Work function changes produced by chemisorption due to site heterogeneity

A quantum theory of elastic scattering of atoms from crystal surfaces is presented, based on a hard corrugated surface model. It is shown in detail how the rainbow effect arises and determines the diffraction probabilities, such a rainbow effect being the quantum analogon of McClure's classical rainbow. Further topics considered are the influence of a potential well and the reasons why diffraction hardly occurs from metal surfaces. The basis for a possible extension to inelastic scattering is sketched.     

Classical surface scattering computations; Rainbows and energy exchange

Computational techniques (a “response-function” method and a molecular dynamics procedure) for classical calculations of atom-surface scattering are described. The methods are illustrated by calculations for a model of neon scattering from the silver (111) surface. Calculations for clamped and initially stationary lattices show complex classical rainbow effects with multiple rainbows due to scattering from different regions of the crystal surface. These effects are not destroyed by inelasticity or energy exchange with cold crystals. Calculations at higher temperatures show, however, that thermal effects do smear out the rainbow effects and lead to rather featureless angular distributions similar to those observed experimentally for this system.     

Temperature dependence in atom–surface scattering

It is shown that a straightforward measure of the temperature dependence of energy resolved atom–surface scattering spectra measured under classical conditions can be related to the strength of the surface corrugation. Using classical perturbation theory combined with a Langevin bath formalism for describing energy transfer, explicit expressions for the scattering probabilities are obtained for both two-dimensional, in-plane scattering and full three-dimensional scattering. For strong surface corrugations results expressed as analytic closed-form equations for the scattering probability are derived which demonstrate that the temperature dependence of the scattering probability weakens with increasing corrugation strength. The relationship to the inelastic rainbow is briefly discussed.     

Classical theory of atom–surface scattering: The rainbow effect

The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom–surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom–surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle–surface interactions.     

Der Regenbogeneffekt und Interferenzerscheinungen bei molekularen Stößen

Crossed beam measurements of differential elastic scattering cross sections for collisions of alkali atoms with mercury and xenon atoms as well as with different molecules are presented. Special attention is given to the rainbow effect including supernumary rainbows and to interference effects connected with rainbow scattering. The observation of well resolved primary and supernumary rainbows together with interference patterns make the determination of a three parameter potential model possible. Partial wave numerical calculations of differential cross sections are used to evaluate potential parameters and to discuss the limits of the semiclassical rainbow theory. Elastic scattering between reactive collision partners is investigated too and interpreted in terms of a simple optical model.     

Selective adsorption resonances at rainbow conditions in the scattering of atoms by stepped surfaces: application to the He/Cu(117) system

For stepped surfaces, dynamics is not parity reversal invariant with respect to the step configuration and the way the atomic beam approaches the surface, downstairs or upstairs scattering, should dramatically change rainbow patterns. We show that only one close-coupling calculation provides us information of the two possible scatterings at once. Furthermore, it is possible to find some incident conditions where surface rainbow is displayed for both configurations. At the same time, if resonances are analysed at rainbow conditions, we could enhance resonant features in the diffraction channel displaying rainbow. An application to the study of diffraction of ⁴He atoms by the Cu(117) surface is presented.     

Cutoffs and shadows in classical scattering of atoms from surfaces

A commonly used model for the scattering of atoms from crystalline surfaces is that of a classical hard sphere interacting with a hard, corrugated surface. This model is simple enough to permit the study of the effect on the scattering of variation of parameters of the model. We examine here how changes in the amplitude and symmetry of the corrugations, the size of the sphere, and the depth of an attractive well near the surface modify the scattering. We show, in particular, how edge effects due to shadowing of parts of the surface and second hits by the sphere distort the classical rainbow structure. We show the results as topological and intensity plots for special cases. The edge effects give new information on the structure of the surface. For suitable real systems, experimental measurement of the angular and energy dependence of the fraction of the scattering that is elastic may show some of the features described.     

均匀球形液滴二阶和五阶彩虹的重建及应用

从理论和实验两方面研究了不同温度下球形液滴的彩虹强度分布及在粒度测量中的应用。研究结果表明折射率为 1.33附近液滴在 117°～ 134°散射角范围内的散射强度分布不是单一的二阶彩虹强度分布 ,而是二阶和五阶彩虹的干涉强度分布。基于散射强度频谱特点 ,提出了一种从干涉强度谱中重建二阶和五阶彩虹强度分布的方法 :逆快速傅里叶变换 (IFFT)。利用洛伦兹米理论 (LMT)模拟计算了温度为 2 0℃和 80℃下水粒子二阶彩虹的高频结构与粒子直径的关系 ,获得了经验公式。该关系式可用来测量确定温度下均匀水粒子直径。还利用激光彩虹测试系统测量了水柱二阶彩虹角度范围内的散射强度分布。上述理论研究结果与实验结果进行了比较 ,两者吻合得很好。基于上述研究 ,可以从单一阵列探测器获取的彩虹信号提取不同阶次彩虹分布 ,用于液滴多参量的反演测量。     

H++CO2散射在30电子伏能量下电荷转移和非电荷转移的非绝热分子动力学模拟

在大气化学、天体物理学和癌症质子疗法中都涉及到高能H⁺+CO₂散射反应.本文在最简电子-核动力学（SLEND）基础上系统研究在30 eV下的H⁺+CO₂散射.SLEND用经典力学描述核,用单行列式Thouless波函数描述电子.本文模拟了CO₂在42个取向共3402条轨线,为理解H⁺+CO₂散射中的各个反应过程和机制提供了系统描述：非电荷转移散射（NCTS）,电荷转移散射（CTS）和C=O双键的断裂,这些关于反应的有用信息不能完全从实验中获取.本文提供了散射的详尽细节,包括随CO₂取向不同主彩虹角和次彩虹角的出现和合并.SLEND NCTS和CTS的微分散射截面通过高等半经典方法计算,显示NCTS散射截面对所有散射角都同实验符合得很好,而CTS散射截面只大散射角时同实验结果符合得很好而在小角散射时稍差.无论是CTS还是NCTS SLEND都预言了主彩虹角的特征,这同实验完全一致.     

Anomalous scattering from dielectric bispheres in the specular direction

Resonant scattering from dielectric bispheres in the specular direction (the so-called specular resonance), previously known only in the microwave range, has been observed at the optical wavelength. Systematic experiments with micrometer-sized dielectric bispheres assembled by micromanipulation, together with rigorous numerical calculations, reveal that this scattering is a precursor of the classical rainbow and is a general phenomenon observed in the wide range of size parameters (>5 for n=1.59) for various refractive indices.     

Diffractive scattering in the Ericson model for the S matrix

The elastic scattering of spinless charged particles on nuclei is considered within the strong-absorption model proposed by Ericson for the S matrix in the angular-momentum representation. Our analytic method for summing partial-wave amplitudes, which is based on a generalization of the Abel-Plana formula, makes it possible to take into account the contributions from the possible singularities of the S matrix in the right-hand half-plane of the complex-valued variable l. The uniform asymptotic behavior obtained in the present study for the scattering amplitude offers a fresh view on the origin of the diffraction patterns in the angular distributions of elastically scattered heavy particles. Special attention is given to Coulomb-nuclear interference (in particular, to refraction phenomena) in the case of scattering into the classically allowed region (illuminated region) and the classically forbidden region (shadow region). In contrast to other analytic results, our solutions to the diffraction problem within the Ericson model do not give grounds whatsoever to draw profound analogies either with Fresnel diffraction in optics or with the phenomenon of rainbow scattering in classical mechanics.     

Simple approach to refraction effects in atom-surface scattering

A simple method of calculating low energy atom-surface diffraction intensities is presented for the case in which the scattering is dominated by a single rainbow pattern. Good agreement is obtained when these calculations are compared with recent results for the scattering of He by a Pt(997) surface.     

非球形大气粒子对任意波束的电磁散射特性

研究大气中变形球状的气象粒子对电磁波以及激光的散射特性,采用广义米氏(Mie)理论,精确地求解在任意波束中大气粒子的散射强度,数值计算激光束腰位置对散射强度分布的影响,分析彩虹强度和散射角与变形球状粒子偏心率的关系,研究随着长短轴比例增加,彩虹强度峰值的偏移。计算结果表明雨滴在下降过程中,它在各个方向的光散射强度逐步减弱,即随着雨滴偏心率的增大,散射强度减少,彩虹角变大。对于激光入射,当粒子距离波束中心位置越远,粒子的散射就越弱,并且随尺寸参量增加,后向散射振荡的频率要大于前向散射,当束腰位置矢径的大小增加时,后向散射和前向散射强度均变小。     

Rainbow interference effects in heavy ion elastic scattering

It is shown that the oscillatory behaviour of differential cross section of heavy ion elastic scattering, which satisfies the semi classical conditions, is well described in terms of interference effects due to a rainbow.     

Description of elastic heavy-ion scattering within the Glauber-Sitenko approach

Analytic expressions for the amplitudes of elastic nucleus-nucleus scattering for various collision regimes are derived within the Glauber-Sitenko approach. The procedure used to do this employs an extended optical potential of the Woods-Saxon type and takes into account the deflection of trajectories by a strong Coulomb field. A comparison of the analytically calculated cross sections with numerical results and experimental data shows that the approach in question can be successfully used in the energy range from 10 to 100 MeV per nucleon. It is demonstrated that, for a preset potential, it is possible to find angular ranges dominated by specific patterns of scattering, such as classical or rainbow scattering and Fresnel or Fraunhofer diffraction.     

Pauli exchange effects in the elastic scattering of O + O

The real optical potential for ¹⁶O+¹⁶O system is calculated within a generalized version of the double-folding model with the Pauli knock-on exchange effects between the projectile nucleons and the target nucleons taken into account from first principle. The elastic scattering data at E_lab=350 MeV supplemented by the new measurement at larger angles seem to be the first case in heavy-ion scattering where one can test the reliability of different theoretical heavy-ion optical potentials. Predictions are made for the elastic scattering of ¹⁶O+¹⁶O at laboratory energies of 240–480 MeV to illustrare the energy dependence of the rainbow structure which has been clearly observed in experiment at 350 MeV.     

Nuclear-rainbow scattering and nucleus-nucleus potentials at short distances

The elastic scattering of strongly bound nuclei at energies of 10 to 70 MeV per nucleon shows the phenomenon of “rainbow scattering.” A nuclear rainbow appears because of deflection to negative angles. This process involves a strong overlap of nuclear densities, with values of up to twice the saturation density of nuclear matter. The ¹⁶O+¹⁶O system is studied with a high precision over a wide energy range from 7 to 70 MeV per nucleon in several laboratories. Primary Airy maxima and higher order Airy structures are observed. At all energies, excellent fits are obtained with deep potentials as deduced from the double-folding model involving a nucleon-nucleon interaction weakly dependent on the density. It is shown that Pauli blocking expected at low energies is strongly reduced if the local momenta are calculated self-consistently. Systematics confirms a refractive origin of large-angle scattering, at low energies inclusive. Thus, nuclear-rainbow scattering yields unique information about the properties of cold nuclear matter at higher densities.     

On the scattering properties of a weakly charged polymer gel

A phenomenological model is presented to describe weakly charged polymer gels based on the classical elasticity theory. The structure factor of the gel is calculated considering both thermal and frozen concentration fluctuations as well as the screened Coulomb interaction. In agreement with the recent experimental finding the result shows anomalous crosslink-density dependence of the scattering profiles. Received: 28 March 1997 / Revised: 4 September 1997 / Accepted: 23 October 1997     

A semiclassical approach to inelastic scattering from solid surfaces and to the Debye-Waller factor

A semiclassical formulation of inelastic atom-surface scattering is presented. This formulation is a mixture of classical S-matrix theory and a classical path model. A Debye-Waller factor enters this theory very naturally as the probability of elastic reflection in the presence of inelastic channels. Because of its importance the Debye-Waller factor is discussed in some detail. Finally, assuming a simplified model of the gas-surface system, the whole scattering problem is solved analytically.