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Bose-Einstein Condensation in liquid $^4$He near the liquid-solid transition line

We present precision neutron scattering measurements of the Bose-Einstein condensate fraction, n0(T), and the atomic momentum distribution, n\star(k), of liquid 4He at pressure p =24 bar. Both the temperature dependence of n0(T) and of the width of n\star(k) are determined. The n0(T) can be represented by n0(T) = n0(0)[1-(T/Tλ)γ] with a small n0(0) = 2.80\pm0.20% and large γ = 13\pm2 for T < Tλ indicating strong interaction. The onset of BEC is accompanied by a significant narrowing of the n\star(k). The narrowing accounts for 65% of the drop in kinetic energy below Tλ and reveals an important coupling between BEC and k > 0 states. The experimental results are well reproduced by Path Integral Monte Carlo calculations.