Further Computations of Quantum Fluid Triplet Structures at Equilibrium in the Diffraction Regime

Path integral Monte Carlo simulations and closure computations of quantum fluid triplet structures in the diffraction regime are presented. The systems selected are helium-3 under supercritical conditions and the quantum hard-sphere fluid on its crystallization line. The fourth-order propagator in the form given by Voth et al (helium-3) and Cao-Berne’s pair action (hard spheres) are employed in the path integral simulations; helium-3 interactions are described with Janzen-Aziz’s pair potential. The closures used are Kirkwood superposition, Jackson-Feenberg convolution, the intermediate AV3, and the symmetrized form of Denton-Ashcroft approximation. The centroid and instantaneous triplet structures, in the real and the Fourier spaces, are investigated by focusing on salient equilateral and isosceles features. To accomplish this goal, complementary simulations and closure calculations at the structural pair level are also carried out. The basic theoretical and technical points are described in some detail, the obtained results complete the structural properties reported by this author elsewhere for the abovementioned systems, and a meaningful comparison between the path integral and the closure results is made. The present works intends to shed some more light on the incipient general knowledge of this topic (e.g., the very slow convergence of path integral calculations, the behavior of certain salient Fourier components, such as the double-zero momentum transfers or the equilateral maxima, etc.). Also, closures are proven to provide valuable information on these computationally demanding quantum problems, over a wide range of conditions and at a much lower cost. Thus, the study with and the further development of closure approaches, in the real and the Fourier spaces, do appear as targets well-worth pursuing in this context.