Atomic momentum distribution and Bose-Einstein condensation in liquid4He under pressure

Abstract

Neutron-scattering measurements of the dynamic structure factor, $S(Q,\ensuremath{\omega})$, of liquid ${}^{4}$He as a function of pressure at high-momentum transfer, $\ensuremath{\hbar}Q$, are presented. At high $\ensuremath{\hbar}Q$ the dynamics of single atoms in the liquid is observed. From $S(Q,\ensuremath{\omega})$ the atomic momentum distribution, $n(\mathbf{k})$, the Bose-Einstein condensate fraction, ${n}_{0}$, and the final-state (FS) broadening function are obtained. The shape of $n(\mathbf{k})$ differs from a classical, Maxwell-Boltzmann distribution with higher occupation of low-momentum states in the quantum liquid. The width of $n(\mathbf{k})$ and the atomic kinetic energy, $\ensuremath{\langle}K\ensuremath{\rangle}$, increase with pressure but the shape of $n(\mathbf{k})$ remains approximately independent of pressure. The present observed and Monte Carlo (MC) calculations of $\ensuremath{\langle}K\ensuremath{\rangle}$ agree within error. The condensate fraction decreases from ${n}_{0}=7.25%\ifmmode\pm\else\textpm\fi{}0.75$% at saturated vapor pressure ($p\ensuremath{\simeq}$ 0) to ${n}_{0}=3.2%\ifmmode\pm\else\textpm\fi{}0.75$% at pressure $p=24$ bar, a density dependence that is again reproduced by MC calculations within observed error. The FS function is the contribution to $S(Q,\ensuremath{\omega})$ arising from the interaction of the struck atom with its neighbors following the scattering. The FS function broadens with increasing pressure reflecting the increased importance of FS effects at higher pressure.