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.
Efficient implementation of the Hellmann-Feynman theorem in a diffusion Monte Carlo calculation.
Kinetic and potential energies of systems of (4)He atoms in the solid phase are computed at T = 0. Results at two densities of the liquid phase are presented as well. Calculations are performed by the multiweight extension to the diffusion Monte Carlo method that allows the application of the Hellmann-Feynman theorem in a robust and efficient way. This is a general method that can be applied in other situations of interest as well.
Direct measurements and path integral Monte Carlo calculations of kinetic energies of solid neon
Direct measurements are reported of the kinetic energies of FCC neon at seven temperatures between 4.25 and 20.2 K. The measurements employed the electronvolt spectrometer which is the neutron scattering instrument at the ISIS neutron source, UK. Wavevector transfers Q from 306 to were used, far larger than previously, in a regime where possible final-state-effect corrections to the observed longitudinal neutron Compton profile J(y) are easily deal with by a simple correctional procedure. The results are of comparable precision with the best previous work, carried out using the HRMECS instrument at IPNS, Argonne. From those previous measurements, Peek et al give a ground-state kinetic energy of . Path-integral Monte Carlo calculations were performed using both HFD-C2 and Lennard-Jones pair potentials. At 4.13 K, 10.13 K, 15.69 K and 20.31 K the HFD results were , , and , respectively. These values are broadly in agreement with the current measurements. They are significantly lower than the published values obtained from an HFD-based Wigner - Kirkwood high-temperature expansion including terms up to .