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.
Neutron measurements of the single-particle kinetic energies in solid neon
Direct measurements of the mean atomic kinetic energy of solid neon have been made at 16 temperatures in the range 5-22 K and saturated vapor pressure. The measurements were made at high momentum and energy transfers using the technique of neutron Compton scattering. These extensive data have been compared with published calculations, and there is general agreement. The ground-state kinetic energy in condensed neon has been determined to be 41(2) K.
Deep Inelastic Neutron Scattering in the Study of Atomic Momentum Distributions
Abstract The electron-volt spectrometer (EVS) at the pulsed neutron source facility (ISIS) is being developed for the study of atomic momentum distributions. Neutrons with energies in the range 1 to 100 eV are incident on the sample, and the time-of-flight (TOF) spectrum of the scattered beam is measured by an array of fixed detectors. A resonant foil difference technique is used to yield a set of TOF spectra for those neutrons scattered into a fixed energy and through fixed angles. Information on the momentum distribution of the target nuclei can be deduced within an impulse approximation in a procedure analogous to that in Compton scattering of electrons by photons. Crystalline compounds containing aligned hydrogen bonds and other hydrogenous compounds are of particular interest owing to the high cross-section of the proton at these neutron energies. With improved statistical accuracy of the data it is anticipated that deviations of the proton's potential from a harmonic potential may be determined. Non-hydrogenous systems have also been investigated. A description is given of the basic theory and interpretive method. Data obtained on numerous systems are presented and discussed.