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

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.