Calculation of inelastic helium atom scattering from H2/NaCl(001)

The one-phonon inelastic low energy helium atom scattering theory is adapted to cases where the target monolayer is a p(1 × 1) commensurate square lattice. Experimental data for para-H(2)/NaCl(001) are re-analyzed and the relative intensities of energy loss peaks in the range 6 to 9 meV are determined. The case of the H(2)/NaCl(001) monolayer for 26 meV scattering energy is computationally challenging and difficult because it has a much more corrugated surface than those in the previous applications for triangular lattices. This requires a large number of coupled channels for convergence in the wave-packet-scattering calculation and a long series of Fourier amplitudes to represent the helium-target potential energy surface. A modified series is constructed in which a truncated Fourier expansion of the potential is constrained to give the exact value of the potential at some key points and which mimics the potential with fewer Fourier amplitudes. The shear horizontal phonon mode is again accessed by the helium scattering for small misalignment of the scattering plane relative to symmetry axes of the monolayer. For 1° misalignment, the calculated intensity of the longitudinal acoustic phonon mode frequently is higher than that of the shear horizontal phonon mode in contrast to what was found at scattering energies near 10 meV for triangular lattices of Ar, Kr, and Xe on Pt(111).     

Direct calculation of resonant states in reactive scattering. Application to linear triatomic systems

A direct method for calculating resonant states in reactive scattering is suggested, permitting us to obtain the characteristics of multichannel resonances (partial width amplitudes). The method is based on the construction of a Laurent expansion of the scattering matrix S(? ?iΓ/2) in the complex plane. The position of the poles of the S matrix are derived by solving the dynamical problem with complex energy values. The residue at the pole gives all the information concerning the partial widths. The method is applied to a linear triatomic reactive scattering problem. The properties of the resonant states in the H + H₂ system are calculated as an example. Two broad resonances are found which have not been reported in previous calculations. The interference of overlapping resonances is shown to have a profound effect on the energy dependence of the transition probabilities.     

Proton and antiproton impact ionization of atomic hydrogen and helium

Single ionization of helium and atomic hydrogen by the impact of protons and antiprotons is considered. Using a multiple scattering model, first proposed by Garibotti and Miraglia [1], angular and energy distributions of the ejected electrons are calculated. Structures arising in the cross section, especially the Coulomb density of states effect (CDS), are analysed. The contributions of various scattering amplitudes to the cross section are studied. It is concluded that multiple scattering together with the CDS-effect play an important role in determining the transition amplitude. Differences between particle and antiparticle impact are examined. In addition to the different behaviour of the CDS-effect, the interference of two scattering amplitudes turns out to be decisive in ionization by particle and antiparticle impact.     

Volterra inverse scattering series method for one‐dimensional quantum barrier scattering

The Volterra inverse scattering series method is developed to obtain the interaction potential for one‐dimensional quantum barrier scattering problems. The Lippmann–Schwinger equation describing quantum barrier scattering is renormalized from a Fredholm to a Volterra integral equation. Employing the Born–Neumann series solution of the Lippmann–Schwinger Volterra equation and a related expansion of the interaction potential in orders of the data, we derive the Volterra inverse scattering series for the reflection and transmission amplitudes. Each term of the interaction potential is computed using the scattering amplitude and the Volterra Green's function. We do not consider the separate issue of extracting scattering amplitudes from quantum cross sections. The triangular nature of the Volterra Green's function significantly reduces computational effort. The Volterra series is then applied to several one‐dimensional quantum barrier scattering problems. Computational results show that the first few terms in the Volterra series can yield accurate interaction barriers. In addition, the potential barriers are calculated using the Born inverse scattering series based on the Lippmann–Schwinger Fredholm equation with the reflection amplitude. The comparison between the Born and Volterra results demonstrates that the Volterra inverse scattering series can provide a more accurate and more efficient method for determining the interaction potential.     

Effects of memory on the coherent scattering function for the rouse–zimm model of dilute polymer solutions

We study the effect of the memory function on the coherent scattering function of a dilute polymer solution, taking into account hydrodynamic interactions among the polymer segments. The line shape, given by a sum of two exponentials, is very accurate numerically for ka ? 3 (with a the length of a polymer segment) and for times such that ω₀(k)t ? 1.5 [with ω₀(k) the initial slope]. However, this approximation to the scattering function is not nearly so accurate at the smaller values of ka encountered in light scattering experiments. The amplitudes and relaxation times associated with the two exponentials are found to be markedly dependent on the strength of the hydrodynamic interactions.     

Structure-parameter and force-field refinement for lead dihalide molecules

Conclusions It has been shown for PbF₂ that one can process electron-diffraction data for molecules containing heavy atoms on the basis of atomic scattering amplitudes calculated with a relativistic approximation for the atomic electron density. The errors in calculating the atomicscattering amplitudes explain the previous discrepancies in the observed values for the Pb-Cl amplitudes in PbCl₂ derived in two independent researches. The differences between those values are now not so considerable, and they may be explained as due to experimental error or to the processing of the measurements in Hungary for most of the scattering angles having been performed without the relativistic corrections to the electron density.Our mean-square vibration amplitudes and the measured frequencies can be used with our semiempirical relationships for the force constants to determine the potential-energy parameters for those molecules and to estimate the vibrational frequencies for PbI₂, which have not been measured.I am indebted to Professor V. P. Spiridonov and staff at the vapor electron-diffraction laboratory at Moscow University for providing the observed values for the reduced molecular component of the scattering intensities for lead dihalides and for valuable comments in discussion on the draft.High-Temperature Institute, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 1, pp. 54–59, January–February, 1991.     

Simulation of scattering and phase behavior around the isotropic-nematic transition of discotic particles

The detailed study of the isotropic-nematic phase transition in a system of discotic particles of aspect ratios L/D≤0.1 presented here is relevant to a broad range of colloidal suspensions of chemically modified clay particles. Using Monte Carlo simulation techniques the equation of state, radial distribution functions, structure factors and normalized scattering intensities are calculated for each phase. The results are interpreted and related to previously reported free energy calculations [Fartaria and Sweatman, Chem. Phys. Lett. 478 (2009) 150], suggesting a nearly continuous isotropic-nematic transition for lower aspect ratios. Given this behavior we examined the structural information for each phase to determine how experimental scattering data might be used to distinguish the two phases. The radial distribution functions in each phase depend strongly on aspect ratio, and for larger aspect ratios a dramatic increase in the local ordering of discotic particles (represented here as cut-spheres) is observed just before the phase transition. However, this nearest-neighbor ordering seen in g(r) around r/D=0.1 would hardly be discernible in experimental scattering data subject to usual statistical errors. The structure factors and scattering intensities were calculated for L/D=0.1, 0.04 and 0.01 for the isotropic and nematic phases at and away from the isotropic-nematic transition. While the isotropic-nematic phase transition can be detected from the height and shape of the first scattering peak around 7QD for larger aspect ratios, this feature becomes much less discriminatory with decreasing aspect ratio. Instead, scattering intensities at low scattering vector amplitudes (Q→0) can be used for detection of the phase transition at low aspect ratios. These results provide useful insight to guide interpretation of X-ray and light scattering measurements for colloidal dispersions of thin platelets undergoing isotropic-nematic transitions.     

The average hamiltonian view of low-energy scattering by a vibrating molecule

The average hamiltonian theory is used to examine the effect of molecular vibration on low-energy scattering. When the relative motion of the colliding molecules is slow on the timescale of molecular vibration, it is appropriate to transform the problem into an oscillating reference frame and to describe the collision in that frame by the average hamiltonian over one period of oscillation. The first-order result is identical to the distorted-wave Born approximation. High-order corrections introduce phase shifts for elastic scattering due to molecular vibration and provide transition amplitudes for inelastic scattering. The extent to which the higher-order corrections modify the distorted waves establishes criteria for the validity of the DWA. These criteria are used to examine recent distorted-wave calculations of V-V energy transfer rate constants.     

Relativistic calculation of Stokes' parameters for intermediate energy electron impact excitation of cesium atoms

The integrated and differential Stokes' parameters of the light emitted in the decay 6p ² P _1/2,3/2→6s ² S _1/2 fore-Cs scattering in the intermediate energy range are presented. These have been calculated using scattering amplitudes obtained by a relativistic distorted-wave method.     

Collisionally damped ion motion in ICR spectrometry

A Schrödinger equation equivalent to the Langevin equation of ion motion in ICR cells is presented. A wave function for the scattering states has been found as the solution to the equation of ion motion under the influence of electric and magnetic fields perturbed by a scattering potential. Applying the minimized wave packet as a wave function describing coherent states, the scattering amplitudes are determined explicitly. The connection between the collision cross section and the scattering amplitudes is found by making use of the incoming and outgoing particle flux density. The collision cross section found in this way is converted from quantum theory to classical physics. The collision cross section, which plays an essential role in the determination of rate constants can be determined by the aid of ICR experimental data if the contribution of an alternating electric field is taken into account.     

Molecular dynamics,root-mean-square amplitudes,statistical thermodynamics,and molecular polarizability for the isotopic species of dioxygen monofluoride

A brief survey of vibrational spectral studies for the four isotopic species of dioxygen monofluoride has been made. On the basis of group theoretical considerations, symmetry coordinates have been constructed and kinetic energy matrices (orG matrix elements), potential energy matrices, and secular equations have been derived to calculate the valence force constants. The mean-square amplitudes and root-mean-square amplitudes for both the bonded and nonbonded atom pairs have been calculated at the room temperature. On the basis of a rigid rotator and harmonic oscillator model, enthalpy function, free enthalpy function, entropy, and heat capacity have been calculated from 200 to 2000 °K for all the four isotopic species. On the basis of a delta-function potential model based on the variational method and delta-function electronic wave functions, the bond parallel components, the bond perpendicular components, the contribution by the nonbonding electrons, and the average molecular polarizability have been calculated. The results obtained from these studies clearly confirm a double bond character for the oxygen—oxygen distance and a bond order of less than one-half for the oxygen—fluorine distance. The results have been discussed in relation to the nature of the two characteristic bonds involved in this molecular system.     

Influence de la non stoechiométrie sur les modes de vibration,les amplitudes vibrationnelles,et les intensités infra-rouge dans les alumines β

The normal coordinate analysis of nonstoichiometric β-alumina containing cations such as Na⁺, K⁺, Tl⁺, or Ag⁺ with different nonstoichiometric models (Frenkel defect associated with various cation distribution in the conducting plane) is reported. Mean square amplitudes and infrared intensities have been estimated on the basis of normal mode calculations for sodium β-alumina (stoichiometric and nonstoichiometric). The results obtained are in good agreement with experimental data. The spectral modifications that have been observed can be explained by splitting of degenerate levels and modification of selection rules due to the loss of local symmetry induced by the Frenkel defect. The good agreement between the in-plane (a, b) vibrational calculated frequencies of interstitial oxygen (O_i) and Raman or neutron scattering data shows that the compensating oxygen is tightly bounded to the spinel blocks. The difference between the calculated and crystallographic mean square amplitudes can be explained in terms of the static deviation of the bridging oxygen (O(5)) of 0.1 Å (at 300 K) from its ideal site.     

Fundamentals of tandem mass spectrometry: a dynamics study of simple C−C bond cleavage in collision-activated dissociation of polyatomic ions at low energy

The loss of methyl radical in collision-activated dissociation (CAD) of acetone and propane molecular ions has been studied at low energy using a tandem hybrid mass spectrometer. Although the two processes are very similar chemically and energetically, very different dynamical features are observed. Acetyl ions from acetone ion are predominantly backward-scattered, with intensity maxima lying inside and outside the elastic scattering circle, confirming our previous observation that electronically excited states are important in low-energy acetone CAD. Ethyl ions from propane ion show a forward-scattered peak maximum at a nonzero scattering angle, which is consistent with generally accepted models for vibrational excitation and redistribution of energy before dissociation. Both processes demonstrate that CAD at low energy proceeds via small-impact-parameter collisions with momentum transfer. Comparison of the present results with higher energy CAD dynamics studies and earlier work leads to some tentative general conclusions about energy transfer in these processes.     

Identification of intermediate species in protein-folding by quantitative analysis of amplitudes in time-domain fluorescence spectroscopy

In protein-folding studies it is often required to differentiate a system with only two-states, namely the native (N) and unfolded (U) forms of the protein present at any condition of the solvent, from a situation wherein intermediate state(s) could also be present. This differentiation of a two-state from a multi-state structural transition is non-trivial when studied by the several steady-state spectroscopic methods that are popular in protein-folding studies. In contrast to the steady-state methods, time-resolved fluorescence has the capability to reveal the presence of heterogeneity of structural forms due to the ‘fingerprint’ nature of fluorescence lifetimes of various forms. In this work, we establish this method by quantitative analysis of amplitudes associated with fluorescence lifetimes in multiexponential decays. First, we show that we can estimate, accurately, the relative population of species from two-component mixtures of non-interacting molecules such as fluorescent dyes, peptides and proteins. Subsequently, we demonstrate, by analysing the amplitudes of fluorescence lifetimes which are controlled by fluorescence resonance energy transfer (FRET), that the equilibrium folding-unfolding transition of the small single-domain protein barstar is not a two-step process.     

Structural and vibrational properties of vanadium (III) oxofluoride and oxochloride—a theoretical study

The potential energy surfaces of FVO and ClVO are studied using the density functional theory. It is found that the potential energy surface of both molecules is dominated by triplet states. Several singlet states are found close in energy, though. A good agreement is found between experimental and calculated vibrational frequencies except for the V–F stretching mode, which is predicted to be too low by the present results. The frequencies corresponding to the O–V–X bending mode are provided as a guide for future experimental studies. An estimation of the force constants, mean amplitudes of vibration, and thermodynamic functions is performed, too, in order to get a deeper insight into the bond properties of the title molecules.     

Quantum tunneling in an exactly solvable double-barrier potential: barrier transmission near the zero energy

The one-dimensional wave equation is solved in the presence of a symmetric double-barrier potential. An exact, analytical solution is obtained for the scattering states. The transmission and reflection amplitudes are calculated using the method of logarithmic derivative of the exact wave function. In the case of double-barrier potentials, perfect transmission (or zero reflectivity) at zero kinetic energy is non-intuitive. This phenomenon has been revealed and called the “threshold anomaly” in the previous investigations. Here we show that it is a critical phenomenon provided that the inter-barrier distance satisfies a resonance condition. When the resonance condition is fulfilled, the perfect transmission occurs at any energy, including the zero one.     

Field-theoretical approach to vibrational excitation in atom—diatom collinear collisions

The field-theoretical atom—diatom scattering equations of Csanak have been tested numerically, assuming a collinear collision model, with an exponential repulsive interaction potential and with a harmonic oscillator approximation for the molecule. Dyson's equation, in its integral form, has been solved obtaining orbitals representing the elastic scattering of an atom off the target and these Dyson's orbitals have been used to evaluate a matrix element containing a transition potential. This has been obtained by approximating Bethe—Salpeter's equation and yields directly the transition amplitudes for inelastic scattering. The results for single and multiple-jumps compare favourably with the exact values of Secrest and Johnson, and refinements of the model are suggested for further improvements.     

Frequency distribution of radiation emitted from excited atomic systems

General expressions for the time-dependent probability amplitudes of the quantum states of two arbitrary, interacting atoms are calculated when one atom is initially in an excited p state and the other atom is in an s ground state. The lifetimes of the excited states and the line shape of the emitted radiation are obtained as functions of both the atomic separation and the energy difference between the excited states of the two atoms. The emission line shape is shown to be doubly peaked and to agree with the line shape of the radiation scattered by a system of two interacting atoms. The expressions for the lifetimes of the excited states are found to be identical to those obtained for the radiation scattering situation.     

Angle‐dependent light scattering by highly uniform colloidal rod‐shaped microparticles: Experiment and simulation

While extensive theoretical work has been devoted to analyzing scattering behavior for nonspherical particles, few experimental studies of the light‐scattering properties of such particles are available, largely because of the difficulty of synthesizing such particles with uniform geometries. Here we report the synthesis of highly uniform, volume‐equivalent rod‐shaped colloidal particles prepared from their commercial spherical counterparts, on which we performed light scattering experiments as a function of scattering angle for micro rods with varying aspect ratio and volume. These results were compared to values calculated using the T‐Matrix method. Good agreement with theoretical predictions was found for the experimentally measured scattering cross sections and the angular dependence of the scattering intensity. An increase in the forward scattering intensity is observed and predicted for particles with larger aspect ratios relative to their volume equivalent spheres, with only minor differences observed at both mid‐range and backscattering angles. Furthermore, the light scattering results for the rod‐shaped particles did not show the scattering fringes seen in scattering by the spheres, indicating that as three‐dimensional symmetry is broken, the associated Lorenz–Mie resonances are strongly attenuated. This observation also was predicted by theory. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1889–1895     

Hyperthermal Ar atom scattering from a C(0001) surface

Experiments and simulations on the scattering of hyperthermal Ar from a C(0001) surface have been conducted. Measurements of the energy and angular distributions of the scattered Ar flux were made over a range of incident angles, incident energies (2.8-14.1 eV), and surface temperatures (150-700 K). In all cases, the scattering is concentrated in a narrow superspecular peak, with significant energy exchange with the surface. The simulations closely reproduce the experimental observations. Unlike recent experiments on hyperthermal Xe scattering from graphite [Watanabe et al., Eur. Phys. J. D 38, 103 (2006)], the angular dependence of the energy loss is not approximated by the hard cubes model. The simulations are used to investigate why parallel momentum conservation describes Xe scattering, but not Ar scattering, from the surface of graphite. These studies extend our knowledge of gas-surface collisional energy transfer in the hyperthermal regime, and also demonstrate the importance of performing realistic numerical simulations for modeling such encounters.