Short-range Term Research Articles

The lattice dynamics and thermodynamics of the Mg2SiO4 polymorphs

We use an approach based upon the Born model of solids, in which potential functions represent the interactions between atoms in a structure, to calculate the phonon dispersion of forsterite and the lattice dynamical behaviour of the beta-phase and spinel polymorphs of Mg2SiO4. The potential used (THB1) was derived largely empirically using data from simple binary oxides, and has previously been successfully used to model the infrared and Raman behaviour of forsterite. It includes ‘bond bending’ terms, that model the directionality of the Si-O bond, in addition to the pair-wise additive Coulombic and short range terms. The phonon dispersion relationships of the Mg2SiO4 polymorphs predicted by THB1 were used to calculate the heat capacities, entropies, thermal expansion coefficients and Gruneisen parameters of these phases. The predicted heat capacities and entropies are in outstandingly good agreement with those determined experimentally. The predicted thermodynamic data of these phases were used to construct a phase diagram for this system, which has Clausius-Clapeyron slopes in very close agreement with those found by experiment, but which has predicted transformation pressures that show less close agreement with those inferred from experiment. The overall success, however, that we have in predicting the lattice dynamical and thermodynamic properties of the Mg2SiO4 polymorphs shows that our potential THB1 represents a significant step towards finding the elusive quantitative link between the microscopic or atomistic behaviour of minerals and their macroscopic properties.

Properties of the square-well fluid of variable width

Etude de la variation de l'energie libre de Helmholtz d'un tel fluide en fonction de la largeur du puits de potentiel, λ, par un developpement de perturbation a haute temperature jusqu'au 2eme ordre en puissance de λ, dans l'approximation a longue portee: les resultats sont asymptotiquement exacts pour λ eleve, donnent une correction a la limite de van der Waals; pour λ≥3, le developpement a basse densite exact jusqu'a l'ordre du 4eme coefficient viriel

Self-consistent interaction potential for a molecule adsorbed on a dielectric surface: A symmetric top molecule on an ionic crystal

An iterative self-consistent determination of the long range interaction energy between an admolecule and a ionic crystal is performed within the scheme of local and response potentials and the definition of the generalized electric susceptibilities of the two partners. The multipolar (electrostatic+induction) contributions and the quantum (dispersion+empirical short range) terms are determined as a sum of interactions between the molecule and the atomic planes parallel to the surface, constituting the crystal. The discrete structure of each plane is described with an increasing accuracy by increasing the order of the Fourier expansion in the reciprocal planar lattice. A semianalytical expression of each contribution is given for a symmetric top molecule adsorbed on a NaCl surface as a function of the location of the center of mass and of the orientation of the molecule.

On the scattering intensity distribution from disordered binary alloys

An expression for the total scattering from a disordered binary alloy is developed through the use of a cumulant expansion method. The technique permits the authors to formulate the scattered intensity exactly without limiting approximations for the static and dynamic displacements. The intensity is naturally decomposed into a Bragg term (including the attendant static and dynamic diffuse scattering), a symmetric short-range order term and a size-effect modulation term. In a null-matrix alloy, for which the Bragg term vanishes, only the symmetric short-range scattering survives.

Many-body effects on Schottky defect formation energy in ionic solids

Abstract A three-body interaction potential for the study of point defect properties in ionic crystals is proposed. This potential consists of long-range Coulomb and three-body interactions and short-range van der Waals' (vdW) attraction and overlap repulsion terms. In this potential, the three-body interactions are considered to arise from charge transfer due to the deformation of electron shells of overlapping ions. The vdW coefficients have been obtained from the Slater-Kirkwood variational method. This potential has been used for the first time to calculate the Schottky defect formation energies in solids with caesium chloride structure, namely caesium, thallium and ammonium halide crystals within the framework of the polarizable point-ion (PPI) model. It is shown that the proposed three-body force PPI (TPPI) model takes proper account of the elastic and dielectric properties of ionic solids. The calculated values of Schottky defect formation energies in caesium, thallium and ammonium halide crystals ...

Electron impact excitation of Fe II using the R-matrix method

The authors present collision strengths in the LS-coupling scheme for transitions between the ground state 3d64s6D and the first three excited states 3d74F, 3d64s4D and 3d74P of Fe II using the R-matrix method. The authors include these four target states and all the appropriate short-range correlation terms in the expansion of the total wavefunction of the system. The target states are described by configuration interaction wavefunctions. Since the cross sections are dominated by resonances, the authors tabulate effective collision strengths for a wide range of electron temperatures assuming a Maxwellian distribution.

The influence of short-range collisions on the Vlasov equation for plasmas

Abstract The linearized Vlasov-Maxwell equations, describing longitudinal plasma waves, are studied with the addition of a simple short-range collision term and for a given equilibrium distribution. The problem of stability, and of existence and location of isolated eigenvalues determining the asymptotic time behavior of the plasma following a small plane wave initial perturbation with given arbitrary wave number are investigated.

The NN interaction in a quark model with quark-antiquark excitations

Quark-antiquark excitations inherent in the quark-gluon interaction have been incorporated into a quark model of the nucleon to study the effects of such excitations on the NN interaction within the framework of the resonating group method. The three-quark (3q) components of a single nucleon are augmented by ( 3 q)( q q ) excitations with the 24 possible spin, isospin, color combinations for the energetically lowest p-wave relative motion function. Quark exchange kernels are then calculated for the two-nucleon system described by these improved nucleon internal functions; and these exchange kernels are converted to phase-shift-equivalent effective NN potentials by the Wigner-transform WKB technique. The off-shell qq̄ pair-creation terms are derived from the one-gluon exchange diagrams in the Breit approximation in analogy with the derivation of the qq and qq̄ potentials. The parameters of the interaction are chosen to be consistent with the experimental Δ-N mass difference, the nucleon-vector-meson coupling constants, and the nucleon magnetic moments. Within these constraints, the predicted amplitudes of the ( 3 q)( q q ) components of the nucleon internal functions have been shown to be insensitive to the precise values of the model parameters. In particular, they pass the crucial test of being insensitive to very large changes in the magnitude of the confinement potential constant which is a necessary ingredient of the model. The qq̄ excitations lead to the following effects in the S-wave NN potentials: (i) The repulsive core heights of the simple 3q-3q model are greatly reduced but retain their strong essentially linear energy dependence, with numerical values very similar to those of the short-range phenomenological terms of the Paris potential. (ii) The effective potentials have acquired an attractive part in the 0.8-1.5 fm range. However, this attraction is too weak to bind the deuteron or fit the extreme low-energy S-wave phase shifts.

The energetics of polytypic structures: a computer simulation of magnesium silicate spinelloids

A computer simulation technique is used to predict the lattice energies, structures and physical properties of magnesium silicate spinelloids from given interatomic potentials. Two types of potential models are considered, a fully ionic model, which includes electrostatic, short-range and dispersive terms, and a partially ionic model, in which fractional charges are allocated to the component ions and a Morse function is included to describe the effect of covalency in the Si-O bond. The calculated energies of the spinelloid polytypes are analysed in terms of the interaction energies between component structural units. The calculated spinelloid energetics are discussed in the light of recently developed models of polytypism. The predicted values of the interaction energy terms are tested by using them to calculate the energy of a 1/21101](010) stacking fault in the naturally occurring magnesium silicate spinelloid wadsleyite. The calculated stacking-fault energies are in excellent agreement with the value inferred from transmission electron microscopy.

A blip-function calculation of the structure of liquid binary alloys

The authors present an extension of the blip-function expansion of Weeks, Chandler and Andersen (WCA) (1971) to liquid binary alloys. It turns out that the fact that realistic interionic pair potentials tend to be non-additive for most alloys poses a serious problem. They propose to resolve this problem by modifying the separation of the pair potentials in repulsive short-range and long-range terms in such a way that the repulsive parts are always additive, the non-additivity being entirely absorbed in the long-range terms. They show that this results in a first important improvement of the structure of liquid alloys over a simple hard-sphere picture. However, we emphasise that this should only be considered as a first step towards a systematic application of thermodynamic perturbation theory to liquid alloys.

Dynamical effects of the repulsive core in 54.7 MeV 16O + 28Si large-angle elastic scattering

The inclusion of a short-range repulsive term in the real part of the optical potential has previously been shown to be needed to explain the 54.7 MeV 16O + 28Si large-angle scattering data. The dynamical effects arising from this repulsive core are studied here. The changes in the angular distribution for this system brought about by the presence of the core are shown to be due to an increased reflectivity in the low-angular-momentum partial waves affecting mostly the nearside component of the scattering amplitude. From this study we draw inferences about the expected behaviour of the elastic scattering cross section for heavier systems where anomalous large-angle scattering is also observed.

Positronium formation in p-wave positron-hydrogen scattering

Calculations have been made of the p-wave contributions to the elastic scattering and positronium formation cross sections for positron-hydrogen scattering in the ore gap, 6.8-10.2 eV. The Kohn and inverse Kohn variational methods were used with trial functions containing as many as 84 short-range correlation terms of each symmetry, and there is considerable evidence that the most accurate of the results obtained are close to being fully converged.

Positronium formation in s-wave positron-hydrogen scattering

Detailed investigations are made of the convergence of the K-matrix elements and the cross sections for elastic scattering and positronium formation in the s-wave scattering of positrons by atomic hydrogen in the energy range 6.8-10.2 eV. The Kohn and inverse Kohn variational methods are used with trial functions containing many linear variational parameters and associated short-range correlation terms, and results are obtained for a set of systematically improved trial functions. The diagonal elements of the K matrix and the eigenphase shifts obtained with these trial functions can be fitted very accurately to a convergence formula which permits extrapolation to the essentially exact results corresponding to an infinite number of short-range correlation functions. No such convergence formula applies to the off-diagonal matrix element K12, nor to the cross sections, but the very slight changes in the results as the trial functions undergo their final improvements strongly suggest that the most accurate values obtained here for K12 and the cross sections for positronium formation and elastic scattering are in error by no more than 5%, 10% and 5% respectively.

Computer simulations of the structural and physical properties of the olivine and spinel polymorphs of Mg2SiO4

The aim of the work presented is to develop a computer simulation technique which will predict the structure and physical properties of forsterite and ringwoodite, the major mantle-forming polymorphs of Mg2SiO4. The technique is based upon energy minimization, in which all structural parameters are varied until the configuration with the lowest energy is achieved. The lattice energy and physical properties (e.g. elasticity and dielectric constants) are calculated from interatomic potentials, which generally include electrostatic and short-range terms. We investigate several types of traditional potential models, and present a new type of model which includes partial ionic charges and a Morse potential to describe the effect of covalency on the Si-O bond. This new form of potential model is highly successful, and not only reproduces the zero-pressure structural, elastic and dielectric properties of forsterite and ringwoodite, but also accurately describes their pressure dependence.

Fock potentials. II. Atomic potentials and intra-atomic electronic interactions

The expressions for atomic potentials obtained from Slater basis functions are presented. Angular and radial factors are separated, and short- and long-range terms are identified. Long-range terms are retained, and a simplified (but faithful) representation of the short-range terms is analyzed. The interactions between charge distributions placed on the same atom and both types of terms are also presented. Finally, the theoretical developments are tested on several atomic calculations and the advantages of this approach in order to calculate the electronic structure of large molecules are pointed out.

Interaction among systems of finite size in predictive relativistic mechanics. III. Short-range interaction and second-order terms

We compute up to and including all the ${c}^{\ensuremath{-}2}$ terms in the dynamical equations for extended bodies interacting through electromagnetic, gravitational, or short-range fields. We show that these equations can be reduced to those of point particles with intrinsic angular momentum assuming spherical symmetry.

Parity nonconserving asymmetry in neutron-deuteron and proton-deuteron scattering

Parity nonconservation in nucleon ($N$)-deuteron$(d)$ scattering is examined at low energies (\ensuremath{\le}40 MeV), particularly at 15 MeV. A Faddeev treatment is employed. For the strong $N$- force a separable interaction, which fits scattering cross sections up to 60-100 MeV, is used; for the weak parity nonconserving $\mathrm{NN}$ force, an isoscalar short range term due to $\ensuremath{\rho}$ and $\ensuremath{\omega}$ exchanges and an isovector pion exchange contribution are included. Comparisons with parity nonconserving experimental asymmetries in $\mathrm{NN}$ scattering are made. For the parity nonconserving asymmetry in $N\ensuremath{-}d$ scattering the contributions of various terms are separated, so that the model dependence of our results can be discussed. It is found that multiple scattering effects are important. The energy dependence of the parity nonconserving asymmetry in $N\ensuremath{-}d$ scattering is found to differ qualitatively from that in $\mathrm{NN}$ scattering.

Prediction of mineral crystal structures

The aim of our work has been to develop a computer simulation technique that can predict the structure of minerals. The basis of the technique is energy minimisation, i.e. all structural parameters are varied until the configuration with the lowest lattice energy is achieved; the initial configuration usually corresponds to an “ideal” structure based on regular polyhedra. The lattice energy is calculated using a specified potential model which includes electrostatic and short-range terms. These techniques can be applied to two distinct areas of structure prediction. The first concerns discrimination between alternative space groups proposed for the same structure. The second concerns the calculation of distortions from ideal close-packed structures. Here we concentrated mainly on silicate minerals. Furthermore, by varying the cell parameters we were able to simulate the effect of pressure on the crystal structure. Our results show that it is possible to establish potential models which predict detailed features of mineral structural chemistry.

Short range part of theNNinteraction: Equivalent local potentials from quark exchange kernels

To focus on the nature of the short range part of the $\mathrm{NN}$ interaction, the intrinsically nonlocal interaction among the quark constituents of colorless nucleons is converted to an equivalent local potential using resonating group kernels which can be evaluated in analytic form. The WKB approximation based on the Wigner transform of the nonlocal kernels has been used to construct the equivalent potentials without recourse to the long range part of the $\mathrm{NN}$ interaction. The relative importance of the various components of the exchange kernels can be examined: The results indicate the importance of the color magnetic part of the exchange kernel for the repulsive part in the $(\mathrm{ST})=(10), (01)$ channels, in particular since the energy dependence of the effective local potentials seems to be set by this term. Large cancellations of color Coulombic and quark confining contributions, together with the kinetic energy and norm exchange terms, indicate that the exact nature of the equivalent local potential may be sensitive to the details of the parametrization of the underlying quark-quark interaction. The equivalent local potentials show some of the characteristics of the phenomenological short range terms of the Paris potential.NUCLEAR REACTIONS Short range part of $\mathrm{NN}$ interaction, six-quark model, RGM quark exchange kernels, equivalent local potentials via WKB and Wigner transforms.

Self-trapped excitons in rare-gas dimers and solids

The excited electron states in isolated rare-gas dimers are described by a model Hamiltonian with appropriate simplifications for the short-range terms. Then the energies of self-trapped excitons are obtained by including solid state effects. The results are compared with the available transient absorption spectroscopy measurements.