Journal of Physical Studies 19(1/2), Article 1005 [14 pages] (2015)
DOI: https://doi.org/10.30970/jps.19.1005

## INTERNAL ENERGY OF THE MANY-BOSON SYSTEM WITH THREE- AND FOUR-PARTICLE DIRECT CORRELATIONS TAKEN INTO ACCOUNT

I. O. Vakarchuk, O. I. Hryhorchak

Department for Theoretical Physics, Ivan Franko National University of Lviv,
12, Drahomanov St., Lviv, UA-79005, Ukraine

In this paper we calculate the kinetic, potential and full internal energy with three- and four-particle direct correlations taken into account at the wide temperature region on the base of the density matrix of the interacting Bose-particles [I. O. Vakarchuk, O. I. Hryhorchak, J. Phys. Stud. {\bf 13}, 3004 (2009)]. All the final formulae are written via the Fourier coefficient of the pair interparticle interaction energy. At the same time we are not interested in the explicit form of the interatomic potential because for our numeric calculations we express its Fourier coefficient from the experimentally measured structure factor and first sound velocity extrapolated to $T=0$. The found values for the kinetic, potential and full internal energy demonstrate that the accounting of three- and four-particle direct correlations gives a better matching of the theoretical results with the experimental data. In the low temperature limit the obtained expression for the full internal energy is equal to the well-known expression for the ground state energy in the approximation of two sums over the wave vector''. For the high temperatures in the quasi-classical limit the found expression for the full internal energy reproduces the ideal gas energy expression.

The results of this work can be applied for the numeric calculation of the heat capacity of the liquid $^4$He in order to check the theoretical and experimental results quantitatively, especially in the $\lambda$-transition region.

PACS number(s): 05.30.Jp, 67.25.bd, 67.25.de