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

We study the applicability of the semiclassical Feynman and Hibbs (FH) (second-order orfourth-order) effective potentials to the description of the thermodynamic properties of quantumfluids at finite temperatures. First, we use path integral Monte Carlo (PIMC) simulations toestimate the thermodynamic/static properties of our model quantum fluid, i.e. low-density 4He at10 K. With PIMC we obtain the experimental equation of state, the single-particle mean kineticenergy, the single-particle density matrix and the single-particle momentum distribution of thissystem at low densities. We show that our PIMC results are in full agreement with experimentaldata 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 4Hephase diagram, quantum effects modify the width of the single-particle momentum distributionbut do not alter its Gaussian shape. Knowing the exact values of density, pressure andsingle-particle mean kinetic energy for our model quantum fluid, we investigate the limitationsof 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 beapplied in a very limited range of the 4He phase diagram. We found that FH effective potentialsreproduce the experimental densities of 4He at 10 K for L/a o 0.45 (L = 2.73 A ° denotes thethermal de Broglie wavelength, a = r1/3 is the mean nearest-neighbor distance in the fluid andr denotes fluid density). Moreover, semiclassical FH effective potentials are able to correctlypredict the single-particle mean kinetic energy of 4He at 10 K in a very limited range of fluiddensities, i.e. L/a o 0.17. We show that the ad hoc application of the semiclassical FH effectivepotentials for the calculation of the thermodynamic properties of dense liquid-like para-hydrogen(para-H2) adsorbed in nanoporous materials below 72 K is questionable