Structure functions of many-boson system with regard for direct three- and four-particle correlations

TL;DR

This paper calculates the structure factors of liquid helium-4 considering three- and four-particle correlations across various temperatures, bridging known low- and high-temperature limits, and aiding thermodynamic and sound velocity analyses.

Contribution

It introduces a comprehensive calculation of many-particle structure factors including higher-order correlations in a many-boson system, extending previous models.

Findings

Structure factors match known limits at low and high temperatures.

Results applicable to thermodynamic functions of liquid helium-4.

Provides temperature dependence of first-sound velocity.

Abstract

On the basis of the expression for the density matrix of interacting Bose particles in the coordinate representation with regard for the direct three- and four-particle correlations [I.O.\,\,Vakarchuk and O.I.\,\,Hryhorchak, J.\,\,Phys.\,\,Stud.\,\,\textbf{3}, 3005 (2009)], the two-, three-, and four-particle structure factors of liquid $^{4}$He in a wide temperature interval were calculated in the approximation "one sum over the wave vector".\,\,In the low-temperature limit, the expression obtained for the two-particle structure factor transforms into the well-known one.\,\,In the high-temperature limit, the expressions for the two-, three-, and four-particle structure factors are reduced to those for the ideal Bose gas.\,\,The results obtained can be applied to calculations of the thermodynamic functions of liquid $^{4}$He and to the determination of the temperature dependence of the first-sound velocity in a many-boson system.