Condensed phase of liquidHe4

Abstract

The long-range order of the one- and two-body density matrices is analyzed for the ground state of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ described by suitable Jastrow wave functions $\Psi =\Pi {i<j}^{}\left[f\right(r_{\mathrm{ij}}\left)\right]$. The condensate fraction, pairing function, pairing energy, and related quantities are calculated as functions of density. The evaluations are performed within the diagrammatic formalism developed by Ristig and Clark. For the most part we employ the optimal correlation functions $f\left(r\right)\mathrm{}$ and associated radial distribution functions $g\left(r\right)\mathrm{}$. Both quantities are determined self-consistently by performing a paired-phonon analysis. The numerical treatment is based on the hypernetted-chain procedure for the structure function as well as for the one-body density matrix. The condensate fraction is found to be 0.113 at the experimental equilibrium value of the particle density, and shrinks to a value ∼0.05 at densities in the solidification region of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The pairing functions show remarkable intermediate structure. The pairing energy is negative, about -50 mK at saturation density, and increases rapidly with increasing density. It changes sign at a density close to the experimental melting point. It is found that the condensate fraction depends only weakly on temperature in the range of temperatures considered.