Effective Interaction Potential Research Articles

High-pressure phase transformation and elastic behavior of XC (X = Si, Ge, Sn and Pt) compounds

Pressure-induced structural aspects of ZnS-type (B3) to NaCl-type (B1) structure in XC (X = Si, Ge, Sn and Pt) compounds are presented. An effective interionic interaction potential with long-range Coulomb, van der Waals (vdW) interaction and the short-range repulsive interaction up to second-neighbor ions within the Hafemeister and Flygare approach with modified ionic charge is developed. Particular attention is devoted to evaluate the vdW coefficients following the Slater–Kirkwood variational method, as both the ions are polarizable. Our results on vast volume discontinuity in pressure volume phase diagram identify the structural phase transition from B3 to B1 structure. The estimated value of the phase transition pressure (Pt) and the magnitude of the discontinuity in volume at the transition pressure are consistent as compared to the reported data. The variations of elastic constants with pressure follow a systematic trend identical to that observed in other compounds of ZnS and NaCl-type structure family and the Born relative stability criteria are valid in XC compounds.

Effects of turbulence on the Thomson scattering process in turbulent plasmas by the scattering of electromagnetic waves

The effects of turbulence on the Thomson scattering process are investigated in turbulent plasmas. The Thomson scattering cross section in turbulent plasmas is obtained by the fluctuation-dissipation theorem and plasma dielectric function as a function of the diffusion coefficient, wave number, and Debye length. It is demonstrated that the turbulence effect suppresses the Thomson scattering cross section. It is also shown that the turbulence effect on the Thomson scattering process decreases with increasing thermal energy. The dependence of the wave number on the total Thomson scattering cross section including the turbulent structure factor is also discussed.This paper is dedicated to the late Prof. P. K. Shukla in memory of exciting and stimulating collaborations on effective interaction potentials in various astrophysical and laboratory plasmas.

Anisotropy in a high Landau level due to effective electron-electron interactions

Quantization of Hall resistivity in strongly correlated two-dimensional electronic systems at high magnetic fields generally indicates the stabilization of novel electronic quantum liquid phases of matter. This is the nature of the integer and fractional quantum Hall states that stabilize at integer and fractional odd-denominator (not always, though) filling factors of the Landau level. Away from certain filling factors that represent quantum Hall liquid states, different phases, some of them with unusually high magneto-transport anisotropy have been known to stabilize specially in high Landau levels. In this work, we try to understand this anisotropic behaviour in terms of effective electron-electron interaction potentials. To this effect, we implement a full projection of the original Coulomb interaction potential in the suitable Landau level. We find out that, in high Landau levels, thus for relatively weak magnetic fields, a semi-classical description of the interaction potential between electrons appear to be an adequate choice. The features of this semi-classical interaction potential in this limit suggest ways how the energetic balance between density waves and/or liquid crystalline phases might be sensitively affected.

Newtonian Kinetic Theory and the Ergodic-Nonergodic Transition

In a recent work we have discussed how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. In the present work we use this development for investigating ergodic-nonergodic (ENE) transitions in dense fluids. The theory is developed in terms of a core problem spanned by the variables $\rho$, the number density, and $B$, a response density. We set up the perturbation theory expansion for studying the self-consistent model which gives rise to a ENE transition. Our main result is that the low-frequency dynamics near the ENE transition is the same for Smoluchowski and Newtonian dynamics. This is true despite the fact that term by term in a density expansion the results for the two dynamics are fundamentally different.

An Effective Description of Electron Correlation in the Green Function Approach

Beyond the usual many body perturbation theory, with the eigenfunctional theory, we directly calculate the correlation function produced by the Coulomb interaction of electrons in the equation of one-electron Green function, and give the general expression of the non-local effective interaction potential in a Hartree-type potential, which is absent in all previous many body perturbation theories. This effective interaction potential originates from the quantum many body effect of the system, and it cannot be obtained directly by the usual perturbation expression approach. Moreover, using theoretical models, we demonstrate that this effective interaction potential can be used to characterize the electron correlation strength of the system.

Interaction potential and gaseous ion mobility of CO+ ions in He

An effective spherical interaction potential for HeCO+ and values for the momentum-transfer collision integral are obtained from experimental ion mobility data by using the direct inversion method. The potential is fitted to a Morse–Spline–van der Waals (MSV) model potential. Consistency is checked by calculating collision integrals and the mobilities of CO+ ions in He gas from the MSV potential and showing that they agree with the experimental data. The separation- and angle-dependent interaction potential energy surface is calculated from the spin-unrestricted, fourth-order Moller–Ploesset theory with single, double, triple and quadruple excitations, using a 6-311++G(3df,3pd) basis set while correcting for basis set superposition error. Full and partial versions of the ab initio potentials are used to determine the transport cross-sections for the collisions of CO+ with He as a function of the collision energy at fixed angles between the C–O bond axis and the internuclear axis. Finally, the transport coefficients of CO+ ions moving through He are calculated accurately, over a wide range of reduced electric field and gas temperature, using an extension of the Monchick–Mason approximation.

Atomic collisional orientation for the electron-impact excitations: Quantum shielding effect

The influence of the quantum shielding on the collisional atomic orientation phenomena is investigated for the electron-impact excitations of the hydrogenic ion. The excitation probabilities are derived as a function of the collision energy, impact parameter, and quantum wave number by using the semiclassical method and effective interaction potential. It is found that the influence of the oscillatory quantum shielding enhances the excitation probabilities. The detailed investigation on the variation of excitation preference due to the influence of the quantum shielding is also given.

Characteristics of the dynamic shielding on the Wannier-ridge electron escapes by electron impact in weakly coupled plasmas

The influence of the dynamic shielding on the Wannier ridge electron escapes into the continuum states by the electron-impact is investigated in weakly coupled plasmas. The dynamically shielded renormalized electron charge and screened Wannier exponent are obtained by considering the equation of motion in the Wannier configuration mode with the effective interaction potential as functions of the charge of the residual ion, Debye length, projectile energy, and thermal energy. The result shows that the dynamic renormalized effective electron charge decreases with an increase of the thermal energy, especially for large distances. It is found that the dynamic shielding effect enhances the Wannier exponent for the double-electron escape. The variation of the dynamic shielding effect on the screened Wannier exponent is also discussed.

Renormalized dynamic charge shielding on the electron-atom collision: Eikonal analysis

The influence of the dynamic renormalization plasma shielding on the electron-atom collision is investigated in a dense strongly coupled electron system. The semiclassical eikonal method and effective interaction potential are employed to obtain the eikonal scattering phase shift and eikonal collision cross section as functions of the Debye length, impact parameter, projectile energy, and thermal energy. It is found that the renormalized dynamic charge shielding effect enhances the eikonal collision cross section. The variation of the dynamic renormalization shielding on the electron-atom collision is also discussed.

Effective pair potential for atoms in the Coulomb model of substance

An explicit expression for the pair short-range effective interaction potential of “atoms” is derived based on the model of “pure” matter. This model represents the equilibrium Coulomb system of interacting electrons and nuclei of the same type, using the adiabatic approximation for nuclei, the self-consistent Hartree-Fock approximation for the electronic subsystem, the “one-center” approximation to describe localized electronic states, and the perturbation theory with respect to the fluctuating field. It is shown that the found potential is completely defined by the inhomogeneous density and inhomogeneous density matrix of electronic states in the isolated “atom”.

Aggregation of rod-like polyelectrolyte chains in the presence of monovalent counterions

Using molecular dynamics simulations, it is demonstrated that monovalent counterions can induce aggregation of similarly charged rod-like polyelectrolyte chains. The critical value of the linear charge density for aggregation is shown to be close to the critical value for the extended-collapsed transition of a single flexible polyelectrolyte chain, and decreases with increasing valency of the counterions. The potential of mean force along the center of mass reaction coordinate between two similarly charged rod-like polyelectrolytes is shown to develop an attractive well for large linear charge densities. In the attractive regime, the angular distribution of the condensed counterions is no longer isotropic.

Melting pressure of saturated helium mixture at temperatures between 10 mK and 0.5 K

The melting curves of helium mixtures are, in general, equilibrium states between one or two liquid phases and one solid phase. In the case of a solubility saturated system, three phases coexist and the melting pressure depends uniquely on temperature. Thus, it forms a univariant system and can be used as a thermometric standard. The melting pressure of the saturated helium mixture has been studied experimentally, but an independent calculation of this quantity supports its use in thermometry. We have calculated the melting pressure of the saturated helium mixture as a function of temperature between 10 mK and 0.5 K by using thermodynamic considerations and recently determined effective interaction potential between 3He quasiparticles in the liquid mixture.

Field Theoretic Formulation of Kinetic Theory: Basic Development

We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. The need for a self-consistent approach is suggested by our interest in investigating ergodic-nonergodic transitions in dense fluids. The formal structure we develop has been implemented in detail for the simpler case of Smoluchowski dynamics. One aspect of the approach is the identification of a core problem spanned by the variables \rho the number density and B a response density. In this paper we set up the perturbation theory expansion with explicit development at zeroth and first order. We also determine all of the cumulants in the noninteracting limit among the core variables \rho and B.

Interatomic collisions in two-dimensional and quasi-two-dimensional confinements with spin-orbit coupling

We investigate the low-energy scattering and bound states of two two-component fermionic atoms in pure two-dimensional (2D) and quasi-2D confinements with Rashba spin-orbit coupling (SOC). We find that the SOC qualitatively changes the behavior of the 2D scattering amplitude in the low-energy limit. For quasi-2D systems we obtain the analytic expression for the effective-2D scattering amplitude and the algebraic equations for the two-atom bound state energy. Based on these results, we further derive the effective 2D interaction potential between two ultracold atoms in the quasi-2D confinement with Rashba SOC. These results are crucial for the control of the 2D effective physics in quasi-2D geometry via the confinement intensity and the atomic three-dimensional scattering length.

Some problems of the theory of quantum statistical systems with an energy spectrum of the fractional-power type

We consider the problem of the effective interaction potential in a quantum many-particle system leading to the fractional-power dispersion law. We show that passing to fractional-order derivatives is equivalent to introducing a pair interparticle potential. We consider the case of a degenerate electron gas. Using the van der Waals equation, we study the equation of state for systems with a fractional-power spectrum. We obtain a relation between the van der Waals constant and the phenomenological parameter α, the fractional-derivative order. We obtain a relation between energy, pressure, and volume for such systems: the coefficient of the thermal energy is a simple function of α. We consider Bose—Einstein condensation in a system with a fractional-power spectrum. The critical condensation temperature for 1 < α < 2 is greater in the case under consideration than in the case of an ideal system, where α = 2.

Tuning effective interactions close to the critical point in colloidal suspensions

We report a numerical investigation of two colloids immersed in a critical solvent, with the aim of quantifying the effective colloid-colloid interaction potential. By turning on an attraction between the colloid and the solvent particles we follow the evolution from the case in which the solvent density close to the colloids changes from values smaller than the bulk to values larger than the bulk. We thus effectively implement the so-called (+, +) and (-, -) boundary conditions defined in field theoretical approaches focused on the description of critical Casimir forces. We find that the effective potential at large distances decays exponentially, with a characteristic decay length compatible with the bulk critical correlation length, in full agreement with theoretical predictions. We also investigate the case of (+, -) boundary condition, where the effective potential becomes repulsive. Our study provides a guidance for a design of the interaction potential which can be exploited to control the stability of colloidal systems.

Coarse-Graining of Ionic Microgels: Theory and Experiment

Abstract In this work, we discuss the statistical mechanics of many-body systems consisting of electrically charged microgels, and we show that their collective behavior is determined by an interplay between the screened electrostatic and the elastic contributions to their effective interaction potential. The former is derived by means of a statistical-mechanical approach due to Denton [A. R. Denton, Phys. Rev. E 67, 011804 (2003)], and it includes the screened electrostatic potential between penetrable spheres and the counterion entropic contribution. The latter is based on the Hertzian model of the theory of elasticity. Comparisons with experimental results demonstrate the realistic nature of the coarse-graining procedure, which makes it possible to put forward theoretical predictions on the phase diagram of ionic microgels and on the behavior of soft, neutral microgels under confinement in narrow pores.

Study of pressure induced structural phase transition and elastic properties of lanthanum pnictides

We evolve an effective interatomic interaction potential with long range Coulomb interactions, Hafemeister and Flygare type short range overlap repulsion extended up to second neighbor ions and van der Waals interaction to discuss the pressure dependent first order phase transition, mechanical, elastic, and thermodynamical properties of NaCl-type (B1) to CsCl-type (B2) structure in lanthanum pnictides (LaY, Y = N, P, As, Sb, and Bi). Both charge transfer interactions and covalency effect apart from long range Coulomb are important in revealing the high-pressure structural phase transition, associated volume collapse, elastic and thermodynamical properties. By analyzing the aggregate elastic constants pressure (temperature) dependence, the rare earth lanthanum pnictides are mechanically stiffened as a consequence of bond compression and bond strengthening attributed to mechanical work hardening, thermally softening arose due to bond expansion and bond weakening due to lattice vibrations, brittle (ductile) nature at zero (increased) pressure and temperature dependent brittleness from room temperature to high temperatures. To our knowledge these are the first quantitative theoretical prediction of the pressure and temperature dependence of elastic and thermodynamical properties explicitly the mechanical stiffening, thermally softening, and brittle (ductile) nature of rare earth LaY (Y = N, P, As, Sb and Bi) pnictides and still awaits experimental confirmations.

Structural phase transition and elastic properties of mercury chalcogenides

Pressure induced structural transition and elastic properties of ZnS-type (B3) to NaCl-type (B1) structure in mercury chalcogenides (HgX; X = S, Se and Te) are presented. An effective interionic interaction potential (EIOP) with long-range Coulomb, as well charge transfer interactions, Hafemeister and Flygare type short-range overlap repulsion extended up to the second neighbor ions and van der Waals interactions are considered. Emphasis is on the evaluation of the pressure dependent Poisson's ratio ν, the ratio RBT/G of B (bulk modulus) over G (shear modulus), anisotropy parameter, Shear and Young's modulus, Lame constant, Kleinman parameter, elastic wave velocity and thermodynamical property as Debye temperature. The Poisson's ratio behavior infers that Mercury chalcogenides are brittle in nature. To our knowledge this is the first quantitative theoretical prediction of the pressure dependence of elastic and thermodynamical properties explicitly the ductile (brittle) nature of HgX and still awaits experimental confirmations.

Influence of the nonthermal plasma shielding on the ion collisions in Lorentzian semiclassical plasmas

The influence of the nonthermal plasma shielding on the elastic ion-ion collision is investigated in dense Lorentzian semiclassical plasmas. The effective interaction potential and phase theory are applied to obtain the scattering phase shift and collision cross section as functions of the spectral index of the Lorentzian plasma, impact parameter, collision energy, and plasma parameters. The result shows that the nonthermal plasma shielding effect reduces the magnitude of the scattering phase shift. It is also found that the nonthermal plasma shielding effect suppresses the ion-ion collision cross section. Hence, we have found that the ion-ion collision cross sections in thermal plasmas are always greater than those in nonthermal plasmas. In addition, it is found that the nonthermal shielding effect on the collision cross section increases with an increase of the Debye length in Lorentzian semiclassical plasmas.