Triplet correlation and pair potential functions in liquid neon and sodium

Recent neutron diffraction data for liquid neon and X-ray diffraction data for liquid sodium have been analyzed with the purpose of studying the triplet correlation function in these liquids by means of the method suggested by Egelstaff, Page and Heard. In both cases, it was found that the function H(Q) which expresses the deviation from the superposition approximation indicates the deviation from zero and the effect of the pressure derivative of the structure factor to the function H(Q) is little. Besides, the pair potentials have been investigated from these diffraction data at various pressures using the Born-Green equation. The pair potential functions obtained for three states of liquid neon are the Lennard-Jones type, whereas those obtained for liquid sodium with a provisional assumption based on the experimental data are of the long-range oscillatory type. The pair potentials obtained in this work are useful for the interpretation on the difference in the pressure dependence of the structure factor for liquid neon and sodium.     

Computer simulation of the structure of liquid cesium and determination of the pair potentials over a wide temperature range

Using diffraction data for liquid cesium structure over a wide temperature range, models of liquid cesium are constructed and the effective pair potentials are extracted using the theory of liquids. The iterative procedure proposed by L. Reatto is used. In the range 323-1923 K the pair potentials are weakly temperature-dependent. The potentials extracted from the diffraction data differ from the potentials calculated using the Animalu-Heine pseudopotential. The self-diffusion coefficients in liquid cesium are determined. Their temperature dependence is described satisfactorily by a power-law function. Zh. éksp. Teor. Fiz. 115, 50–60 (January 1999)     

Molecular dynamics of liquid lead near its melting point

The molecular dynamics of liquid lead is simulated at T = 613 K using the following three models of an interparticle interaction potential: the Dzugutov pair potential and two multiparticle potentials (the “glue” potential and the Gupta potential). One of the purposes of this work is to determine the optimal model potential of the interatomic interaction in liquid lead. The calculated structural static and dynamic characteristics are compared with the experimental data on X-ray and neutron scattering. On the whole, all three model potentials adequately reproduce the experimental data. The calculations using the Dzugutov pair potential are found to reproduce the structural properties and dynamics of liquid lead on the nanoscale best of all. The role of a multiparticle contribution to the glue and Gupta potentials is studied, and its effect on the dynamic properties of liquid lead in nanoregions is revealed. In particular, the neglect of this contribution is shown to noticeably decrease the acoustic-mode frequency.     

Free energy of mixing of an Fe–Co liquid alloy taking into account nondiagonal <Emphasis Type="Italic">d−d</Emphasis>-electron coupling in the framework of the Willis−Harrison model

Within the framework of the Willis?Harrison model, the effect of taking into account d?d-electron couplings nondiagonal in the magnetic quantum number between the neighboring atoms in a transition metal on the partial pair potentials and the free energy of mixing of an Fe–Co liquid alloy near the melting temperature is investigated. It is found that an increase in the fraction of nondiagonal couplings results in a decrease in the depth of the first minimum of the partial pair potentials and in the displacement of its position towards larger r. It is shown that taking this factor into account considerably improves the agreement with experimental data of the concentration dependence of the free energy of mixing of the system under consideration.     

Luminescence excitation spectroscopy of NN pairs in GaP:N under uniaxial stress

We present an investigation of the luminescence excitation spectra of the NN₁ nitrogen pairs in gallium phosphide under uniaxial stress at liquid helium temperature. The main stress effect being to lift the spatial degeneracy of the star of configurations associated with a given NN_i pair, we find that the luminescence excitation spectroscopy is a necessary tool in order to understand anambiguously these complex splitting patterns. We deduce the bound hole deformation potentials.     

A one parameter model potential for noble metals

A phenomenological one parameter model potential which includes s-d hybridization and core-core exchange contributions is proposed for noble metals. A number of interesting properties like liquid metal resistivities, band gaps, thermoeletric powers and ion-ion interaction potentials are calculated for Cu, Ag and Au. The results obtained are in better agreement with experiment than the ones predicted by the other model potentials in the literature.     

On the interaction of excited alkali atoms with rare gas targets in scattering processes

A model potential calculation has been applied to evaluate scattering experiments for Na and K in the groundstate and the resonance state interacting with Ar. The model potential has only two free parameters which are determined by a best fit of the interatomic potentials to experimental results. Satisfactory agreement between calculated and experimental results is found for the differential cross sections in the groundstate and the excited state, for satellites in theK(4P),K(5P) and Na(3P) line profile, for the van der Waals constantsC ⁽⁶⁾ andC ⁽⁸⁾, the alkali ion-rare gas interaction and the vibrational energy levels of the Na-Ar molecule. As maior advantages we point out that for a given pair of atoms all these calculated data are given with one single pair of values for the free parameters and that with this set also the interatomic potentials for the higher alkali states (specifically up to 5f for Na and K) are obtained.     

Interionic potentials for alkali halide crystals derived by the hybrid Thomas-Fermi-Dirac method

The first results of a systematic study of interatomic potentials in sixteen alkali halides derived using the hybrid Thomas-Fermi-Dirac method are presented. Both the basic method and modifications to (a) correct the exchange energy to exclude the self-exchange part and (b) scale the kinetic and exchange energy terms are employed. The interactions between ion pairs are calculated at a set of interionic distances in a range corresponding to ± 30% deviations from the appropriate measured equilibrium separation. In this way a tabular function for the lattice energy/ion pair is constructed and predicted values of the equilibrium nearest neighbour interionic distance, the equilibrium lattice energy/ion pair and the Smith stiffness parameter are found numerically. The derived short-range interactions between ion pairs are fitted over the whole range to the analytic form A exp($\text{?R}\text{ρ}$) + CR^?6. It is shown that the use of an expression for the lattice energy/ion pair involving these analytic forms introduces significant errors in the predicted physical parameters.     

On the existence of the thermodynamic limit for classical systems with nonspherical potentials

It is shown, that the configurational partition function for a classical system of molecules interacting with nonspherical pair potential is proportionals to the configurational partition function for a system of particles interacting with temperature-dependent spherical k-body potentials (k ?2). Therefore, the thermodynamic limit for nonspherical molecules exists if the effective k-body interaction is stable and tempered. A number of criteria for the nonspherical potential are developed which ensure these properties. In case the nonsphericity is small in a certain sense, stability and temperedness of the angle-averaged nonspherical potential are sufficient to ensure thermodynamic behaviour.     

Interaction between a He atom and a graphite surface

A study is presented of the interaction V(r) between a He atom and a graphite surface. V(r) is assumed equal to a sum of pair interactions U(r ? R_i) between the He and C atoms. None of a set of isotropic potentials (dependent only on the magnitude ¦r ? R_i¦) is consistent with recent scattering data. Anisotropie pair potentials, in contrast, are found to yield good agreement. The origin of this anisotropy is analyzed in terms of the graphite dielectric function and charge density.     

The Bethe-Goldstone equation with singular interactions: A fully off-shell solution for the boundary condition model

The mutual interaction of a pair of fermions imbedded in a many-body system of identical particles when they are excited out of the filled Fermi sea, is studied via the T-matrix or transition amplitude specified by the Bethe-Goldstone (BG) equation. The role of the bare two-body interaction is emphasised, and in particular the consequences are elucidated of whether the potential is “well-behaved” (nonsingular) or not. The properties of the BG T-matrix, including generalized orthonormality and completeness relations, are derived both for nonsingular potentials and for singular potentials containing an infinite hard core. General analytic properties are exploited to derive relations that express the fully off-shell BG T-matrix purely in terms of the half-shell amplitude (and the properties of any possible bound states in the medium). The general formalism is illustrated by deriving exact analytic expressions for the fully off-shell BG T-matrices for a pair of particles with equal and opposite momenta interacting via either of two singular model interactions; namely, the pure hard-core interaction and the boundary condition model. Results for both models are expressed in terms of the solution to a simple one-dimensional Fredholm integral equation. The analytic properties of the solutions are discussed and exploited to prove both their uniqueness and that they satisfy the various general relations derived. To our knowledge, these results represent the first exact nontrivial solution to the fully off-shell BG equation for any local potential, or singular limiting case thereof.     

Comparative study of recent phenomenological potentials for the NaCl-type alkali halides derived from elastic and dielectric data

A comparative study is presented of various phenomenological potentials for the NaCl-type alkali halides-based on elastic and dielectric data and on a “combination” of the Born model with a deformable ion mode-reported in recent years by Catlow, Diller and Norgett, by Corish, Parker and Jacobs, by Sangster et al. and by Hardy and Karo. First a critical analysis is made of the models adopted by the various AA and of the procedures to determine the pertinent parameters, emphasizing the different, often crude approximations used and the thermodynamic inconsistencies present in them. The quality of the fits achieved, and of the predictions made with the different models is then discussed. Finally, one compares directly the resulting effective pair potentials for the short-range interactions cation-anion, anion-anion and cation-cation, as well as the various types of parameters (specifically the potential parameters (Born repulsive parameters and van der Waals coefficients) and the shell-model parameters). One finds that the effective short-range potentials for each pair interaction in a given salt reported by the various AA-taken as a whole-have a sizeable indeterminacy, due both to the Born repulsive and vdW contributions.     

Statistical-mechanical perturbation theory for liquid metals

The techniques of statistical mechanical perturbation theory are applied to liquid metals. An ion-ion repulsive pair potential is determined from an experimental structure factor curve at a temperature β₀=1/kT₀. The theory then permits the prediction of radial distribution functions, structure factors, compressibilities, and other properties at all liquid temperatures. As a preliminary test of the theory, it has been used to calculate the isothermal compressibilities of Na, Hg and Ga. The results are in very good agreement with the experimental values, which for the last metals differ from earlier theoretical predictions by almost a factor of five.     

Influence of the two-body potential on the radial distribution function of liquid 4He

The theoretical ground-state radial distribution function of liquid ⁴He appears to depend much more sensitively on the range of the assumed two-body potential than on its depth. Fairly good agreement with experiment is obtained by using realistic pair potentials.     

Structure factors and phonon dispersion in liquid Li<Subscript>0.61</Subscript>Na<Subscript>0.39</Subscript> alloy

The phonon spectra for liquid Li and Na have been computed through the phenomenological model of Bhatia and Singh for disordered systems like liquids and glasses and the obtained results have been compared with the available data obtained by inelastic neutron scattering (INS) and inelastic X-ray scattering (IXS) experiments. The effective pair potentials and their space derivatives are important ingredients in the computation of the dispersion curves. The pair potentials are obtained using the pseudo-potential theory. The empty core model proposed by Ashcroft is widely used for pseudo-potential calculations for alkali metals. But, it is thought to be unsuitable for Li because of its simple 1s electronic structure. However, it can be used with an additional term known as Born-Mayer (BM) core term. The influence of the BM core term on the phonon dispersion is discussed. The same pseudo-potential formalism has been employed to obtain the dispersion relation in liquid Li_0.61Na_0.39 alloy. Apart from the phonon spectra, the Ashcroft-Langreth structure factors in the alloy are derived in the Percus-Yevick approximation.     

Dobrushin's compactness criterion for euclidean gibbs measures

We prove existence and uniform á priori estimates for Euclidean Gibbs measures corresponding to certain quantum systems with unbounded spins, pair potentials of superquadratic growth, and infinite radius of interaction. The quantum particles are indexed by the elements of a countable, possibly irregular, set L ⊂ ∝^d. We use Dobrushin's criterion and give a direct construction of appropriate compact functions on (infinite dimensional) loop spaces. For the quantum systems on L := ∝^d, with the superquadratic interactions of finite range, a new uniqueness result is established by means of the Dobrushin-Pechersky criterion.     

A general local composition and coordination number model for square-well fluids with variable well width and diameter ratio

A radial distribution function for attractive hard-core systems is obtained from the equilibrium of a molecular pair between local and bulk environments. With this function, a general model is established for the coordination number (CN) and local composition (LC) of square-well fluids. It meets the low-density, high-density and high-temperature limit conditions, as well as the unlike pair conservation and quasi-chemical equilibrium conditions. It also has some other features that many other models do not have: (1) its CN and LC expressions contain all pair potentials; (2) it yields temperature-dependent CN and LC for closely packed mixtures with different pair potentials; (3) its energy parameter is the difference of the total potentials of one pair in local and bulk environments, not the difference of two pair potentials. This model can accurately predict the CN, LC and compressibility factors of square-well fluids from computer simulation over a wide range of density, well width (λ?=?1–2) and diameter ratio. For the case λ?=?1.5, this model is better than or comparable with semi-empirical models; in other cases, it is far better than semi-empirical models. It does not need any empirical parameter for LC prediction. For the prediction of CN and compressibility factors, it only needs the smoothed radial distribution function of pure hard-sphere fluids. It also gives excellent results for lattice gases and highly nonideal lattice mixtures.     

The influence of pair potentials on the structure of polyvalent liquid metals

The structure factors of some polyvalent liquid metals show a shoulder on their first peak. We explain these shoulders on the basis of ionic pair potentials : a shoulder is expected near the wave vector 2k_F, the wave length of the oscillations in the metallic pair potentials. To show this quantitatively, we used the “optimized random phase approximation” of Andersen et al.