Excitations of metastable superfluid $^4$He at pressures up to 40 bars

We have performed neutron scattering measurements~${^{[1]}}$ of the fundamental excitations of liquid $^4$He confined in 44 {\AA} pore diameter gelsil glass at pressures up to 40 bars in the wave vector range 0.4 $$ 1.6 {\AA}$^{-1}$, especially the rotons, are observed up to complete solidification of all the liquid at $p\sim$ 40 bars, where the roton disappears. Simultaneous neutron diffraction measurements show the existence of Bragg peaks at and above 35.1 bars, indicating co-existence of liquid and solid in the pores at pressures $35 \leq p \leq$ 40 bars. These measurements are presented in conjunction with a measurement of the phase diagram of this system using ultrasound. %$\lesssim P\lesssim$ \vspace{.5cm} \\ ${^{[1]}}$J. V. Pearce et al. Phys. Rev. Lett. 93, 145303 (2004)