Bose-Einstein condensation in solid 4He.

We present neutron scattering measurements of the atomic momentum distribution n(k) in solid helium under a pressure p=41 bar (molar volume Vm=20.01+/-0.02 cm3/mol) and at temperatures between 80 and 500 mK. The aim is to determine whether there is Bose-Einstein condensation (BEC) below the critical temperature, Tc=200 mK, where a superfluid density has been observed. Assuming BEC appears as a macroscopic occupation of the k=0 state below Tc, we find a condensate fraction of n0=(-0.10+/-1.20)% at T=80 mK and n0=(0.08+/-0.78)% at T=120 mK, consistent with zero. The shape of n(k) also does not change on crossing Tc within measurement precision.

One-dimensional and two-dimensional quantum systems on carbon nanotube bundles.

We report the first measurement of the structure of 4He atoms adsorbed on bundles of single-walled carbon nanotubes. Neutron diffraction techniques and nanotube samples closed at the end were used. At low coverage, 4He forms a 1D, single line lattice along the grooves between two nanotubes on the surface of the nanotube bundles. As coverage is increased, additional lines of 1D lattices form along the grooves. This is followed by an incommensurate, 2D monolayer covering the whole nanotube bundle surface. The lattice constants of these 1D and 2D systems are largely independent of filling once a single 1D line is formed. No occupation of the interstitial channels between nanotubes is observed in the present sample.

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

Neutron scattering measurements of the fundamental excitations of liquid 4He confined in 44 A pore diameter gelsil glass at pressures up to 40 bars in the wave vector range 0.41.6 A(-1), especially the rotons, are observed up to complete solidification of all the liquid at a pressure of approximately 40 bars where the roton vanishes. At and above a pressure of 35.1 bars, Bragg peaks are observed, indicating coexistence of liquid and solid in the pores at pressures 35 less than or approximately equal P less than or approximately equal 40 bars.

Quantum momentum distribution and kinetic energy in solid 4He.

We present measurements of neutron scattering from solid 4He at high momentum transfer. The solid is held close to the melting line at molar volume 20.87 cm3/mol and temperature T=1.6 K. From the data, we determine the shape of the momentum distribution, n(k), of atoms in the solid and the leading final state contribution to the scattering. We show that n(k) in this highly anharmonic, quantum solid differs significantly from a Gaussian. The n(k) is more sharply peaked with larger occupation of low momentum states than in a Maxwell-Boltzmann distribution, as found in liquid 4He and predicted qualitatively by path integral Monte Carlo calculations. The atomic kinetic energy is =(24.25+/-0.30) K. If n(k) is assumed to be Gaussian, as is usually the practice, a 10% smaller is obtained.