13C hyperfine splitting in the benzene negative ion

A method is developed to calculate the coefficients appearing in the Høye, Stell and Waisman analytic solution of the Ornstein-Zernike equation for a hard core potential with a direct correlation function of the two Yukawa form. The method is simple and makes the choice of a physical solution easy. The compressibility, energy and virial pressures are calculated in the vicinity of the liquid-gas transition region and their dependence on changing K ₂, the amplitude of the repulsive Yukawa part, is analysed. This method offers promising possibilities for the application of the hard core, two Yukawa (HCTY) system in the theory of fluids.     

Vapour-liquid equilibria of the two- and three-dimensional monoatomic classical fluids interacting via double Yukawa potential

We have carried out Monte Carlo simulations in Gibbs ensemble for two-and three-dimensional double Yukawa fluid. We have compared liquid-vapour equilibrium curve with that of Lennard-Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. The role of repulsive and attractive contributions for the potential on the liquid-vapour coexistence region as well as on critical temperature and critical density has been studied. The critical temperature is found to be more sensitive than the critical density to the variation in repulsive and attractive parts of the potential. Also, the range of the attractive interaction directly influences range of the liquid vapour coexistence region. It has been found that smaller the values of the attractive parameter, larger is the coexistence region.     

Dynamical Background for L-G Phase Transition in QHD-I Model

Starting from the QHD-I model, the nucleon-nucleon interaction potential in hot/dense nuclear matter is studied. We find that the attractive and repulsive Yukawa potential between nucleons is modified by the variation of Debye mass directly and, especially, the nucleon system described by this Yukawa potential will be unbounded at some critical T and μ. The critical point we get accords with that of L-G phase transition given by the P - pB phase diagram.     

Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field

Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field.     

Dynamical Background for L-G Phase Transition in QHD-I Model

Starting from the QHD-I model, the nucleon-nucleon interaction potential in hot/dense nuclear matter is studied. We find that the attractive and repulsive Yukawa potential between nucleons is modified by the variation of Debye mass directly and, especially, the nucleon system described by this Yukawa potential will be unbounded at some critical T and μ. The critical point we get accords with that of L-G phase transition given by the P - ρs phase diagram.     

Critical behaviour in MSA for a symmetric Yukawa mixture

We study a symmetric binary mixture of equidiameter hard-spheres with repulsive Yukawa interaction for unlike atoms and attractive Yukawa interaction for like atoms. Due to a fully analytical approach we find that, for all values of the Yukawa exponentz0, the critical exponents are of the mean-spherical type. The critical region gets narrower with the increase of the range of the potential, causing a failure of the ordinary numerical analysis. Therefore, the previous analysis, based on numerically accessible region near the critical point, that predicted the mean-field structure of the critical exponents for small values ofz, was not adequate.     

Approximate <Emphasis Type="Italic">κ</Emphasis>-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C _s from the valence energy spectrum of particle and also for pseudospin symmetry constant C _ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.     

Phase diagram of two-dimensional binary Yukawa mixtures

We have used Ramakrishnan–Yussouff (RY) density functional theory (DFT) to explore the topology of the phase diagram of two-component charge stabilised colloidal suspensions confined to a two-dimensional plane. The particles of the system interact via purely repulsive soft core Yukawa potential. Pair correlation functions (PCFs) used as input informations in DFT were calculated by solving both the hypernetted chain (HNC) and Percus–Yevick (PY) integral equation theories. To test the relative performance of the HNC and PY theories in the context of phase transitions, we have also studied the corresponding one-component systems. We found that RY DFT with HNC PCFs does not stabilise solid in both the one- and two-component cases, whereas the PY theory does. By considering the freezing into the substitutionally disordered triangular solid, we found that the temperature-composition phase diagrams of the binary mixture are narrow spindles whose thickness depends on the symmetry of the mixture components and the value of the screening constant of the Yukawa potential. Although the phase diagram obtained by RY DFT with structural inputs calculated by the PY theory is found to be shifted to higher temperature region in the temperature-composition plane, however, it captures qualitatively all the essential features of the phase diagram. Our results are in principle verifiable through computer simulations and experiments.     

Solution of the Bethe-Goldstone equation for the reaction matrix in finite nuclei

A method for solving the BG equation for the reaction matrixt in finite nuclei is presented. The application of this method is demonstrated for a one-dimensional case, which is similar to the problem where the internucleon potential acts only in the relatives-state. The single particle potential has a harmonic oscillator form and the phenomenological internucleon potentialv(r) contains a hard core and an attractive part of the Yukawa type. By taking the exclusion principle into account exactly an infinite system of integral equations is obtained. It is proved that the solution of the corresponding finite system converges to the exact solution. An iteration method for solving such a finite system with an arbitrary number of equations is developed. Its main feature consists in the exclusion of the dependence on the hard core part ofv(r) (which is treated as the limit case of a rectangular repulsive potential with a variable heightv ₀). This exclusion transforms the original system to a system of integral equations depending only on the attractive part ofv(r) and to a linear algebraic system. Both these systems can be solved by iteration for all values ofv ₀ as well as for v₀= +. The numerical results confirm the rapid convergence of the proposed iteration method and demonstrate that the solution of the finite system with a sufficiently large number of equations approximates the exact solution very precisely.     

Shear Viscosity of Liquid‐Phase Yukawa Plasmas from Molecular Dynamics Simulations on Graphics Processing Units

We have carried out million‐particle equilibrium molecular dynamics simulations of 3‐dimensional Yukawa liquids in order to determine the shear viscosity coefficient. The computations have been executed on Graphics Processing Unit (GPU) architectures with our largely parallelized code. The results cover the strongly coupled liquid phase, with Γ up to the vicinity of the freezing transition, for the 1 ≤ κ ≤ 3 domain of the screening parameter of the Yukawa potential. The good agreement of the present results with those obtained from earlier simulations of significantly smaller systems (consisting of several hundred to several thousand particles) verifies that the viscosity data derived in these smaller scale simulations are also acceptable (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of overlapping Debye spheres on structures of 2D dusty plasmas

In dusty plasmas, overlapping Debye spheres around dust grains could produce an attractive force between them. Its effects on static structures of two-dimensional (2D) dusty plasmas are studied here by using molecular dynamics simulations. Results, in terms of the equilibrium radial distribution function, are compared with those deduced from purely repulsive Debye-Hückel or Yukawa potential for different Coulomb-coupling and screening parameters. The effect of the attractive force is found quite noticeable for usual experimental conditions, and becomes more pronounced for larger screening parameter κ. In particular, it is observed that for large κ the attractive force is dominant, and dust grains tend to aggregate and form patterns with scattering voids.     

Mixing and phase separation in molecular fluid mixtures

The equation of state for a hard convex body (HCB) fluid mixture, which is based on the scaled particle theory, is utilized to derive the Helmholtz free energy, F, and the concentration fluctuations, S.,(O), to investigate the thermodynamic stability of athermal and not athermal molecular fluid mixtures. The role of the size and the non-sphericity geometrical factor of the molecule on the stability of the mixture is critically examined. The energetics of long-range attractive forces for not athermal mixtures have been introduced through the double Yukawa potential in conjunction with a realistic distribution function. The formalism allows one to investigate the properties of molecular mixtures under induced conditions of extreme temperature and pressure. The results suggest that geometrical factors coupled with energetics play a dominant role in phase separation.     

Some constraints on the Yukawa parameters in the neutrino modification of the Standard Model (ν<Emphasis Type="Italic">MSM</Emphasis>) and CP-violation

The equations connecting elements of the Yukawa matrix to elements of the active neutrino mass matrix in the νMSM theory (an extension of the Standard Model by a singlet of three right-handed neutrinos) was analyzed, and explicit relations for the ratio of the Yukawa matrix elements and elements of the active neutrino mass matrix were obtained. This relation can be used for getting more accurate constraints on the model parameters. Particularly, with the help of the obtained results we investigated CP-violating phase in the νMSM theory. We demonstrate that even in the case when elements of the active neutrino mass matrix are real the baryon asymmetry can be generated also.     

Yukawa potentials in systems with partial periodic boundary conditions. I. Ewald sums for quasi-two-dimensional systems

Yukawa potentials are often used as effective potentials for systems such as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential; in this small screening limit, or Coulomb limit, the potential is long-ranged. As is well known in computer simulation, a simple truncation of the long-ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of space, has already been derived for the Yukawa potential [Molec. Phys. 88, 1357 (1996); J. Chem. Phys. 113, 10459 (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [J. Chem. Phys. 126, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. Special attention is paid to the Coulomb limit and its relation to the electroneutrality of systems.     

RESEARCH NOTE WCA repulsive and attractive contributions to the thermodynamic properties at the vapour-liquid equilibrium

The Lennard-Jones attractive and repulsive contributions of intermolecular forces (as separated in the Weeks-Chandler-Andersen (WCA) theory) to the pressure and chemical potential of coexisting vapour and liquid phases are obtained by using an equation of state recently proposed by us. Some comments are given about the computer simulation results obtained by Plackov and Sadus (1997, Fluid Phase Equilib., 134, 77) using the McQuarrie-Katz separation of the intermolecular potential.     

Quantum fluid-solid transition in a simple variational approach

A determinant (permanent) of plane waves for N fermions (bosons) in their lowest-energy state, and a determinant (permanent) of spatially-localized, nonoverlapping, single-particle functions are used to determine conditions on the short-ranged, square-well repulsive plus Yukawa attractive, two-body potential for which the spatially homogeneous or periodic particle-density states are energetically preferred. A considerable region in the coupling parameter-density plane is found where “crystalline” solutions are preferred. In particular, for purely repulsive forces, the low-density region for which the “fluid” solution is lowest shrinks to zero in the limit of infinitely repulsive cores, but faster for bosons than fermions. Inclusion of attractive forces is seen not to alter qualitatively the main results.     

Molecular dynamics study of two-and three-dimensional classical fluids using double Yukawa potential

We have carried out a molecular dynamics simulation of two- and three-dimensional double Yukawa fluids near the triple point. We have compared some of the static and dynamic correlation functions with those of Lennard—Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. However, when repulsive and attractive parameters occurring in double Yukawa potential are varied, we found distinct differences in static and dynamic correlation functions. We have also compared the two-dimensional correlation functions with those of three-dimensional to study the effect of dimensionality, near the triple point region.     

Kaonic atoms and the Λ(1405)

Kaonic shifts and widths for ¹²C and ³²S are analysed using an optical potential, which selectively incorporates nuclear shell structure aspects as well as effects of Λ(1405) dynamics inside the nucleus. Good agreement with data is found and suggests a moderately repulsive interaction of the Λ(1405) with surrounding nucleons.