Inelastic Diffraction Research Articles

Inelastic low energy electron diffraction at metal surfaces

The role of incident electrons penetration under a metal surface in electron energy loss spectroscopy is considered within the fully quantum-mechanical approach. The stabilized jellium model of the surface in the semi-infinite geometry and the time-dependent local density approximation for the dynamical response are used. The travel of the projectile electron inside the target metal is treated within the kinematic low energy electron diffraction theory. Confirming our simplified hard-wall reflection model results [Phys. Rev. B 59 (1999) 9866], the dramatic enhancement of the multipole plasmon peak as compared with the dipole-mode calculations is obtained for Na and Cs, which is in a qualitative agreement with the experiment. However, for K the calculation fails to explain the experiment, which discrepancy is discussed and the future improvements of the method are outlined.

High-pressure vessel for elastic and inelastic x-ray diffraction experiments for liquids over a wide temperature range

A new x-ray scattering environment is presented which can be employed at high temperatures up to 2000 K and high pressures up to 150 bar. This device is especially designed for angle-dispersive scattering experiments. It consists of a thick closed-end aluminum cylinder equipped with a steel flange. Incident and scattered radiation passes through continuous Be windows which cover an angle range up to 55°. The high potential of this scattering setup is demonstrated by representative example experiments at high temperatures and high pressures, which could be carried out in combination with a single-crystal sapphire cell. Inelastic-, elastic-, and anomalous scattering experiments using synchrotron radiation and energy dispersive static measurements employing a conventional tube device are reported.

固体表面での水素分子の回転励起を伴う回折現象

We investigate the rotationally inelastic diffraction (RID) of D2(H2) scattered from Cu(001) and discuss how isotope effects influence the RID probabilities of D2(H2) by performing First Principles Quantum Dynamics Calculations that include all six degrees of freedom of D2(H2) on a density functional theory based potential energy surface. We show that the RID probabilities initially increase with increasing incident energies due to the activated nature of D2(H2) dissociation on Cu(001), which qualitatively agree with recent experimental RID peaks measured for D2/Cu(001). Furthermore, comparing the RID probabilities of D2 and H2, we observe strong isotope effects. Due to the small threshold energy of D2 for rotational excitation and diffraction, as compared to H2, the RID probabilities of D2 are larger than those of H2 in the low incident energy region. With further increase in incident energies, however, the RID probabilities of D2 become smaller than those of H2. We explain these isotope effects on the RID by showing the wave functions of D2(H2) on Cu(001).

Color transparency in deeply inelastic diffraction

We suggest a simple physical picture for the diffractive parton distributions that appear in diffractive deeply inelastic scattering. In this picture, partons impinging on the proton can have any transverse separation, but only when the separation is small can they penetrate the proton without breaking it up. By comparing the predictions from this picture with the diffractive data from DESY HERA, we determine rough values for the small separations that dominate the diffraction process.

The effect of corrugation on the quantum dynamics of dissociative and diffractive scattering of H2 from Pt(111)

We present results of two dimensional (2D) and three dimensional (3D) calculations for dissociative and diffractive scattering of H2 from Pt(111), using a potential energy surface obtained from density functional theory (DFT) employing the generalized gradient approximation (GGA) in conjunction with a slab representation of the metal surface. The present study is motivated by the importance of Pt as a hydrogenation catalyst, and by a paradox regarding the amount of corrugation of the H2+Pt(111) potential energy surface (PES). Molecular beam experiments on dissociation of D2 from a Pt(111) surface suggest a rather corrugated PES, which is at odds with results from molecular beam experiments on rotationally inelastic diffraction of HD from Pt(111), where only very little diffraction is found, suggesting a weakly corrugated PES. Results of our 3D calculations for off-normal incidence show that the present 3D model does not obey normal energy scaling, and that parallel motion inhibits dissociation at low collision energies, in agreement with the dissociation experiment. On the other hand, substantial diffraction is found, where the diffraction experiment found almost none. For each impact site considered in the 2D calculations, the computed dynamical barrier height, E0, is substantially lower than the barrier height in the PES, Eb, at that site. Both the 2D and the 3D calculations show a large vibrational enhancement of reaction. These effects are not due to a reduced mass effect, the barrier to dissociation being early, but to a decrease in the force constant of the H2 vibration upon approaching the barrier to dissociative adsorption from the gas phase. The vibrational enhancement computed for H2+Pt(111) was not observed in seeded beam experiments on D2+Pt(111) [A. C. Luntz, J. K. Brown, and M. D. Williams, J. Chem. Phys. 93, 5240 (1990)]. However, an analysis performed here strongly suggests that seeded beam experiments will be unable to observe vibrational enhancement if the dissociation of the molecule in ν=0 proceeds without an energetic threshold, as is the case for H2+Pt(111).

Inelastic diffraction data and the effective [formula omitted]omeron trajectory

A further analysis of inelastic diffraction data at the ISR and SPS-Collider confirms the relatively flat s-independent P omeron trajectory in the high-| t| domain, 1<| t|<2 GeV 2, reported earlier by the UA8 Collaboration. At | t|=1.5 GeV 2, α=0.92±0.03 is in agreement with the trajectories found in diffractive photoproduction of vector mesons at HERA. This suggests a universal fixed P omeron trajectory at high-| t|. We also show that a triple-Regge P omeron-exchange parametrization fit to the data requires an s-dependent (effective) P omeron trajectory intercept, α(0), which decreases with increasing s, as expected from unitarization (multi- P omeron-exchange) calculations. α(0) = 1.10 at the lowest ISR energy, 1.03 at the SPS-Collider and perhaps smaller at the Tevatron.

How to study the elusive efimov state of the 4He3 molecule through a new atom-optical state-selection technique

Excited states and excitation energies of weakly bound systems, e.g., atomic few-body systems and clusters, are difficult to study experimentally. For this purpose we propose a new and very general atom-optical method which is based on inelastic diffraction from transmission gratings. The technique is applicable to the recently found helium trimer molecule 4He3, allowing for the first time an investigation of the possible existence of an excited trimer state and determination of its excitation energy. This would be of fundamental importance for the famous Efimov effect.

Magnetism of ternary alkali metal–transition metal chalcogenides with binuclear units

The compounds Na 3FeS 3, Na 3FeSe 3, K 3FeSe 3, Cs 3FeS 3 and Cs 3FeSe 3 are characterised by isolated binuclear double tetrahedra [Fe 2S 6] 6− or [Fe 2Se 6] 6−. The magnetic susceptibilities reveal the typical temperature dependence expected for antiferromagnetically coupled binuclear complexes. To characterise the magnetic properties by an independent method, inelastic neutron diffraction experiments have been carried out. Deviations from a Heisenberg level spacing reveal a biquadratic exchange term in the case of Na 3FeS 3 and Na 3FeSe 3.

Spin dependence of deep inelastic diffraction

Using a perturbative model for diffractive interactions, we derive an expression for the polarized diffractive structure function \(g_1^D\) in the high energy limit. This structure function is given by the interference of diffractive amplitudes with polarized and unpolarized exchanges. For the polarized exchange we consider both two-gluon and quark-antiquark amplitudes. The polarized diffractive amplitude receives sizable contributions from non-strongly ordered regions in phase space, resulting in a double logarithmic enhancement at small x. The resummation of these double logarithmic terms is outlined. We also discuss the transition from our perturbative expression to the nonperturbative region. A first numerical estimate indicates that the perturbative contribution to the spin asymmetry is substantially larger than the nonperturbative one.

Epitaxial growth of Fe(001) onCoSi2(001)/Si(001)surfaces: Structural and electronic properties

Ultrathin Fe films, in the thickness range 0\char21{}40 monolayers (ML), have been grown on Si(001) by molecular-beam epitaxy and characterized by low-energy electron diffraction, inelastic medium-energy electron diffraction, x-ray photoelectron spectroscopy, angular-resolved ultraviolet spectroscopy, x-ray photoelectron diffraction, ion scattering spectroscopy, and transmission electron microscopy. For Fe depositions onto Si(001) at room temperature, a disordered layer is obtained due to a high degree of intermixing between the Fe deposit and the Si substrate. Successful epitaxial growth of Fe at room temperature is achieved by use of a thin (\ensuremath{\sim}10 \AA{}) ${\mathrm{CoSi}}_{2}$ silicide interlayer epitaxially grown on the Si(001) substrate prior to the Fe deposition, which prevents the intermixing of the Si substrate atoms into the Fe overlayer. Below a coverage of \ensuremath{\sim}2 ML, a reacted ordered iron-rich phase forms at the surface. At higher coverages, there is growth of an epitaxial essentially body-centered cubic (bcc) Fe(001) overlayer with the orientational relationships $\mathrm{Fe}(001)\mathrm{〈}001\mathrm{〉}\ensuremath{\parallel}{\mathrm{CoSi}}_{2}(001)\mathrm{〈}001\mathrm{〉}\ensuremath{\parallel}\mathrm{Si}(001)\mathrm{〈}001\mathrm{〉}.$ Finally, a well-ordered ${\mathrm{F}\mathrm{e}/\mathrm{C}\mathrm{o}\mathrm{S}\mathrm{i}}_{2}$ interface is formed even at room temperature.

Inelastic Diffraction and Color-Singlet Gluon Clusters in High-Energy Hadron-Hadron and Lepton-Hadron Collisions

It is proposed that the ``colorless'' objects which manifest themselves in large-rapidity-gap events are color-singlet gluon clusters due to self-organized criticality (SOC), and that optical-geometrical concepts and methods are useful in examining the space-time properties of such objects. A simple analytical expression for the $t$ dependence of the inelastic single diffractive cross section $d\ensuremath{\sigma}/dt$ ( $t$ is the four-momentum transfer squared) is derived. Comparison with existing data and predictions for future experiments are presented. The main differences and similarities between the SOC approach and the ``partons in the Pomeron (Pomeron and Reggeon)'' approach are discussed.

Spin dependence of deep inelastic diffraction

Using a perturbative model for diffractive interactions, we derive an expression for the polarized diffractive structure function $g_1^D$ in the high energy limit. This structure function is given by the interference of diffractive amplitudes with polarized and unpolarized exchanges. For the polarized exchange we consider both two-gluon and quark-antiquark amplitudes. The polarized diffractive amplitude receives sizable contributions from non-strongly ordered regions in phase space, resulting in a double logarithmic enhancement at small $x$. The resummation of these double logarithmic terms is outlined. We also discuss the transition from our perturbative expression to the nonperturbative region. A first numerical estimate indicates that the perturbative contribution to the spin asymmetry is substantially larger than the nonperturbative one.

Spin structure in deep inelastic diffraction

Spin structure in deep inelastic diffraction

Inelastic diffraction in coadsorbed periodic structures

We show for the first time that, with two coadsorbed periodic structures it is possible to observe in a diffraction condition unique to one structure a relative enhancement of the vibrational losses characteristic of the species contained in the respective periodic structure. A recently developed SPA-LEED instrument equipped with an electron monochromator and analyser was used to distinguish true elastic diffraction from inelastic diffraction in the vibrational losses of coadsorbed (2×3)N/Cu(110) and the α-phase benzoate 4 3 −1 5 structure on Cu(110). Vibrational enhancements by factors of 4–20 were found in energy loss spectra and momentum-resolved spot profiles. Inelastic spot profiles are qualitatively consistent with a kinematic description of the energy–momentum conservation induced broadening from both loss-before-diffraction (L-D) and diffraction-before-loss (D-L) events.

Diffraction and rotational transitions in the scattering of D2 from Cu(001) at energies up to 250 meV

Absolute diffraction probabilities for the scattering of D2 from a clean Cu(001) surface along the [100] azimuth have been measured at incident kinetic energies between 20 and 250 meV. The measured attenuation of the diffraction intensities with surface temperature corresponds to a surface Debye temperature of ΘD=341 K. The high-resolution angular distributions show clear evidence of rotationally inelastic diffraction (RID) peaks. The RID probability increases with incident energy and represents as much as 30% of the elastic diffraction probability at energies above Ei=200 meV. An Eikonal approximation analysis gives a value h=0.075 Å for the surface corrugation which is independent of incident energy. The rotational transition probabilities correspond to an effective value of δ=0.3 for the molecular eccentricity. The experimental results indicate that diffraction of D2 from Cu(001) can be accounted for by a hard-wall collision mechanism over the whole range of investigated energies.

Inelastic focusing effects in atom-surface scattering

An inelastic focusing mechanism has been identified in the angular distributions of helium atoms scattered from single-crystal NaCl~001! surfaces as being due to energy exchange with a Rayleigh phonon mode. This effect, called inelastic focusing, occurs under special conditions in which the small spread of energies in the incident beam is sharply focused into a very narrow range of final angles. For a fixed initial scattering angle this is mathematically described as a singularity associated with the density of states in the incident momentum as a function of final scattering angle. This effect is an intrinsic feature of any scattering event of particles from surfaces and could be used to greatly enhance the intensity of weak single-phonon features in inelastic timeof-flight spectra. @S0163-1829~98!50416-X# The scattering of atoms and molecules from single-crystal surfaces has provided a wealth of information both on the physical properties of surfaces 1 and also on the interactions of the particles with the surface. Initially, most experiments concentrated on diffraction studies of the surface structure, but during the last two decades, the development of highintensity nearly monoenergetic helium-atom beams has provided sufficiently high intensities so that dynamical features of the surface such as phonon dispersion curves could also be explored. 2 In the ensuing period many of the unexpected features observed in these measurements 2‐6 were explained in terms of selective adsorption resonances, both elastic and those involving phonons, as well as kinematic focusing. 7 More recently, focused inelastic resonance ~FIR !~ Refs. 8 and 9! and diffuse elastic 10 resonance ~DER! effects have also been identified as causing distinct features in heliumatom scattering experiments. Since the interaction potential between He atoms and the NaCl~001! surface is reasonably well known, 9‐11 many of these new resonance mechanisms and focusing phenomena have first been studied on this surface. In parallel with experiments, the theory of atom-surface scattering has also undergone significant development. However, the energy resolution of the incident He-atom beam has usually been considered to have no substantial effect on the distribution of the scattering intensity. Thus, for example, in the calculations of the differential reflection coefficients for elastic and inelastic scattering the incident beam of the He atoms is usually considered to be sharp in both energy and angles, i.e., the finite energetic width of the incident beam is neglected and it is usually represented by a well-defined plane wave. In practice, this would appear to be justified since in most He-atom scattering experiments the energy resolution is usually as small as DEi /Ei’2%. If the finite angular width of the incident beam is included in the calculations several singularities appear that strongly modify the final scattering intensity. One of these new singularities, the inelastic focusing ~IF! singularity discussed here, was observed previously in the rotationally inelastic diffraction of molecular beams of H2 and its isotopes from single crystals of MgO~001 !~ Ref. 12! as well as in the inelastic scattering of D2 from NaF~001!. 13 In this communication, experimental evidence for the atomic IF effect in the scattering of He from NaCl~001! is presented. Moreover, in atomic scattering from other surfaces such as, for example, He/LiF~001!, 6 certain features were previously observed that can now be attributed to IF. In this work, the IF singularity is reexamined and found to have more far-reaching physical implications than previously envisaged. We note that the IF is a quite distinct effect from the previously investigated FIR ~Ref. 9! and DER ~Ref. 10! resonances. Both FIR and DER involve a resonant transition through a bound state of the interaction potential, whereas the IF is a kinematic enhancement of any selected inelastic feature and does not require the presence of a bound state. To experimentally demonstrate the IF singularity, highresolution helium-atom scattering experiments were carried on the well-studied NaCl~001! surface. In the scattering apparatus, which has been described in detail previously, 14 a nearly monoenergetic helium-atom beam (DEi /Ei<2%) is scattered through a fixed angle of 90° between source and detector in a plane perpendicular to the crystal surface. The parallel wave-vector transfer DK is changed by rotating the crystal and is given by 15

Geometrical correction to plasmon effects in energy-filtered RHEED spectra

We investigate a recent experimental study of Si(111)7 × 7 using energy-filtered reflection high energy electron diffraction (EF-RHEED). Using a simple single scattering model incorporating both surface and bulk plasmons we consider the relative intensities of the diffraction peaks of the corresponding specular and 11 rocking curves as a function of energy-loss of the reflected electrons. At its simplest level, the model predicts the inelastic EF-RHEED rocking curves will scale with their elastic counterpart approximately as the inverse of the incident angle in the specular case, and as a sum of the inverses of the incident angle and reflecting angle in the non-specular case. This is found to work remarkably well for Si(111)7 × 7 for small energy losses (<20−30 eV), becoming progressively worse at higher energy-loss windows due to the inclusion of multiple plasmon creation. The exceptions to this are those specular and non-specular diffraction peaks that satisfy the emergence condition of higher-order beams. In these cases, the inelastic diffraction peaks concur more closely with their elastic counterparts, demonstrating a dominant coupling between these modes.

Inelastic Scattering and Interference

Abstract Recently it has been a matter of controversy whether inelastically scattered electrons can yield interference fringes so as to obtain holograms, and in particular whether compensation of energy loss in the object by energy gain in the source will maintain coherence [1]. In discussions about coherence (and wave mechanisms in general) it is always dangerous to rely on intuitive arguments (exchange of energy, time of interaction, etc.). In this work we will start from the most general approach, which is inspired by the treatment of inelastic electron diffraction crystals by Yoshioka in 1957 [2]. Energy exchanges are always described quantummechanically by an Hamiltonian. Therefore we can only investigate the balance between energy exchange properly if electron, object, and source are described by one global Hamiltonian. With source we mean the whole electron generating system (emitter, accelerator, condensor). Consider a global system consisting of an electron, with position vector r, an object with particle vectors ri, and a source with particles at rα.

A model for slope-mass correlation in nuclear diffraction dissociation

The increase of the slope of nuclear diffraction with the dissociated mass is described by a model of multiple incoherent inelastic diffraction of nucleons. The results obtained are in good agreement compared with experimental data.

The effect of dissociative chemisorption on the diffraction of D2 from Ni(110)

Absolute scattering probabilities of nearly monoenergetic D2 and He beams are compared for the highly reactive clean Ni(110) surface at a surface temperature Ts=700 K along the more corrugated [001] direction. At incident energies between 20 and 110 meV the total reflectivity of D2 is about a factor 200 smaller than for He, whereas the first order diffraction intensities relative to the specular peak are a factor 7 larger. The D2 angular distributions also show clear evidence of rotationally inelastic diffraction peaks. The diffraction intensities of both He and D2 can be accounted for by a conventional hard wall model with reasonable values of the corrugation amplitudes of 0.060 Å for He and 0.091 Å for D2 without including a lateral variation in the probability for chemisorption. The reflectivity results when extrapolated to Ts=0 indicate that for He only 33% of the incident atoms are coherently reflected. For D2 only 9% are coherently scattered and approximately 24% are chemisorbed. The coherently scattered fraction is attributed to D2 molecules with orientations not sufficiently parallel to the surface plane to permit chemisorption to occur.