Multiple collisions in molecular beam scattering experiments

Due to the forward peaked differential cross section for elastic atom—atom scattering the effect of multiple collisions has to be considered in the analysis of crossed beam measurements of the total cross section and especially of the small angle differential cross section at large values of the beam attenuation. At angles θ ≈ θ₀, with θ₀ the quantum mechanical scaling angle of the elastic differential cross section, the correction for the latter case amounts to 20% at beam attenuations I/I₀ = exp(?1). Firstly, a careful analysis of the probabilities for single and multiple scattering is given, resulting in an expression for the measured beam signals which is correct for all values of the beam attenuation. The probability for multiple scattering is then calculated for an inverse power potential V(r) = ?C_sr^?s, with s = 4 through s = 7, which include both the case of ion—atom scattering (s = 4) and atom—atom scattering (s = 6). The results are given as effective differential cross sections σ_n(θ) for n-fold scattering. They are described by a single, simple analytical function with four free parameters that have been determined for n = 2, 3 and 4 by a least squares method. The σ_n(θ) are normalised to the total cross section Q.     

A one-dimensional kalman filter for peak resolution

A one-dimensional Kalman filter algorithm is presented that resolves several overlapped liquid chromatographic peaks without algebraic operations of matrices. The resolving powers or filtering reliability of the algorithm is independent of the number of peaks, but depends on both the peak overlap (resolution value R_s) and the signal-to-noise ratio more significantly than the usual multi-dimensional Kalman filter. The reliability is shown to be similar to that of the multi-dimensional filter for the resolution of overlapped Gaussian peaks with limited R_s and S/N values.     

The convective model of cross-flow microfiltration is not inconsistent

The approximate analytical equations of the convective model and of the model of Romero and Davis are compared. Introducing the approximations used by Romero and Davis in the convective model gives the same functional dependence of the average filtration flux, 〈ν〉, on particle radius and solute volume fraction and a different dependence on the shear rate, γ_s. The convective model gives an explicit dependence of 〈ν〉 on transmembrane pressure and non-Newtonian ‘apparent’ viscosity of the cake. It is shown that the pseudoplastic rheological behaviour of concentrated colloidal solutions (cakes) rationalizes the experimentally established dependence 〈nu;〉 ∼ γ^m_s with 0.4 < m < 1.5.     

Charge cloud orientation in excitation or deexcitation of Na* (3p) in Na-He collisions

The direct excitation and deexcitation probabilities of Na(3p) are calculated in an 8-state model using the Projected Valence Bond potential energies of NaHe, the impact parameter method is used in the 0.5 keV<E _CM<100 keV energy range. A 3-state model predicts propensity rules which are confirmed by the present more elaborate model in the energy range of the maximum of the 3s–3p transition, but a discrepancy attributed to ionisation of Na occurs at energies beyond the excitation probability maximum (E _CM>2 keV).     

A quantized approach to space-time

Some consequences are traced of a simple approach to the concept of a quantized relativistic space-time. It is assumed that the basic unit of space-time s₀ depends on the rest-mass of the individual particle m₀ and that the location in space-time of the particle cannot be defined more closely than s₀, where s₀ equals h/m₀ic in space coordinates or h/m₀c² in time coordinates. This leads to the same expressions for the uncertainty in space and time, the de Broglie wavelength, basic frequency and energy levels, and phase velocity as in conventional quantum theory but without the need to introduce a physically significant wave function. This avoids the difficulty in accepting a probability explanation for the wave function and the apparently contradictory wave and particle concepts when dealing with interference and detection from large volumes at very low intensities as well as a possible inversion of cause and effect.Interference appears as the segregation of beams into different units of space-time, each with its own selection of quantum numbers n_i of units s₀ along the four axes but with the same total Σn_i. The different beams correspond merely to a (quantized) change of axes.This approach is compared with that involved in the Schrodinger equation, which leads to an extensive wave function, and this must then be “reduced” by an observation or measurement to establish a localized particle. Prior to such a measurement, the nature of the particle, spread in some sense over the wave function raises questions of reality in unobserved objects. No such problems of reality need arise with the concept of quantized space-time, and the observer intervenes only by choosing the framework axes.     

Scattering experiments with hydrogen atoms: Velocity dependence of the integral total cross section with simple molecules in the energy range 0.01–1.00 eV (c.m.)

Integral total cross sections for hydrogen atoms scattered by H₂, D₂, N₂, CO, NO, O₂, CO₂, C₂H₂ have been measured for H atom velocities in the range 1.2 to 13.4 × 10⁵ cm s^?1 (0.007 ? E_c.m. ? 0.94 eV). The data have been fitted to a Lennard-Jones (12,6) model potential for which the product of the potential well parameters, ?R_m, was determined (? is the well depth and R_m the location of the potential minimum). Separate values for ? and R_m are estimated using a combination rule procedure tested in earlier work on fi— rare gas scattering.     

Selectivity of electron capture probabilities on the initial state magnetic quantum numbers in ion-atom collisions

Close-coupling calculations have been carried out for ion-atom collisions to show that electron capture probabilities depend strongly on the magnetic quantum number of the initial target state ifthe quantization axis is chosen to be perpendicular to the scattering plane. In thenatural frame of reference, the probability for electron capture is largest form _i=?l substates and decreases rapidly with increasingm _i. This propensity rule is the result of the rotation of the electron cloud following the rotation of the internuclear axis during the collision.     

Polarization in elastic scattering: close-coupling studies on ArN2

We present the results of close-coupling calculations of m_j-dependent differential and integral cross sections forj₁ = 2 → j₂ = 2 rotationally elastic ArN₂ collisions. Two potential surfaces were used with differing long-and short-range anisotropies. If the anisotropy is long-ranged the scattering of an isotropic beam results in a significant angle dependent polarization of the elastically scattered products. To a certain extent this reflects a selective loss of m_j-state population due to rotationally inelastic transitions. For quantization along the initial relative velocity vector or perpendicular to the scattering plane, the depolarization of an initially m_j-state selected beam vanishes in the forward direction and is significantly less than the statistical limit at all angles, which indicates a dynamical conservation of the direction of the molecular rotational angular momentum. By contrast, in the helicity frame depolarization is much more pronounced. The oscillatory structure present in the rotationally inelastic differential cross section does not appear to be quenched by the interference between various m → m′ transitions.     

Small-angle x-ray scattering of semicrystalline polymers. I. Review of existing models

The effect of previously proposed distributions of particle size and interparticle “gap” lengths on the small-angle x-ray scattering of a paracrystalline one-dimensional macrolattice has been examined. It was concluded that the general paracrystalline model, in which the fluctuations of crystalline and amorphous thickness both contribute to the destruction of long-range order, best describes the structure of lamellar aggregates in semicrystalline polymers. By using this model, the influence of symmetric and asymmetric lattice statistics on the positions of the scattering maxima were investigated. It was found that positively skewed thickness distributions result in the second-order maximum occurring at an angle greater than twice that of the first-order maximum (sx?₂/sx?₁ > 2.0); the position of the first-order maximum is generally greater than the Bragg angle of the structure. With negatively skewed distributions, the ratio of the scattering angles, sx?₂/sx?₁, is less than 2.0, and the first maximum is displaced below the Bragg angle. Qualitatively similar behavior is found with lattices characterized by symmetric lattice statistics, though these deviations from the Bragg conditions are smaller than in the case of negatively skewed distributions. The ratio of the scattering angles of the second and first maxima best reflects the general shape of the lattice statistics in a paracrystalline lattice. The effect of a transition zone, having properties intermediate between those of the crystalline and amorphous regions, was also considered. While the intensity of the higher-order maxima is decreased, no significant shift of the scattering angles results from the incorporation of such a transition zone.     

An optically pumped,highly polarized cesium beam for the study of spin-dependent electron scattering

We have set up an atomic beam of cesium for the study of spin-dependent electron-cesium scattering. The beam is produced by an effusive oven with continuous recirculation of the condensed metal. The beam is optically pumped by circularly polarized light from two laser diodes tuned to the 6² S _1/2(F=3)→6² P _3/2(F′=4) and 6² S _1/2(F=4)→6² P _3/2(F′=5) transitions, respectively. Nearly all atoms are transferred into theF=4,m _F =+4 orm _F =?4 Zeeman level of the ground state, depending on the sense of circular polarization of the pumping light. The population distribution in the optically pumped beam is analyzed in terms of them _J =?1/2 andm _J =+1/2 components with a Stern-Gerlach magnet. We find the atomic polarization to be very close to unity at a density of 8×10⁸ atoms/cm³ in the scattering center. The polarization decreases slightly with increasing density of the cesium beam due to radiation trapping. A spin flipper serves as a means of polarization reversal, introducing no systematic errors in the spin asymmetry measurements. Lock-in technique is used to stabilize the atomic beam polarization by detecting fluorescence light signals.     

A topotactic tailored synthesis of waxberry-like mixed-phase TiO2 hollow spheres for dye-sensitized solar cells

The waxberry-like mixed-phase Ti O₂hollow microstructures （WMTHMs） are controllably prepared via a topotactic synthetic method,involving the synthesis of monodispersed Ca Ti O₃precursors by a solvothermal method and subsequently transforming them into Ti O₂through a Na₂EDTA-assisted ion-exchange process.The ratio of anatase-rutile is adjustable,and the two phases are connected well with each other.WMTHMs are composed of radially aligned nanorods,speedi...     

Computer simulation of the atomic structure of regenerated cellulose

The atomic structure of amorphous sulfate hardwood pulp obtained via regeneration in a dimethyl acetamide–LiCl solution is studied with the use of X-ray diffraction and computer simulation. When dimethyl acetamide appears within a cellulose chain, it becomes swollen. A chosen cluster has a complex structure and contains two cellulose chains II distorted by twisting and bending and two chains deformed by dimethyl acetamide molecules. A cluster with the formula unit (C₆O₅H_8.5Li_1.5) ? (H₂O)_2.8 is obtained after relaxation with the addition of water. The uncertainty-profile factor for the model and experimental curves of X-ray scattering intensity distribution I(s) is 8%, and the distribution curve of s-weighted interference function H(s) calculated for the model best fits the experimental curve.     

Cytochrome c embraced in sodium dodecyl sulfate nano-micelle as a homogeneous nanostructured peroxidase

A homogeneous nanostructured enzyme (artificial peroxidase, AP) with suitable catalytic efficiency was generated using bovine heart cytochrome c (Cyt c) and sodium dodecyl sulfate nano-micelles in 50?mM phosphate buffer pH 10.5 at 25?°C. The Michaelis?CMenten (K _m) and catalytic rate (k _cat) of the AP were determined to be 21.6?±?1.2???M and 0.474?±?0.013?s^?1, respectively. The catalytic efficiency of the AP was 0.0219?±?0.002???M^?1s^?1, which was 30?±?1.5?% as efficient as the native horseradish peroxidase (HRP). The mean diameter of AP was measured to be 6.4?nm using dynamic light scattering technique. The UV?CVis spectrometry, circular dichroism, surface tension, isothermal titration calorimetric and electrochemistry methods were utilized for additional characterization of the AP. Together our results suggest that the AP generated here can be used in place of HRP in industrial and commercial fields under some extreme conditions.     

The polyurethane membranes with temperature sensitivity for water vapor permeation

The size and shape of free-volume holes available in membrane materials control the rate of gas diffusion and its permeability. Based on this principle, two segmented thermo-sensitive polyurethane (TSPU) membranes with functional gates, i.e. the ability to sense and respond to external thermo-stimuli, were synthesized and used for water vapor controllable permeation. Differential scanning calorimetry (DSC), positron annihilation lifetimes (PAL), water swelling and water vapor permeability (WVP) were used to evaluate how the structure of the polyurethane (PU) and the temperature influence the free-volume holes size and the water vapor permeability (WVP) of the PU membranes. DSC study reveals that TSPU with a glass transition or a crystalline transition reversible phase shows an obvious phase-separated structure and a phase transition temperature (defined as switch temperature, T_s). PAL study indicates that the free-volume holes size of TSPU is closely related to the T_s. When the temperature is higher than the T_s, the ortho-positronium (o-Ps) lifetime (τ₃) and the average radius (R) of free-volume holes of TSPU membrane increase dramatically. As a result, the WVP of TSPU membrane shows a dramatic increase. Additionally, the water swelling and the WVP of TSPU membrane are found to depend on the inner structure of the polymer, and they also give different responses to temperature variation. When the temperature is higher than the T_s, there is a significant increase of WVP from 3.80 kg/m² day to 7.63 kg/m² day for TSPU(a) and from 4.30 kg/m² day to 8.58 kg/m² day for TSPU(b), respectively. Phase transition accompanying significant changes in free-volume holes size and WVP can be used to develop “smart membranes” with functional gates and controllable gas permeation.     

Coherent excitation and isotope selective photoionization of cadmium

Coherence between the magnetic sub-levels of the 5s5p ³ P ₁ level of cadmium is induced by excitation. A second excitation step and photo-ionization are used to detect the coherence and perturbations by the nuclear angular momentum. The ionization probability of even isotopes is suppressed with respect to the odd isotopes by a factor 59.     

mj Rainbows in molecule-surface scattering

A quasiclassical trajectory study of N₂ scattering from a rigid corrugated crystal surface was carried out. Rainbow maxima were seen in the m_j distribution. The maximum value of product j at which m_j, rainbows occur is found to increase linearly with the corrugation and decrease linearly with the hardness of the interaction potential.     

The enthalpimetric determination of the michaelis constant of the α-chymotrypsin-catalysed hydrolysis of n-acetyl-l-tyrosine ethyl ester based on the integrated michaelis—menten equation

An enthalpimetric method is discussed for the determination of the Michaelis constant (K_m )for the α-chymotrypsin-catalysed hydrolysis of N-acetyl-L-tyrosine ethyl ester (ATEE). The integrated form of the Michaelis—Menten equation is used to achieve a graphical determination of K_m in a single experiment (s_r = 7.6%). The inhibitory effect of ethanol is briefly described.     

Orientation of Na(3p) states excited in Na-He collisions

The orientation of Na(3p) states created in 3–13 keV Na(3s)-He collisions has been studied by the polarised photon-scattered particle coincidence technique at scattering angles corresponding to the impact-parameter range 1–2 a.u. In the standard geometry, at large impact parameters the excitation process exhibits a very high degree of orientation with about 90% of the Na(3p) states havingm ₁=?1. Strong reduction in this propensity is observed at impact parameters smaller than about 1.3 a.u., where a molecular curve crossing causes simultaneous He(n=2) excitation. In this region, also ionisation becomes important.