Three-Particle Effects in the Pair Distribution Function forHe4Gas

Abstract

The diagonal elements of the three-particle density matrix for ${\mathrm{He}}^4$ have been formulated in terms of Wiener functional integrals in order to compute both that part of the pair distribution function linear in the density and the third virial coefficient. The three-particle interaction energy was taken to be a sum of Lennard-Jones (12-6) potentials between pairs of particles. Evaluation of the Wiener integrals was carried out by a Monte Carlo sampling technique to yield the pair distribution function and third virial coefficient for temperatures from 273 to 5°K. Comparison of the linear portion of the density expansion of the pair distribution function gave qualitative agreement with experimental values for the pair distribution function in liquid ${\mathrm{He}}^4$ measured by neutron diffraction. The values of the third virial coefficient calculated by this method are consistently smaller than the experimental values and consistently larger than the classical values of this quantity over the given temperature range.