Three-body Correlation Function Research Articles

Evidence of three-body correlation functions in Rb+ and Sr2+ acetonitrile solutions

The local structure of Sr2+ and Rb+ ions in acetonitrile has been investigated by x-ray absorption spectroscopy (XAS) and molecular dynamics simulations. The extended x-ray absorption fine structure above the Sr and Rb K edges has been interpreted in the framework of multiple scattering (MS) formalism and, for the first time, clear evidence of MS contributions has been found in noncomplexing ion solutions. Molecular dynamics has been used to generate the partial pair and triangular distribution functions from which model χ(k) signals have been constructed. The Sr2+ and Rb+ acetonitrile pair distribution functions show very sharp and well-defined first peaks indicating the presence of a well organized first solvation shell. Most of the linear acetonitrile molecules have been found to be distributed like hedgehog spines around the Sr2+ and Rb+ ions. The presence of three-body correlations has been singled out by the existence of well-defined peaks in the triangular configurations. Excellent agreement has been found between the theoretical and experimental data enforcing the reliability of the interatomic potentials used in the simulations. These results demonstrate the ability of the XAS technique in probing the higher-order correlation functions in solution.

Coulomb corrections to the three-body correlation function in high-energy heavy ion reactions

Starting from an asymptotically correct three-body Coulomb wave-function, we determine the effect of Coulomb final state interaction on the three-particle Bose-Einstein correlation function of similarly charged particles. We numerically estimate that the Riverside approximation is not precise enough to determine the three-body Coulomb correction factor in the correlation function, if the characteristic HBT radius parameter is 5–10 fm, which is the range of interest in high-energy heavy ion physics.

Determination of two- and three-body correlation functions in ionic solutions by means of MD and EXAFS investigations.

0 ' ' • ' ' ' ' ' ~ The solvation structure of Sr 2+ ions in acetonitrile has been studied by x-ray absorption spectroscopy (XAS) and molecular dynamics (MD) simulations. The extended x-ray absorption fine structure (EXAFS) above the Sr K-edge has been interpreted in the framework of the multiple scattering (MS) formalism and, for the first time, clear evidence of MS contributions has been found for noncomplexing ions in solution. Molecular dynamics has been used to generate the partial pair 9(r) and the three-body 9(rl , r2, 0) distribution functions from which a model x(k) has been constructed. An excellent agreement has been found between the theoretical and experimental data. This result demonstrates the ability of the XAS technique in probing three-body correlation functions in solutions.

A perturbative density functional theory of inhomogeneous fluid mixture

A simple perturbative density functional approach has been developed for an inhomogeneous fluid mixture based on a functional Taylor expansion of the free energy in terms of the density inhomogeneity up to third order. A new approximation for the three-body correlation function for the mixture is proposed and the theory is applied to predict the structure of hard-sphere mixture near a hard wall. The calculated density profiles for both the components are found to agree quite well with the corresponding computer simulation results. This theory for an inhomogeneous fluid is also applied to study the structure of a homogeneous hard-sphere mixture, for which the calculated radial distribution functions are found to compare well with the corresponding results obtained from the Fourier transform of the structure factors from the Percus–Yevick theory of liquid mixtures.

3Heimpurity excitation spectrum in liquid4He

We evaluate microscopically the excitation spectrum of the 3He impurity in liquid 4He at T=0 and compare it with the experimental curve at the equilibrium density. The adopted correlated basis perturbative scheme includes up to two independent phonons, intermediate correlated states and the correlation operator is built up with two- and three-body correlation functions. The experimental spectrum is well described by the theory along all the available momentum range. A marked deviation from the simple Landau-Pomeranchuck, quadratic behavior is found and the momentum dependent effective mass of the impurity increases of about 50% at q around 1.7 A^-1 respect to its q=0 value. No signature of roton-like structures is found.

Ground-State Properties of Two-Dimensional 3He-4He Mixtures: Energetics and Structures

Using a variational Jastrow wavefunction extended to include a three-body correlation function and a hypernetted chain (HNC) and Fermi hypernetted chain (FHNC) scheme with contribution from elementary diagrams, we analyze ground-state energies and structural properties of two-dimensional3He-4He mixtures. The mixtures are in equilibrium at lower density compared to a pure4He system because of the large zero-point energy and statistical correlations due to the fermionic nature of3He. We evaluate the lowering of ground-state energies as a function of the impurity concentration and total density of mixtures. Comparing the results with boson3He-4He mixtures, we evaluate the energy shifts coming from the statistics and analyze the enthalpy to study the miscibility and mobility of each component of the mixture.

A theoretical approach to the tight-binding band structure of liquid carbon and silicon beyond linear approximations

We present a study of the band structure of liquid Carbon and Silicon modelled in a Tight-Binding Hamiltonian approximation by means of an integral equation approximation that includes non-linear corrections. The theoretical predictions are contrasted with Tight Binding Molecular Dynamics simulations in which the energy bands are obtained by direct diagonalization of the Hamiltonian matrix. The results for Silicon are excellent, whereas in liquid Carbon only some of the qualitative features of the band structure are captured by the non-linear corrections. We find that this can largely be understood as an effect of missing three-body correlation functions in the theoretical treatment of the energy bands. This is particularly crucial in the case of strongly directional and short range bonding, as it occurs in Carbon.

Ground-state properties of two-dimensional quantum fluid helium: Variational hypernetted chain methods

We calculate the ground-state energies and the radial distribution functions of two-dimensional quantum fluid4He, mass 3 boson3He and3He within a hypernetted chain and a Fermi hypernetted chain summation method. To get more accurate results, we include three-body correlation functions in the trial wavefunctions and consider the contributions arising from elementary diagrams via scaling approximations. The two-dimensional4He system has a binding energy of 0.84 K at an equilibrium density 0.042 A−2, which is closer to the result of a Green's function Monte Carlo calculation than previous ones, while mass 3 boson3He has 0.286 K at 0.025 A−2. The3He system is not self-bound and therefore not a liquid state due to its statistics and light mass of the3He atom. We calculate the ground-state energy of two-dimensional liquid4He through a Lennard-Jones potential and that of Aziz to compare the results of both. Aziz's potential gives lower and more accurate energies than the Lennard-Jones potential, as in three dimensions.

Simulated Bose-Einstein correlations in multiplicity distributions from relativistic heavy-ion collisions.

An algorithm is presented to adjust the uncorrelated momentum vectors of identical bosons produced by models of relativistic heavy-ion collisions to reproduce two-body and three-body Bose-Einstein correlation functions. The method is used to study the quality of the three-body correlations predicted by calculations in which prescribed two-body correlation functions are fit and to study the effects on the two-body distributions when the three-body correlations help constrain the momentum vector adjustment procedure. \textcopyright{} 1996 The American Physical Society.

Concentration Effects in Aqueous NaCl Solutions. A Molecular Dynamics Simulation

A series of constant-temperature/constant-pressure molecular dynamics simulations of aqueous NaCl solutions at different salt concentrations is carried out to investigate the structure and the dynamical properties. The simulations were performed with the number of molecules ranging from 256 to 2000. The simulations cover several nanoseconds to ensure the convergence of the results and to enable a proper determination of ion−ion radial distribution functions. The flexible SPC water model is used as the solvent, while the ions are treated as charged Lennard-Jones particles. Only a weak influence of the salt concentration is found on the ion−ion pair correlation functions. The structures of the hydrated shells around ion pairs are studied using three-body correlation functions. The self-diffusion and interdiffusion coefficients are found to decrease with an increase of salt concentration. Molar conductivities are calculated at different salt concentrations. The residence times of water molecules in the hydra...

Electron Speckle and Higher-Order Correlation Functions from Amorphous Thin Films

ABSTRACTWe obtain valuable information about medium-range order in amorphous semiconductors from variable coherence microscopy, a new quantitative approach to TEM. The technique reveals three-body and higher-order atomic correlation functions, which are sensitive to medium-range order. Preliminary experimental evidence for structural changes on annealing has been found for amorphous semiconductor films, with pronounced medium-range order seen only in unannealed films.

Estimating the three-body correlation function for a liquid using spherical harmonic analysis

Recent studies show how the standard spherical harmonic expanison for the structure factor of a molecular liquid can be used within the Maximum Entropy formalism to extract information about the distribution and relative orientation of neighbouring molecules in a liquid. The expansion is solved by selecting solutions to a many-dimensional problem which are consistent with the supplied diffraction data and which are also the smoothest possible. Because the transform from generalized pair correlation function to structure factor is linear, an ensemble of possible solutions can be built up, and a linear combination of the various particular solutions is itself a possible solution. The distribution of the particular solutions around this average solution gives an idea of the uncertainty associated with the average solution. By treating a pair of atoms in a liquid as a diatomic molecule, it is possible to use the same analysis to map out a three- (or more) body correlation function which is consistent with the data and which is also as smooth as possible. Formally, the only direct access to the three-body correlation function is via the pressure derivative of the structure factor. The method proposed here to extract many-body correlations is in principle much simpler to execute and avoids the need for extra diffraction measurements. The structure factors of liquid argon and liquid water are analysed. Both examples have characteristic features, and in the case of water it is shown that a significant number of near-neighbour molecules are not in the traditional tetrahedrally bonded positions. A wide range of possible solutions is found in both cases and the graphical presentation of the solutions shows that many local configurations of atoms or molecules are present in a liquid. Important qualitative differences between the two liquid structures are highlighted in this way.

Possible quantitative measures of order/disorder in models of liquid and amorphous structures

The variance of the pair correlation function, the triplet correlation function, g(3)(r,s,t), and the three-body contribution to the configurational entropy, S3, were studied as possible tools for distinguishing between three different models of amorphous silicon (a-Si) with (nearly) identical pair correlation functions. All of these quantities were shown to be able to make the distinction unequivocally. For practical reasons, short-range S3 is suggested as the best quantitative measure of disorder, in terms of higher-order correlations. For the first time, various projections of the three-body correlation function of a complicated amorphous material are also shown. On the basis of the current study it is proposed that the most realistic structural model of a-Si is the reverse Monte Carlo fit, starting from the well known Wooten model.

X-Ray Absorption Spectroscopy

X-ray absorption spectroscopy, today widely used as a tool for structural investigations, is described. Theoretically it is shown that above an absorption edge the absorption coefficient is well approximated by a sum of terms, each one describing a particular path followed by the photoelectron outgoing from the atom. Such geometrical feature allows to use X-ray absorption spectroscopy for structural investigations. The data analysis procedures are outhned. Applications of the single scattering region, generally known as EXAFS to semiconductors alloys, to metallic clusters and to the crystallization of amorphous metallic glasses are illustrated. Multiple scattering calculations and their relation to experimental spectra is discussed in the case of Mn ions in solution. Application of the multiple scattering to determine the three-body correlation function in a-Si:H is shown.

Study of dense helium plasma in the optimal hypernetted chain approximation.

We have studied the helium plasma in the hypernetted chain approximation considering both short-ranged internuclear and long-ranged Coulomb interactions. The optimal two-particle wave function has been determined in fourth order; fifth-order corrections have been considered in the calculation of the two-body and three-body correlation functions. The latter has been used to determine the pycnonuclear triple-alpha-fusion rate in the density regime 10[sup 8] g/cm[sup 3][le][rho][le]10[sup 10] g/cm[sup 3], which is of importance for the crust evolution of an accreting old neutron star. The influence of three-particle terms in the many-body wave function on the rate is estimated within an additional variational hypernetted chain calculation. Our results support the idea that the helium liquid undergoes a phase transition to stable [sup 8]Be matter at densities [rho][approx]3[times]10[sup 9] g/cm[sup 3] as the plasma induced screening potential then becomes strong enough to bind the [sup 8]Be ground state.

Correlation energy of the anyon gas.

The correlation energy of the anyon gas is expressed in terms of a coupling-constant integral involving two-body and three-body correlation functions. In the random-phase approximation, the dominant two-body contributions involve the energy difference between the collective modes of the interacting and noninteracting systems, which is evaluated numerically for the Bose gas and for semions.

Critical phenomena in liquid phases: Renormalization from the Ornstein-Zernike equation.

When considering critical phenomena in liquid phases we show that the critical exponents can be calculated using the classical components of the liquid-state theory (Ornstein-Zernike equation, n-body direct correlation function, etc.) to which we must add a renormalization procedure. In this approach, we consider the Callan-Symanzik equation as the natural closure of the Ornstein-Zernike equation. Our work allows one to elucidate some points that are generally not investigated in the standard theory. For example, at the liquid-gas critical point, we show that two coupling constants must be introduced; they are not independent. Their definition is given at a microscopic level and their dimensions are calculated. Moreover, we point out the role of the n-body direct correlation functions. Specially, the influence of the three-body correlation functions on the critical exponents is emphasized. In the case of a binary mixture we show that the critical exponents remain those of the pure liquid along the line of critical points. However, some differences between the pure liquid and the mixture appear in the calculation. For instance, the structure of the coupling constants is much more complicated in the mixture than in the case of the pure liquid. This paper represents an extension of a recent work published by the authors [Phys. Rev. Lett. 67, 1598 (1991)].

Quantum magnetotransport in lateral surface superlattices

We calculate the diffusion constant of a two-dimensional electron gas (2DEG) in a uniform perpendicular external magnetic field using the short-time expansion of the Kubo–Greenwood formula. We model the 2DEG as a one-component plasma. The two-body and three-body correlation functions are obtained from the hypernetted-chain integral equation theory and the Kirkwood superposition approximation, respectively. We compare the diffusion constant at two different temperatures. At the lower temperature, the diffusion constant increases as the magnetic field is increased but decreases with increasing magnetic field at the higher temperature. We compare our results when only two-body correlations are taken into account with those when both two-body and three-body correlations are included. These results may be interpreted as being due to the competition between the magnetic force and the force exerted on the target particle by the surrounding electrons in the 2DEG in the presence of a perpendicular magnetic field.

First-order correction to the three-body correlation function

The first-order correction to the Kirkwood superposition approximation of the triplet correlation function, based on the density expansion due to Abe, has been calculated for the high-density Lennard-Jones fluid. While qualitative agreement with computer simulation data has been obtained, substantial disagreement with older literature data and conclusions based thereon have been found.

Theory of liquid-bcc-fcc coexistence in charge-stabilized colloidal systems.

We present a density-functional theory for the phase diagram of charge-stabilized colloids with bcc, fcc, and liquid phases. The theory requires inclusion of terms involving the three-body direct correlation function of the liquid, but even a simple parametrization of these terms reproduces the features of the experimental phase diagram. We make additional directly testable predictions from our theory.