Quantum Momentum Distributions

In classical systems, the atomic momentum distribution (AMD) is always the renowned Maxwell–Boltzmann distribution.1,2 Essentially, the atomic momentum p = k and atomic position r are independent, canonical variables and the momentum distribution n(k) is always a Gaussian independent of the interatomic or any external potential. Neutron scattering measurements3–10 have shown that n(k) for atoms in liquid 4He, solid 4He and liquid neon5,6 differs significantly from a Gaussian. In these quantum systems there is a larger percentage of low-momentum atoms leading to an n(k) that is more sharply peaked around k = 0 than in a Gaussian. The deviation from a Gaussian is particularly pronounced in liquid and solid helium because these are highly quantum systems. The n(k) in liquid neon is nearly Gaussian because liquid neon is nearly a classical liquid. The measurements were chiefly carried out on the MARI instrument at the ISIS neutron scattering facility, UK, which has a high energy resolution option. This makes measurement of the intrinsic shape of n(k) of helium possible independent of the instrument resolution