Second virial coefficient for a d-dimensional Lennard-Jones (2n-n) system

In a previous article \cite{kn:anirban1} a method has been introduced to derive the all order Bose-Einstein distribution of the non interacting Bosons as the solution of the Wigner equation. The process was a perturbative one where the Bose-Einstein distribution was taken as the unperturbed solution. In this article it is shown that the same formalism is also applicable in the case of interacting Bosons. The formalism has been applied to calculate the quantum second virial co...

From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases which are trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in $d=3$ and $d=2$. But more importantly we found that, the virial coefficients of bosons and fermions become equal (except the the second virial coefficient, where the sign is different) when we trap t...

The second viral coefficient calculated using the equation suggested in the paper of Kaplun A.B., Meshalkin A.B. Equation for the second virial coefficient published in High temperature high pressure, 1999, Volume 31, pages 253-258 is compared with experimental data for helium, hydrogen, neon, argon, krypton, xenon, carbon dioxide, water, ammonia, methane, ethylene. It is shown the formula cannot describe the temperature dependence of the experimental data on the second viria...

The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to reproduce ground state properties at low temperature and the non-interacting large temperature limit of constant virial coefficients. This resembles the smearing of shell effects in fin...

We evaluate the virial coefficients B_k for k<=10 for hard spheres in dimensions D=2,...,8. Virial coefficients with k even are found to be negative when D>=5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D>=5. Further analysis provides evidence that negative virial coefficients will be seen for some k>10 for D=4, and there is a distinct possibility that negative virial coefficients will also event...

We present new results for the virial coefficients B_k with k <= 10 for hard spheres in dimensions D=2,...,8.

This paper investigates two conjectures for calculating the density dependence of the density-scaling exponent of a single-component, pair-potential liquid with strong virial potential-energy correlations. The first conjecture gives an analytical expression for the density-scaling exponent directly in terms of the pair potential. The second conjecture is a refined version of this, which involves the most likely nearest-neighbor distance determined from the pair-correlation fu...

It is shown that the interaction potentials for argon, krypton, xenon, carbon dioxide, ammonia, water, n-pentane, n-octane, 1-propanol, suggested in [1] cannot describe experimental second density virial coefficient data within their uncertainty over a wide temperature range.

In terms of the s-wave phase shift of the two-body scattering at thermal wavelength, a systematic perturbative expansion of the virial coefficients is developed for a two-dimensional dilute system of bosons in its gaseous phase at low temperature. The thermodynamic functions are calculated to the second order of the expansion parameter. The observability of the universal low energy limit of the two-dimensional phase shift with a quasi-two dimensional atomic gas in an anisotro...

A result from Dodd and Gibbs[1] for the second virial coefficient of particles in 1 dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be obtained from a phase shift formalism, if one includes the contribution of oscillating terms. The result is important in work to follow, for the third virial coefficient, for which a similar formalism is being developed. We examine a number of fi...