Calculations on the effect of the surface potential barrier in LEED

The main effects of the surface potential barrier in LEED arise from strong internal reflection of diffraction beams for incidence conditions close to those for their grazing emergence. Near each grazing emergence condition, the details of LEED intensity profiles depend on the amplitude coefficient of internal reflection and hence on the shape of the surface potential barrier. Calculations of the amplitude coefficient for real one-dimensional barrier potentials with shapes specified by three parameters are reported. The calculations are done as a function of the energy associated with the surface-normal momentum component of the internally incident beam. The potential has the image form at large distances from the surface and joins smoothly to a quadratic at an intermediate distance. The results are tabulated and an interpolation formula is given so that the amplitude coefficient of reflection can be evaluated readily for potentials of the assumed form. Applications to the calculation of LEED intensity lineshapes are summarized.     

Surface dependence of field ion energy distributions,He on W

Kinetic energy distributions of helium ions produced by field ionization above the (100), (110), and (111) planes of tungsten field emitters are reported. The energy resolution of these measurements if 0.3 eV fwhm. The main peak of these distributions is found to shift by as much as 0.7 eV at $\text{F = 5.3 V/}\text{A}\text{?}$, T = 21 K, when the origin of the ions collected is changed slightly. Several possible explanations for this shift are discussed. The most plausible of these involves electron tunneling through a field adsorbed helium atom. These results have important implications for the use of field ion energy distributions as a probe of the density of electronic states of the emitter.     

Intense-field double ionization of helium: identifying the mechanism

We present quantum mechanical calculations of the electron and ion momentum distributions following double ionization of a one-dimensional helium atom by ultrashort laser pulses (780 nm) at various intensities. The two-electron momentum distributions exhibit a clear transition from nonsequential to sequential double ionization. We provide strong evidence that rescattering is responsible for nonsequential ionization by calculating the momentum spectrum of the He2+ recoil ions-which we find in excellent agreement with recent experiments-and by analyzing the electronic center-of-mass motion via Wigner transforms.     

Ionization of atoms in strong low-frequency electromagnetic field

The ionization of atoms in a low-frequency linearly polarized electromagnetic field (the photon energy is much lower than the ionization potential of an atom) is considered under new conditions, in which the Coulomb interaction of an electron with the atomic core in the final state of the continuum cannot be considered in perturbation theory in the interaction of the electron with the electromagnetic field. The field is assumed to be much weaker that the atomic field. In these conditions, the classical motion of the electron in the final state of the continuum becomes chaotic (so-called dynamic chaos). Using the well-known Chirikov method of averaging over chaotic variations of the phase of motion, the problem can be reduced to non-linear diffusion on the energy scale. We calculate the classical electron energy in the final state, which is averaged over fast chaotic oscillations and takes into account both the Coulomb field and the electromagnetic field. This energy is used to calculate the probability of ionization from the ground state of the atom to a lower-lying state in the continuum using the Landau-Dykhne approximation (to exponential accuracy). This ionization probability noticeably depends on the field frequency. Upon a decrease in frequency, a transition to the well-known tunnel ionization limit with a probability independent of the field frequency is considered.     

LEED fine structure: Origins and applications

For incident energies below 50 eV, high resolution low energy electron diffraction (LEED) spectra exhibit fine structure arising primarily from the scattering of electrons by the surface potential barrier. We review the experimental techniques used for measuring such spectra, and derive a model for the process involved. The comparison between measured spectra and calculations using this model provides details about the surface barrier structure and adsorption sites on metal surfaces. We discuss current applications of this technique and some promising directions for future work.     

Theory of angle-resolved photoemission from localised orbitals at solid surfaces

The theory of angle resolved photoemission from localised orbitals is reviewed and is cast in a form requiring the calculation of the purely outgoing wave emanating from an emitting atom, that describes the final state of the photoelectron, rather than using the more usual approach based on time reversed scattering states. An explicit expression is written down for the superposition of partial waves that results from emission from an atomic orbital, and it is pointed out that emission from more complex initial states such as localised bonds or Bloch and surface states, can be described by coherently combining such sets of partial waves. The effect of the crystal surface environment in damping and scattering the waves is described briefly. Model calculations are performed to investigate the major influences on the angular distribution of the photoelectrons. The profound effect of varying the polarisation direction of the incident light relative to the surface is discussed, with examples from the literature, showing how it can be used to determine the type of initial orbital. Emission from directed orbitals is studied and it is shown that scattering by the emitter potential can be an important effect, so that the radial wave function of the outgoing electron, which determines the amplitudes and phases of the outgoing waves, must be calculated with care. Different choices of these quantities lead in the model calculations to very different angular profiles, that sometimes bear little relation to the shape of the initial orbital. The consideration of emission from localised bonds shows that provided that bonds are not too strongly polarised, interference between waves from different centres is always significant at higher energies, and can also be important at energies of a few eV relative to the vacuum. Scattering by the ion cores of the surface region can strongly distort the angular distribution, or may have little effect. But it is generally difficult to decide a priori which influences are dominant for a particular case, so that the interpretation of angular profiles must be based on careful calculations including all these effects. The optimum energy range for the interpretation of experimental data is that from about 30 to 100 eV.     

Multiple scattering and neutralization aspects of low energy noble gas ions incident on a Cu (110) crystal

Experiments have been done with 1 keV Ne⁺ ions bombarding a Cu (110) single crystal in a (111) plane. From the measured energy spectra of the scattered ions the minimum and maximum scattering angles for multiple scattering on the surface are determined. These minimum and maximum scattering angles were also calculated using a computer model. The parameters for an interatomic potential function between ion and metal atom are determined by comparison of the experimental and calculated scattering angles. A neutralization model for an energetic ion at an atomic surface is given. The reliability of this model is tested by comparison of the results of computer calculations and the measured peak intensity distributions as a function of the scattering angle.     

Calculations of field ionization in the field ion microscope

The ionization of a gas atom as it occurs in the field ion microscope is discussed. A wide range of values for the electric field intensity at the metal surface are considered in calculating the ionization occurring both far away from and close to the tip. Ionization distribution curves are calculated and electric fields strengths are determined at points where the distributions peak. Calculations of ionization zone widths and best image conditions are made and a new interpretation of best image conditions is considered. A new field calibration method is suggested.     

裸核离子与中性原子碰撞电离过程的理论研究

基于处理裸核离子与中性原子碰撞电离过程的OBKN和ECPSSR理论模型,系统计算了不同裸核离子与中性原子碰撞K壳层电子俘获截面和直接电离截面,并与其它文献已有的理论和实验结果进行了比较.研究结果表明:碰撞能量较低时,电子俘获截面大于直接电离截面,随着碰撞能量的增加,电子俘获截面和直接电离截面均是先增大后减小且直接电离截面减小地非常缓慢,高能时,直接电离截面大于电子俘获截面.当入射炮弹离子速度接近0.67倍靶原子K壳层电子速度时,电子俘获截面达到最大值,而当入射炮弹离子速度接近靶原子K壳层电子速度时,直接电离截面达到最大值.     

裸核离子与中性原子碰撞电离过程的理论研究

基于处理裸核离子与中性原子碰撞电离过程的OBKN和ECPSSR理论模型,系统计算了不同裸核离子与中性原子碰撞K壳层电子俘获截面和直接电离截面,并与其它文献已有的理论和实验结果进行了比较.研究结果表明：碰撞能量较低时,电子俘获截面大于直接电离截面,随着碰撞能量的增加,电子俘获截面和直接电离截面均是先增大后减小且直接电离截面减小地非常缓慢,高能时,直接电离截面大于电子俘获截面.当入射炮弹离子速度接近0.67倍靶原子K壳层电子速度时,电子俘获截面达到最大值,而当入射炮弹离子速度接近靶原子K壳层电子速度时,直接电离截面达到最大值.     

Cross sections of electron capture and electron capture ionization versus the impact parameter in collisions of a proton with multielectron atoms

The absolute differential cross sections of scattering of hydrogen atoms resulting from an electron capture and an electron capture ionization are measured for collisions of 4.5- and 11-keV protons with argon and xenon atoms. The range of scattering angles is 0°–2°. From the scattering differential cross section found experimentally, the probabilities of single-electron capture and electron capture ionization as a function of the impact parameter are calculated. The dependences of the incident particle scattering angle on the impact parameter (deviation function) for interactions with Ar and Xe atoms are calculated in terms of classical mechanics using the Moliére—Yukawa potential to describe the interaction of atomic particles. Analysis is given to the probabilities of electron capture and electron capture ionization versus the impact parameter and to the distribution of the electron density on different electron shells in a target atom versus a distance to the core. It is concluded that only electrons from the outer shell of the target atom are involved in the process of electron capture ionization. The cross section of electron capture ionization is calculated in the proton energy range 5–20 keV.     

On the choice of surface barrier models for LEED intensity calculations

The significance of surface barrier scattering in LEED is assessed. The scattering properties of various model barriers are compared. Modifications and improvements are suggested for the simpler barrier models. A computational test for Cu(001) shows that a step barrier is satisfactory for LEED intensity calculations except where details of the surface barrier resonance are desired.     

Model calculations of atom-surface scattering

The elastic scattering of light mass, thermal-energy atoms from simple surfaces is investigated. The surface is represented by the model of a single planar square array of hard spheres. The effect of the surface potential well is treated semiclassically by simply shifting the energy of the incident atom ; furthermore a constant imaginary term is added to the energy to account for inelastic scattering and adsorption. As in the multiple scattering formalism of LEED the total scattering matrix of the lattice is expanded in terms of the individual gas atom-surface atom t-matrices. Propagation of the incident atom on the surface is described in terms of a one particle Green's function propagator with complex energy. The terms in the multiple scattering series are summed to all orders, by using standard matrix inversion techniques. The size of the matrix to be inverted limits to ten the total number of phase shifts that are included in the calculation. Thermal effects are included through angle dependent Debye-Waller factors.Model calculations have been performed to study the intensity of the specular and the diffracted beams as a function of the angles of incidence. The importance of surface temperature (introduced by the Debye-Waller factors), the incident energy and the depth of the potential well of the gas-surface interaction are discussed. The main feature of the results is the decrease of the intensity of the specular beam in going from glancing incidence to normal incidence and the presence of structure due to the appearance and disappearance of diffracted beams across the surface. The azimuthal behavior of the specular beam is in agreement with experimental observations.     

Relativistic effects on LEED intensities from Au(111)

Comparison of relativistically and nonrelativistically calculated intensity versus energy profiles in low energy electron diffraction (LEED) from the (111) surface of Au (Z = 79) reveals that relativistic corrections are quite significant. They can however, be obtained in very good approximation by quasirelativistic calculations, in which spin-averaged relativistic phase shifts are used as input for the nonrelativistic multiple scattering formalism. Further, relativistic effects on intensities are found to be comparable to differences arising from different approximations to the exchange part of the ion core potential.     

Structural analysis of the β-SiC(100)-(2 × 1) surface reconstruction by automated tensor LEED

The atomic structure of the β-SiC(100)-(2 × 1) surface was analyzed using dynamical calculations of low energy electron diffraction (LEED) intensities measured with a video camera. Surface composition was monitored using Auger electron spectroscopy (AES). The LEED calculations utilized our recently developed automated tensor LEED method. The results indicate that the surface is terminated by a monolayer of silicon with the topmost silicon atoms forming asymmetric, buckled dimers.     

Two-dimensional Penning ionization electron spectroscopic study on outer characteristics of molecules

Collision-energy/electron-energy-resolved two-dimensional Penning ionization electron spectroscopy (2D-PIES) has been used to study outer characteristics of molecules. Anisotropic potential energy surfaces for collisional ionization of molecules with a metastable helium atom He*(2³S) have been determined starting from ab initio model potentials via optimization based on trajectory calculations. Since ionization widths in the theoretical model of Penning ionization are functionals of target molecular orbitals, outer electron distributions of molecular orbitals can be determined via optimization procedures of calculated ionization cross-sections by trajectory calculations with respect to observed 2D-PIES data.     

Effect of electron exchange on atomic ionization in a strong electric field

Hartree-Fock atom in a strong electric static field is considered. It is demonstrated that exchange between outer and inner electrons, taken into account by the so-called Fock term affects strongly the long-range behavior of the inner electron wave function. As a result, it dramatically increases its probability to be ionized. A simple model is analyzed demonstrating that the decay probability, compared to the case of a local (Har-tree) atomic potential, increases by many orders of magnitude. As a result of such increase, the ratio of inner to outer electrons ionization probability became not too small. It is essential that the effect of exchange upon probability of inner electron ionization by strong electric field is proportional to the square of the number of outer electrons. It signals that in clusters the inner electron ionization by strong field, the very fact of which is manifested by e.g. high energy quanta emission, has to be essentially increased as compared to this process in gaseous atomic objects.     

Theory of surface dynamic variation during the high-temperature field evaporation

We consider the heated surface of a metallic tip to which a strong electric field is applied. At temperatures activating surface self-diffusion, crystalline outgrowths and microprotrusions arise on the surface. The latter generate ion fluxes, i.e., act as sources of high-temperature field evaporation, when a positive potential is applied to the emitter. The existence conditions for the microprotrusions on the emitter surface are discussed. It is shown that their stability is provided by the balance between three atomic fluxes: diffusion from the top of the tip, diffusion toward the top, and field evaporation from the top. Different ways of providing such a balance are discussed. In a desorption-type field ion microscope, the microprotrusions and evaporating ions are visualized as bright spots. These spots execute random motion and, at the same time, exhibit ordered cyclic displacements: the microprotrusions first form dotted rings along the developed faces of the crystalline emitter, and then these rings quickly collapse toward the center of the face. A quantitative theory of these cyclic processes is developed for the first time. It explains why the rings “calm down” before collapse and why subsequent collapse develops in an avalanchelike manner. The electric field distribution over the surface in the presence of an outgrowth is calculated, and diffusion fluxes at different stages of its growth and dissolution are analyzed. The calculation shows that the outgrowth heights are relatively small and their slopes are rather smooth.     

Multiphoton ionization of the hydrogen atom by a circularly polarized electromagnetic field

This paper examines the multiphoton ionization of the ground state of the hydrogen atom in the field of a circularly polarized intense electromagnetic wave. To describe the states of photoelectrons, quasiclassical wave functions are introduced that partially allow for the effect of an intense electromagnetic wave and that of the Coulomb potential. Expressions are derived for the angular and energy distributions of photoelectrons with energies much lower than the ionization potential of an unperturbed atom. It is found that, due to allowance for the Coulomb potential in the wave function of the final electron states, the transition probability near the ionization threshold tends to a finite value. In addition, the well-known selection rules for multiphoton transitions in a circularly polarized electromagnetic field are derived in a natural way. Finally, the results are compared with those obtained in the Keldysh-Faisal-Reiss approximation. Zh. éksp. Teor. Fiz. 116, 807–820 (September 1999)