On the calculation of the static structure factor of path-integral quantum simple fluids far from exchange

Abstract

This paper addresses several points of interest concerning the computation of the static structure factor of path-integral monatomic quantum fluids. First of all, the connection between the structure factor and the path-integral linear response pair radial correlation function is shown as its defining quantity by assuming a generalized Fermi's potential for the neutron-nuclei interactions, which is to be included in the general expression of the dynamic structure factor. Second, the possibilities of finding Ornstein-Zernike equations for full path-integral fluids, and also for the effective potential models of fluids derived from the path-integral formalism, are explored by working in the grand canonical ensemble. By so doing, the success and features for improvement of the weak-field approach used previously in this context of determining quantum static structure factors [SESÉ, L. M., 1996, Molec. Phys., 89, 1783; SESÉ, L. M., and LEDESMA, R., 1997, J. chem. Phys., 106, 1134] can be understood. New numerical applications are performed within this weak-field approach taking as probes the quantum hard-sphere fluid and dense fluid helium-4, the latter being described through Lennard-Jones and Aziz-Slaman underlying interactions. The results show that the structure factors associated with the linear response and instantaneous path-integral pair radial correlation functions differ noticeably from each other with increasing quantum effects. In particular, the linear response description leads to more compressible fluids than the instantaneous one. Besides, the equality between the isothermal compressibilities fixed via the linear response and the quantum particle centre-of-gravity pair radial correlation functions does not hold beyond the situations that can be treated with the Gaussian Feynman-Hibbs effective potential picture. Comparison with experiment in the case of helium-4 (T = 4.2 K) reveals clearly that, under strong quantum conditions, an operative framework more elaborate than the weak-field approach is needed.