Boson localization and excitations of liquid 4He confined in gelsil

We present neutron scattering measurements of the phonon-roton (P-R) modes of liquid He-4 at saturated vapor pressure confined in 44 A mean pore diameter gelsil in the wave vector range 0.4 <= Q <= 2.15 A(-1). Layer modes, modes which propagate in the liquid layers adjacent to the porous media walls, were also observed at wave vectors in the roton region (Q similar or equal to 1.95 A(-1)) but not at Q less than or similar to 1.7 A(-1). The first goal is to document the filling dependence of the dynamic response and of the P-R mode energies and widths more systematically than has been done in the past. As the gelsil is filled with He-4, the P-R and layer modes are first observed at a fractional filling of f=76% at low temperature (T=0.4 K). At fillings f=76%, the P-R mode energies lie below the bulk superfluid He-4 values in the wave vector range 0.4 <= Q <= 1.7 A(-1), especially at Q similar or equal to 1.1 A(-1), as observed in helium films. As filling is increased, the intensity in the P-R mode increases markedly and the P-R mode energies move toward bulk superfluid values taking bulk values at full filling. The second goal is to determine the temperature dependence of the intensity in the P-R modes in a media in which the superfluid-normal transition temperature T-c=1.92 K is independently known and lies well below the bulk liquid value T-lambda=2.17 K. As temperature is increased, the intensity in the P-R and layer modes decreases. However, a well-defined P-R mode is observed at temperatures up to T similar or equal to 2.15 K, above T-c=1.92 K. Since well-defined modes exist because there is Bose-Einstein condensation (BEC), this suggests that there is BEC above T-c, probably localized. Localized BEC appears to exist up to T similar or equal to T-lambda.