Abstract
We present precision neutron scattering measurements of the Bose-Einstein condensate fraction, $n_0(T)$, and the atomic momentum distribution, $n^{\star}({\bf k})$, of liquid $^4$He at pressure $p=$24 bar. Both the temperature dependence of $n_0(T)$ and of the width of $n^{\star}({\bf k})$ are determined. The $n_0(T)$ can be represented by $n_0(T) = n_0(0) [1 - (T/T_\lambda )^\gamma]$ with a small $n_0(0) = 2.80 \pm 0.20$ \% and large $\gamma = 13\pm 2$ for $T < T_\lambda$ indicating strong interaction. The onset of BEC is accompanied by a significant narrowing of the $n^\star({\bf k})$. The narrowing accounts for 65 \% of the drop in kinetic energy below $T_{\lambda}$ and reveals an important coupling between BEC and $k >0$ states. The experimental results are well reproduced by Path Integral Monte Carlo calculations.
