Role of the phonon trial function in determining the phonon-drag contribution to the low-temperature electrical resistivity

It is demonstrated that there is excellent agreement between the low-temperature electrical resistivity data for potassium and the Bailyn formulation for the phonon-drag electrical resistivity, which is based on a consistent solution for the phonon trial function in terms of the electron trial function.     

Simple method of optimizing structural parameters of system of solid spheres for the calculation of liquid radial function

A thermodynamically consistent representation, in terms of the equation of state, is obtained for the coefficients of the Wertheim-Till direct correlation functions for a system of solid spheres modeling the microstructure of a simple liquid. It is shown that use of the equation of state in Karnahan — Sterling form significantly improves the results for the radial function, giving good agreement with the results of the semiempirical Verlet-Weis approximation for the data of a numerical experiment on a system of solid spheres. Optimization of the sphere diameter using the entropic method proposed earlier is shown to ensure agreement of the nodes of the radial function of the liquid with experimental data. The agreement of the method proposed with other known methods for the calculation and optimization of the radial function of solid spheres is discussed, and its advantages are noted.Thanks are due to Professor V. I. Shimulis for his constant interest in the work.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 28–32, June, 1977.     

A method of measuring the Green's function in an enclosure

The acoustic Green's function can be measured using a device with two matched microphones mounted in a tube driven by a loudspeaker combined with another microphone that represents the observation point. Good agreement is obtained between the measured and theoretical Green's function in a rectangular room below 320 Hz. At higher frequencies the agreement is less good because of the imperfect geometry of the room.     

Solutions of the Percus-Yevick and hyper-netted chain equations near the gas-liquid critical point

An intuitive approach is used to develop a theory of the transverse current correlation function in simple liquids. The memory function obtained on the basis of this approach is expressed in terms of the velocity autocorrelation function for the kinetic part and in terms of the radial distribution function, the interatomic potential and a time-dependent term which describes the relative motion of two atoms in the liquid for the potential part. The results for the memory function and the frequency spectrum are found to be in satisfactory agreement with the computer simulation studies of Levesque et al.     

Target mass correction on the 3He polarized structure function

Target mass correction (TMC) is employed to amend the polarized helium structure functions, ³He . The structure function can be obtained via the convolution of the light cone momentum distribution with the polarized structure of the proton and neutron. The calculation of the polarized structure function of the nucleon is based on the constituent quark model. The analytical result for ³He polarized structure function at low values of Q² is not in good agreement with the available experimental data. The reliability of calculations is increased using TMC effect. New comparison confirms a better agreement with the experimental data.     

Thermodynamic properties for the triangular-well fluid

The thermodynamic properties of the triangular-well fluid with a well range of up to twice the hard sphere diameter were studied by means of a new developed equation of state and molecular simulation. This EoS is based on the perturbation theory of Barker and Henderson with the first and second-order perturbation terms evaluated by molecular simulation and then a fit with a simple function based on the radial distribution function of the reference fluid. The thermodynamic properties for the triangular-well fluid were also obtained directly by Gibbs ensemble and NPT Monte Carlo simulations. Good agreement is observed between the proposed EoS and the molecular simulation results. A model for the triangular-well solid is also presented; this has been used to calculate the solid–liquid transition line. Very good agreement is obtained with previously report values for this line and for the triple point temperature and pressure.     

A parametrisation of the direct correlation function for the square-shoulder fluid

We introduce a parametrisation of the direct correlation function for the square-shoulder fluid and demonstrate that this parametrisation is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. Moreover, the radial distribution function obtained from the parametrisation reproduces quantitatively Monte Carlo simulation data. Our results show that the parametrisation is accurate over a large regime of densities for different interaction ranges and potential strengths.     

On the line-width in critical anisotropic antiferromagnets

We present a calculation of the longitudinal scaling function for the line-width of critical uniaxial antiferromagnets. The agreement with experimental results for MnF₂ is satisfactory.     

Virial expansion for the radial distribution function of a fluid using the 6 : 12 potential

The radial distribution function can be expressed in a virial expansion. Using the 6 : 12 potential the second-order density coefficient, g ₂(r), is numerically calculated for a wide range of temperatures and intermolecular separations. These results are used to calculate the second-order density coefficient, c ₂(r), in the expansion of the direct correlation function and to calculate the fourth virial coefficient, B ₄. In addition, approximate results for g ₂(r), c ₂(r), and B ₄ are calculated on the basis of the Percus-Yevick, hypernetted chain, and the self-consistent approximations of Hurst and Rowlinson. These approximate results are compared with the exact results. The Percus-Yevick theory is in good agreement with the exact results at high temperatures but is unsatisfactory at low temperatures. The hyper-netted-chain approximation is in fair agreement with the exact results at high temperatures, is in poor agreement at intermediate temperatures, but is in good agreement at low temperatures. The self-consistent approximations are in reasonably good agreement with the exact calculations at all temperatures.     

Novel model for the optical function of GaN

In this work we propose an analytical expression for the complex dielectric function which includes both discrete and continuum exciton effects. We have introduced Lorentzian broadening into Elliott’s formula. The introduction of broadening leads to equations for the dielectric function containing only elementary functions. We have applied the proposed model to the dielectric function of wurtzite GaN in the spectral region 1–10 eV. Excellent agreement with the experimental data has been obtained. We show that the Lorentzian-broadened dielectric function decays more slowly than the experimental data for hexagonal GaN at the low-energy side. This indicates that the broadening of the absorption edge in GaN is not purely Lorentzian. The agreement with the experimental data can be improved using adjustable broadening modification. Received: 29 January 2001 / Accepted: 30 May 2001 / Published online: 25 July 2001     

Sticky hard sphere potential—Evaluation of the structure function of liquids

The direct correlation function as obtained by Baxter for a sticky hard sphere potential, which is significant improvement over that of the hard sphere potential, has been used in the evaluation of the structure function of aluminium and lead. The values obtained by the present method are in good agreement with experiment.     

A quantum mechanical expression for the lattice contribution to the total dielectric function of semiconductors

Effects of electron-electron and electron-phonon optical interactions on the lattice dielectric function of the doped polar semiconductors are investigated. A new expression for the lattice contribution to the dielectric function is derived using the remarkable Zubarev double-time Green function. A numerical calculation for the case of GaN is done to highlight the accuracy of the model. The results obtained are in agreement with the available experimental data and reproduce the main features observed in Raman scattering spectra.     

A memory function model for the velocity autocorrelation function and the self-diffusion coefficient in simple dense fluids

A memory-function model is used to compute the velocity autocorrelation function and the self-diffusion coefficient of a dense Lennard-Jones fluid from the zero-time correlation functions of the molecular velocity and its first two time derivatives. It is shown that these zero-time correlation functions can be evaluated in terms of the radial distribution function and the pair potential only, i.e. without considering higher order correlation functions. Since molecular dynamics results are available for the radial distribution function as well as the velocity autocorrelation function and the self-diffusion coefficient, a rigorous test of the chosen memory function is possible. The agreement is reasonable, although generally not within the error bands of the molecular dynamics results.     

Electron momentum distributions and binding energies for the valence orbitals of hydrogen bromide and hydrogen iodide

Electron binding energy spectra and momentum distributions have been obtained for the valence orbitals of HBr and HI using noncoplanar symmetric electron coincidence spectroscopy at 1200 eV. The weakly bonding inner valence ns orbitals, which have not been observed previously, have their spectroscopic (pole) strength severely split among a number of ion states. For HBr the strength of the “main” inner valence (ns) transition is 0.42±0.03 whereas for HI it is 0.37±0.04, in close agreement with the value observed for the valence s orbitals of the corresponding isoelectronic inert-gas atoms. The spectroscopic strength for the two outermost orbitals is found to be close to unity, in agreement with many-body Green's function calculations. The measured momentum distributions are compared with several spherically averaged MO momentum distributions, as well as (for HBr) with a Green's function calculation of the generalized overlap amplitude (GOA). The GOA momentum distributions are in excellent agreement with the HBr data, both in shape and relative magnitude. Not all of the MO momentum distributions are in reasonable agreement with the data. Comparison is also made with the calculated momentum distributions for Kr, Br, Xe and I.     

Macroscopic theory of the electron work function in solids

The approach is based on the dielectric formalism theory. The relations for calculation of the electron work function in solids – metals, semiconductors and dielectrics, were obtained. The calculated results are in an agreement with experimental ones. This approach can be used for computation of work function values of numerous materials.     

Density dependence of the transition temperature in a homogeneous bose-einstein condensate

Transition temperature data obtained as a function of particle density in the 4He-Vycor system are compared with recent theoretical calculations for 3D Bose-condensed systems. In the low density dilute Bose gas regime we find, in agreement with theory, a positive shift in the transition temperature of the form DeltaT/T0 = gamma(na(3))(1/3). At higher densities a maximum is found in the ratio of T(c)/T0 for a value of the interaction parameter, na(3), that is in agreement with path-integral Monte Carlo calculations.     

Temporal dynamics of longitudinal and transverse velocity structure functions retrieved from the data of acoustic sounding

Temporal dynamics of vertical profiles of the longitudinal and transverse velocity structure functions and characteristics retrieved using an original procedure from regular measurements of vertical profiles of the wind velocity vector with a minisodar operating at a frequency of 4900 Hz is discussed. It is established that the structure functions first increase with the separation of the observation points and then are saturated; moreover, in agreement with the data available from the literature, the longitudinal velocity structure function is much greater than the transverse one. The altitude behavior of the velocity structure characteristic is well described by a z ^−2/3 dependence predicted theoretically. In this case, the structure function calculated from one-point measurements of the vertical wind velocity component exceeds the corresponding structure function retrieved for the vertical separation of the observation points. This is also in agreement with generalizations from the theory of isotropic turbulence.     

Theory of the liquid-solid transition

The liquid-solid transition is found by calculating the thermodynamic potential of a dense classical system as a function of order parameters which are proportional to the lattice Fourier components of the density. Properties of the fluid enter $\text{only}$ through the direct two-particle correlation function near freezing. Calculated parameters for freezing into bcc, fcc and hexagonal structures are in good agreement with experimental results.     

Light scattering in monatomic dense gases from a kinetic model of the Enskog equation

The light scattering spectra of dense monatomic gases are determined from a kinetic model of the Enskog equation in which the reference distribution function is a function of the gradients of velocity and temperature. A good agreement between the theoretical and experimental light scattering spectra is found for values of the pressure going from 0.022 to 10 atm, which correspond to the free molecular and hydrodynamic regimes, respectively.