Calculation of the one-particle and two-particle condensates in He-II at T=0

TL;DR

This paper calculates the one- and two-particle condensates in superfluid helium-4 at zero temperature using a parameter-free collective variables method, providing results consistent with experimental data.

Contribution

It introduces a parameter-free approach based on collective variables to compute condensates in He-II, including three-particle corrections.

Findings

Calculated N_1=0.27N and N_2=0.53N in Jastrow approximation.

Including three-particle correction yields N_1=0.06N and N_2=0.16N, matching experiments.

Higher s-particle condensates are absent at T=0.

Abstract

We analyze the microstructure of He-II in the framework of the method of collective variables (CV), which was proposed by Bogolyubov and Zubarev and was developed later by Yukhnovskii and Vakarchuk. The logarithm of the ground-state wave function of He-II, ln(Psi_0), is calculated in the approximation of "two sums", i.e., as a Jastrow function and first (three-particle) correction. In the CV method equations for Psi_0 are deduced from the N-particle Schro'dinger equation. We also take into account the connection between the structure factor and Psi_0, which allows one to obtain Psi_0 from the structure factor of He-II, not from a model potential of interaction between He-II atoms. It should be emphasized that the model does not have any free parameters or functions. The amount of one-particle (N_1) and two-particle (N_2) condensates is calculated for the ground state of He-II: we find N_1=0.27N and N_2=0.53N in the Jastrow approximation for Psi_0, and, taking into account the three-particle correction to ln(Psi_0), we obtain N_1=0.06N (which agrees with the experiment) and $N_2=0.16N. In the approximation of "two sums", we also find that the higher s-particle condensates (s>2) are absent in He-II at T=0.