Fluids of general hard triatomic molecules

The second, third, and fourth virial coefficients, B_i , of a fluid of general symmetric hard triatomic molecules (fused hard spheres) have been calculated both numerically and theoretically for a variety of potential parameters. It has been found that: (i) for B₂ a valency angle ω_c exists such that for ω>w_c, B ₂ is independent of ω, (ii) B ₃ is very flat for ω>w_c, and (iii) B ₄ exhibits a maximum at ω～π/2. Theoretical calculations employing an assigned convex body fit very well the second and fairly well the third virial coefficients, but fail for the fourth except in the case of a linear molecule.     

Equations of state for the hard disk fluids

By using the published accurate new virial coefficients B₁₁～B₁₄ for the hard disk fluids [C. Zhang and B.M. Pettitt, Mol. Phys., 2014, 112, 1427], we here propose a new updated version of Tian-Gui-Mulero equation of state [J.X. Tian, Y.X. Gui and A. Mulero, Phys. Chem. Chem. Phys., 2010, 12, 13597]. Compared with other proposals, the new version stands strongly to be the only which can reproduce the known virial coefficients B₂～B₁₃ at the same time that can describe the relation of the compressibility factor versus the packing fraction for the hard disk fluids with high accuracy.     

The fifth virial coefficients of fused hard sphere fluids

The virial coefficients up toB ₅ of 34 fused hard sphere models have been computed using about (4–10)×10⁵ trial configurations of a modified Monte Carlo integration method. The principle of the conformal behaviour of hard particle systems is tested against these data. It is found that while for the fourth coefficient the principle is satisfied in all the cases, the fifth coefficients exhibit more complicated behaviour and do not conform, in general, to this principle.     

Negative Virial Coefficients and the Dominance of Loose Packed Diagrams for D-Dimensional Hard Spheres

We study the virial coefficients B _k of hard spheres in D dimensions by means of Monte-Carlo integration. We find that B ₅ is positive in all dimensions but that B ₆ is negative for all D≥6. For 7≤k≤17 we compute sets of Ree–Hoover diagrams and find that either for large D or large k the dominant diagrams are “loose packed.” We use these results to study the radius of convergence and the validity of the many approximations used for the equations of state for hard spheres.     

A quasi analytical method for the calculation of virial coefficients for realistic intermolecular potentials

The difficulties of accurately representing the Ursell function, f, for molecules interacting with a Lennard-Jones potential by a hard sphere core and a truncated exponential series are discussed. The range of R for which a hard sphere approximates f with negligible error is established and the range of arguments in f is determined. The accuracy with which the exponential series, S_k , truncated after k terms, represents the function is established for several ranges of arguments. It is shown that it is possible to represent f accurately by a hard sphere core and S ₄ or S ₆ for all values of R except over a short range of R.

Values of B and C, accurate to within a few per cent, can be obtained analytically through approximating f by S ₄ or S ₆ and a hard core whose diameter is determined by the range of arguments for which the series is valid. More accurate values of B and C required additional approximations for f. Two of these, the repulsive square well and the Barker-Henderson radius, give accurate values of B and C at all temperatures that were examined.     

The second dielectric virial coefficient of a dipolar sticky hard sphere fluid

We calculate the second dielectric virial coefficient, B _?, of a fluid whose molecules are sticky hard spheres with embedded central point dipoles. The effect of stickiness is to increases B _? markedly.     

The second virial coefficient of quadrupolar dumbells

To study the effect of the shape of molecules on properties of polar fluids, the second pressure virial coefficient,B(T), of quadrupolar hard homonuclear dumbells is investigated both numerically and analytically. Convergence of the expansion ofB(T) about the hard dumbell reference is examined and a simple approximate analytic formula is derived which provides a good estimate ofB(T) for temperatures higher than the Boyle temperature,T _B. BelowT _B the examined expansion methods break down. Independently of the calculations ofB(T), an approximate analytic expression of the average Boltzmann factor of the model considered has been also derived.     

Overlap graph representation of B6 and B7

The virial coefficients B_n of the pressure of a thermodynamic system can be represented in terms of graphs. The recently defined overlap graphs are studied in detail. Furthermore, the overlap graph representation of the sixth and seventh virial coefficientsB ₆ andB ₇) is determined.     

Multilayer X-ray mirrors based on La/B<Subscript>4</Subscript>C and La/B<Subscript>9</Subscript>C

Multilayer X-ray mirrors that are based on La/B₄C and La/B₉C and intended for the reflection of X-ray radiation in the spectral region near λ = 6.7 nm are prepared and studied. Reflection coefficients at a level of 40–60% are achieved for mirrors with various periods. The difference in the interlayer roughnesses reconstructed from the data measured in the hard and soft X-ray spectral regions is explained using a structural model with an asymmetric permittivity profile in a mirror period. A proximate technique is developed to estimate the permittivity profile in a multilayer-structure period using reflectometry data. The effect of antidiffusion Sn, Cr, and Mo barriers on the reflection coefficient of multilayer La/B₄C structures is studied experimentally     

Resonance fluorescence spectrum of nitrogen dioxide

We report an investigation of the resonance fluorescence spectrum of NO₂ excited by several laser lines. Sixty transitions, mostly in ν₂ progressions of the ground state, have been assigned. Analysis of the spectra extend the knowledge of the ground state constants, especially of the anharmonic coefficients. It is possible to establish that transitions are occurring to a ²B₁ state and to a ²B₂ state in the same energy region.     

Molecular dynamics calculations of the hard-sphere equation of state

The equation of state of the hard-sphere fluid is studied by a Monte Carlomolecular dynamics method for volumes ranging from 25V ₀ to 1.6V ₀ , whereV ₀ is the close-packed volume, and for system sizes from 108 to 4000 particles. TheN dependence of the equation of state is compared to the theoretical dependence given by Salsburg for theNPT ensemble, after correction for the ensemble difference, in order to obtain estimates for the thermodynamic limit. The observed values of the pressure are compared with both the [3/2] and the [2/3] Padé approximants to the virial series, using Kratky's value for the fifth virial coefficientB ₅ and choosingB ₆ andB ₇, to obtain a least-squares fit. The resulting values ofB ₆ andB ₇ lie within the uncertainties of the Ree-Hoover-Kratky Monte Carlo estimates for these virial coefficients. The values ofB ₈,B ₉, andB ₁₀ predicted by our optimal [3/2] approximant are also reported. Finally, the Monte Carlo-molecular dynamics equation of state is compared with a number of analytic expressions for the hard-sphere equation of state.Work supported by the Office of Basic Energy Sciences, U.S. Department of Energy.     

Structure of the superconducting state of superconductors near the critical field Hc2 for values of the Ginzburg-Landau parameter kclose to unity

It is shown that near the transition temperature T _c the coefficients of the second and third terms in the expansion of the free energy in powers of H _c2−B (B is the magnetic field induction inside the superconductor) go to zero simultaneously for a value of κ=1 for the Ginzburg-Landau parameter. Thereby the structure of the mixed state near H _c2 for a value of the parameter κ close to unity is determined by the temperature correction to the coefficient for the third power and the coefficient for the fourth power in the expansion of the free energy in powers of H _c2−B. The values of these coefficients depend on the type of vortex lattice. Zh. éksp. Teor. Fiz. 112, 1499–1509 (October 1997)     

The influence of intermolecular interactions on the Kerr effect in gases

Expressions are derived for the second and third Kerr virial coefficients, B _K and C _K, of spherical top molecules in terms of irreducible cluster polarizabilities, and values are calculated using the dipole-induced dipole model for argon, krypton, xenon, methane, tetrafluoromethane, neopentane and sulphur hexafluoride. For mixtures of rare gases it is shown that the collision-induced dipole moment makes a negligible contribution to B _K. The effect of the choice of intermolecular potential function on the calculated second Kerr virial coefficients is also demonstrated. It is found that the predominant contributions to C _K arise from the pair polarizability, and that the triplet polarizability is only of minor importance.     

Calculation of second Kerr effect virial coefficients of H2S

Second Kerr effect virial coefficients B _K of H₂S have been calculated using our recent molecular tensor theory of B _K for molecules of nonlinear symmetry. After optimization of the intermolecular potential interaction parameters and molecular quadrupole moment for H₂S, the calculated B _K values are seen to agree with the experimental values found in the literature to within 10% over the temperature range of the measured data. The components of the quadrupole moment tensor obtained by optimization are not in good agreement with the one set of calculated values reported in the literature.     

Collision-induced vibrational polarizability and mixed second refractivity virial coefficients B ab R: an experimental study of the SF6—rare gas mixtures

Mixed second refractivity virial coefficients B ^ab _R (ω) are determined in the infrared spectral range from the analysis of the buffer gas-induced intensity redistribution in the ν₃ absorption band at ω ? 930 cm^?1 of ³⁴SF₆ perturbed by the rare gases Ar, Kr, and Xe at relative densities up to 140 Amagat. The values of the refractivity virial coefficients are found to be several orders of magnitude greater than those observed in the spectral regions far removed from single-photon resonances. The undamped dynamic dipole—induced-dipole (DID) model is shown to qualitatively correctly reproduce the observed unusual dispersion of the B ^ab _R (ω) functions. A new estimate of the integrated band intensity S(ν₃) of SF₆ is also obtained.     

Heavy-flavour spectra in high-energy nucleus–nucleus collisions

The propagation of the heavy quarks produced in relativistic nucleus–nucleus collisions at RHIC and LHC is studied within the framework of Langevin dynamics in the background of an expanding deconfined medium described by ideal and viscous hydrodynamics. The transport coefficients entering into the relativistic Langevin equation are evaluated by matching the hard-thermal-loop result for soft collisions with a perturbative QCD calculation for hard scatterings. The heavy-quark spectra thus obtained are employed to compute the differential cross sections, the nuclear modification factors R _AA and the elliptic-flow coefficients v ₂ of electrons from heavy-flavor decay.     

Hadronic <Emphasis Type="Italic">B</Emphasis> decays in the MSSM with large tan <Emphasis Type="Italic">β</Emphasis>

We present an analysis of non-leptonic B decays in the minimally flavour-violating MSSM with large tan β. We relate the Wilson coefficients of the relevant hadronic scalar operators to leptonic observables, showing that the present limits on the B _s →μ ⁺ μ ⁻ and B ⁺→τ ⁺ ν _τ branching fractions exclude any visible effect in hadronic decays. We study the transverse helicity amplitudes of B→VV decays, which exhibit an enhanced sensitivity to the scalar operators, showing that even though an order one modification relative to the SM is not excluded in some of these amplitudes, they are too small to be detected at B factories. X.-Q. Li is a Alexander-von-Humboldt fellow.     

New results for virial coefficients of hard spheres inD dimensions

We present new results for the virial coefficientsB _k for κ<- 10 for hard spheres in dimensionsD = 2,..., 8.