk phonon dynamics of bcc-Cs, on which very little is known from neutron scattering due to its large neutron capture cross-section. Moreover the temperature dependence of the elastic HAS Debye-Waller exponent of Cs(110)/Cu(111) ultrathin films allows for an estimation of the electron-phonon coupling strength λ as a function of the film thickness.