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.
Solvation of molecules in superfluid helium enhances the "interaction induced localization" effect.
Atomic nuclei become delocalized at low temperatures as a result of quantum effects, whereas they are point-like in the high temperature (classical) limit. For non-interacting nuclei, the delocalization upon lowering the temperature is quantitatively described in terms of the thermal de Broglie wavelength of free particles. Clearly, light non-interacting nuclei--the proton being a prominent one--are much more delocalized at low temperatures compared to heavy nuclei, such as non-interacting oxygen having water in mind. However, strong interactions due to chemical bonding in conjunction with ultra-low temperatures characteristic to superfluid helium nanodroplets change this common picture substantially for nuclei in molecules or clusters. It turns out that protons shared in hydrogen bonds undergo an extreme "interaction induced localization" at temperatures on the order of 1 K, which compresses the protonic spatial distributions to the size of the much heavier donor or acceptor atoms, such as O or Cl nuclei, corresponding to about 0.1% of the volume occupied by a non-interacting proton at the same temperature. Moreover, applying our recently developed hybrid ab initio path integral molecular dynamics/bosonic path integral Monte Carlo quantum simulation technique to a HCl/water cluster, HCl(H2O)4, we find that helium solvation has a significant additional localizing effect of up to about 30% in volume. In particular, the solvent-induced excess localization is the stronger the lesser the given nucleus is already localized in the gas phase reference situation.
KINETIC ENERGY OF SOLID NEON BY MONTE CARLO WITH IMPROVED TROTTER AND FINITE-SIZE EXTRAPOLATION
The kinetic energy of solid neon is calculated by a path-integral Monte Carlo approach with a refined Trotter and finite-size extrapolation. These accurate data present significant quantum effects up to temperature $T=20$ K. They confirm previous simulations and are consistent with recent experiments.