Atomic momentum distributions in condensed matter

Abstract

The theory of the momentum distribution function for atoms in condensed matter is reviewed and compared with results of deep-inelastic neutron-scattering experiments. We discuss, in particular, the case of classical and almost-classical liquids, harmonic and anharmonic crystals, and solid and liquid 4He. Except for liquid 4He in the superfluid phase, the momentum distribution is always Gaussian to a good approximation. In some cases this Gaussian behavior is of dynamical origin while, in others, it is a consequence of the central-limit theorem. The observed momentum distribution in superfluid 4He provides direct experimental evidence for the macroscopic occupation of the zero-momentum state and the value of the condensate fraction can be obtained.