Wigner-Kirkwood expansion: Calculation of "almost classical" static properties of a Lennard-Jones many-body system.

Abstract

We have applied the Wigner--distribution-function formalism for the determination of the quantum corrections, which appear in the \ensuremath{\Elzxh} series expansion of the various ``almost classical'' properties of a many-body system. We have calculated the various averages which appear in the quantum corrections by means of molecular-dynamics computer simulation, up to the order ${\ensuremath{\Elzxh}}^{6}$ for the case of Boltzmann particles interacting via a Lennard-Jones potential. Here we report the results of the calculation for the potential and kinetic energies, for the pressure, for the free energy, and for the radial distribution function g(r) at nine different thermodynamic points. The application to the case of He, Ne, Ar, ${\mathrm{H}}_{2}$, and ${\mathrm{D}}_{2}$ are given whenever the \ensuremath{\Elzxh} series expansion can be considered convergent. The advantages and disadvantages of our method are also discussed.