Static and thermodynamic properties of low-density supercritical 4He—breakdown of the Feynman–Hibbs approximation

Abstract

We study the applicability of the semiclassical Feynman and Hibbs (FH) (second-order or fourth-order) effective potentials to the description of the thermodynamic properties of quantum fluids at finite temperatures. First, we use path integral Monte Carlo (PIMC) simulations to estimate the thermodynamic/static properties of our model quantum fluid, i.e. low-density ⁴He at 10 K. With PIMC we obtain the experimental equation of state, the single-particle mean kinetic energy, the single-particle density matrix and the single-particle momentum distribution of this system at low densities. We show that our PIMC results are in full agreement with experimental data obtained with deep inelastic neutron scattering at high momentum transfers (D. Colognesi, C. Andreani, R. Senesi, Europhys. Lett., 2000, 50, 202). As expected, in this region of the ⁴He phase diagram, quantum effects modify the width of the single-particle momentum distribution but do not alter its Gaussian shape. Knowing the exact values of density, pressure and single-particle mean kinetic energy for our model quantum fluid, we investigate the limitations of the semiclassical FH effective potentials. We show that commonly used ‘short-time’ approximations to the high-temperature density matrix due to Feynman and Hibbs can only be applied in a very limited range of the ⁴He phase diagram. We found that FH effective potentials reproduce the experimental densities of ⁴He at 10 K for Λ/a < 0.45 (Λ = 2.73 Å denotes the thermal de Broglie wavelength, a = ρ^−1/3 is the mean nearest-neighbor distance in the fluid and ρ denotes fluid density). Moreover, semiclassical FH effective potentials are able to correctly predict the single-particle mean kinetic energy of ⁴He at 10 K in a very limited range of fluid densities, i.e.Λ/a < 0.17. We show that the ad hoc application of the semiclassical FH effective potentials for the calculation of the thermodynamic properties of dense liquid-like para-hydrogen (para-H₂) adsorbed in nanoporous materials below 72 K is questionable.