Structure study of simple fluids

The structure function of simple monatomic liquids like neon and argon is studied in an approximation scheme where intermediate functionQ(r) is extended beyond hardcore diameter rather than the direct correlation functionC(r). The calculated values show good agreement with experimental values.     

First order quantum correction to the free energy of simple liquids

Using the perturbation theory of Weekset al the first order quantum correction to the free energy of a simple fluid characterised by a double Yukawa potential function has been expressed in a simple closed analytical form which allows numerical calculation simply on a desk calculator.     

Perturbation theory based direct correlation function for fluids with hard core potentials

Using second-order Barker–Henderson perturbation theory we are able to derive an explicit expression for the direct correlation function of fluids with hard core potentials. Using the obtained direct correlation function, one can explicitly calculate all thermodynamic properties of simple fluids with hard core potentials. Comparisons with computer simulation data show good agreement for both thermodynamic properties and the static structure factor of the hard core double Yukawa potential.     

Solution of Ornstein-Zernike equation for one-dimensional fluids

The application of Wiener-Hopf factorisation procedure as adopted by Baxter has been used to solve the one-dimensional Ornstein and Zernike (oz) equation for a fluid of interacting hard rods. Exact solution is obtained for the Kac potential in the van der Waals limit. We also obtain perturbative results which agree exactly with the lowest order calculations of Kac, Uhlenbeck and Hemmer.     

Collision-induced absorption in dense mixtures of simple fluids

Summary Collision-induced absorption (CIA) spectroscopy is a probe of the dynamical properties of dense systems. Two simple cases of CIA spectra are here discussed: the translational band observed in solutions of a noble gas in liquid Ar and the rotational lines of H₂ observed in solutions of H₂ in Ar. In the first case, the analysis of the translational band allows one to derive the characteristic frequency ω₀, associated with the rattling component of the motion of the impurity in the Ar medium. In the second case, the analysis of the rotational lines allows one to derive the parameter δ, that characterizes the density narrowing effect. In the high-density region, the parameter δ is directly related to the diffusive motion of the Ar atoms around the impurity. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Equilibrium properties of a semiclassical fluid with square-well plus hard core potential

A cluster expansion theory, in which the quantum hard sphere system is taken as a reference system and the attractive interactions as a perturbation, is applied to calculate the equilibrium properties of the square-well fluid in the semiclassical limit. The radial distribution function and direct correlation function are obtained using the exponential approximation. The isothermal compressibility is also evaluated.     

Determination of the structure factor for the rare gas fluids based on the ORPA theory and LIR equation of state

Linear isotherm regularity is applied to generate an expression for the direct correlation function (DCF), based on the optimized random-phase approximation theory. We use the Lennard-Jones potential in the modelling of real fluids, in which its molecular parameters are state-dependent. Based on the perturbation theory, we assume that the core contribution of the DCF is related to the geometric effect via a linear form, which arises from the excluded volume, and the tail contribution is related to the long-range intermolecular interactions of the system via a non-linear form. We use this model to predict the behaviour of the structure factor, S(k), in a wide range of k values for the xenon and krypton liquids. Finally, we compare our results with the experimental and theoretical data available in literature. The model is also successful in the presentation of the Ornstein–Zernike behaviour of S(k) at the low-k region.     

Pair correlation function in a dense plasma and pycnonuclear reactions in stars

The short-range behavior of the pair correlation function in a dense onecomponent plasma (jellium) is investigated. As an intermediate step, the short-range behavior of the classical pair correlation function is obtained. Actually, although the temperature and the density are assumed to be such that the thermodynamic properties are almost classical, quantum mechanics (tunnel effect) always dominates the pair correlation function at short distances. The quantum pair correlation function is calculated by treating the many-body quantum effects by a perturbation theory, and by using a semiclassical approximation based on path integrals. The results are applied to the computation of the nuclear reaction rate in dense stellar matter (pycnonuclear reactions).Laboratoire associé au Centre National de la Recherche Scientifique.     

Zero-frequency elastic moduli of uniform fluids

A statistical mechanical treatment of equilibrium elasticity of a uniform fluid phase based on density functional theory is presented. Bulk expressions for the stress tensor and the zero-frequency elastic moduli tensor involving the direct correlation function are found.     

Partial structures and compressibilities of ions in fused potassium bromide

Treating the coulomb interaction between ion species as a perturbation on the Waisman-Lebowitz solution for direct correlation function within the hard core region, the total direct correlation function in K-space has been formulated, which gives a direct method of evaluating the partial structure factors between different ion species of the fused salts through the use of Pearson-Rushbrooke equations. The partial structure factors so obtained have been applied to evaluate the partial radial distribution functions of ion pairs. In addition, many other important associated functions such as the static correlations of total number, mass and charge densities have been computed by particular linear combination of partial structure factors. The charge neutrality relate the partial structure factors to the isothermal compressibility for the wavevectorK → 0 and hence the evaluation of the compressibilities of ions in fused KBr is possible, which agrees well with the observed value. As such the present method is very useful in investigating the structure of molten salts since only the parametersσ _ij , the distances of closest approach between ions andɛ, the effective dielectric constant (which can be estimated from the literature) are enough for this work.     

原子结构的几种处理方法及其比较

主要论述了处理原子结构问题中常见的几种处理方法,着重论述了全实加关联的理论方法,对这几种方法进行了比较,并总结出它们在处理原子结构问题中的优点和缺陷.     

Theoretical and analytical radial distribution function for dense fluids

The ‘identical particles in quasi-mean potential energy field’ assumption was used to derive the approximate theoretical and analytical radial distribution function (RDF) for dense fluids through solving the two-body Schrödinger equation and using the first-order perturbation method. The theoretical and analytical expressions of RDF can save much computation time in calculating the thermodynamics properties of fluids and may make the statistical mechanics theories comparable with the equation of state method that is currently widely used in physics, chemistry and technology. The calculated properties for argon by this RDF fit well with the experimental data of reference over a very wide range of conditions, including dense fluids (liquid phase and dense gas), critical point, and dilute gas, in which the pair potential and the Axilrod-Teller three body interaction were considered. The extensive practical application of this model for science and technology needs further investigation.     

Comments on the variational modified-hypernetted-chain theory for simple fluids

The variational modified-hypernetted-chain (VMHNC) theory, based on the approximation of universality of the bridge functions, is reformulated. The new formulation includes recent calculations by Lado and by Lado, Foiles, and Ashcroft, as two stages in a systematic approach which is analyzed. A variational iterative procedure for solving the exact (diagrammatic) equations for the fluid structure which is formally identical to the VMHNC is described, featuring the theory of simple classical fluids as a one-iteration theory. An accurate method for calculating the pair structure for a given potential and for inverting structure factor data in order to obtain the potentialand the thermodynamic functions, follows from our analysis.     

Resonance structure for 4s subshell in photoionization of Mn

It is shown that the 3d5(4X)4s(5X) of 4s satellites, except to the coupling between 3d54s(7,5S) and 3p→3d transition, plays a key role on the magnitude of photoionization of 4s cross section. The coupled equation method is improved to calculate this resonance by including these channels. The results of calculations are comp ared with the experimental data from 46 eV to 56 eV photon energies, which are in good agreement with the experiment.     

Properties of fully developed chaos in one-dimensional maps

We consider single-humped symmetric one-dimensional maps generating fully developed chaotic iterations specified by the property that on the attractor the mapping is everywhere two to one. To calculate the probability distribution function, and in turn the Lyapunov exponent and the correlation function, a perturbation expansion is developed for the invariant measure. Besides deriving some general results, we treat several examples in detail and compare our theoretical results with recent numerical ones. Furthermore, a necessary condition is deduced for the probability distribution function to be symmetric and an effective functional iteration method for the measure is introduced for numerical purposes.     

A kinetic theory of dense fluids

A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not.     

Thermodynamic perturbation theory for the (12-6-n) fluids

A perturbation method in which attractive forces are taken as perturbation of the repulsive (reference) forces is applied to calculate the thermodynamic properties of (12-6-n) fluids in terms of the properties of hard-sphere fluid. The numerical values of the thermodynamic properties (free energy per particle, compressibility and excess internal energy) for a range of temperature and density are given for (12-6-8) fluids. Further, two perturbation schemes are adopted to evaluate the total radial distribution function using the EXP version of the optimized cluster theory (OCT). The numerical results are reliable as reported at two states (T* = 1·036,ρ* = 0·65 andT* = 0·719ρ* = 0·85) for the (12-6-8) fluid and the Lennard-Jones (12-6) fluid as well.     

On the scattering function of simple fluids in finite systems

The density-density dynamical correlation function of a simple fluid in a finite container subject to a constant temperature difference is explicitly obtained. In small systems, such as those realized in computer experiments, new peaks appear in the scattering spectrum, even at equilibrium, arising from standing waves produced by the fluctuations. Away from equilibrium, these peaks are asymmetric in the same manner as the Brillouin lines. The macroscopic limit is also considered and the correction to the usual infinite system approximation is explicitly obtained.See ref. 14 for a recent review of particle simulations used in the study of nonequilibrium systems.     

A new integral equation for the radial distribution function of a hard sphere fluid

Based on a proposal by Shinomoto, a new integral equation is derived for the radial distribution function of a hard-sphere fluid using mainly geometric arguments. This integral equation is solved by a perturbation expansion in the density of the fluid, and the results obtained are compared with those from molecular dynamics simulations and from the Born-Green-Yvon (BGY) and Percus-Yevick (PY) theories. The present theory provides results for the radial distribution function which are intermediate in accuracy between those obtained from the BGY and from the PY theories.