Deep Inelastic Neutron Scattering Study of Nanoconfined Liquid Helium Mixtures*

The single-particle momentum distribution $n(p)$ plays a central role in the contemporary understanding of quantum many- body systems, especially the helium liquids. The superfluid behavior of liquid He$^{4}$ below the famous lambda-point temperature is associated with the Bose condensation of a macroscopic fraction of the He$^{4}$ atoms to the zero momentum state. This manifests itself in $n(p)$ as a $\delta$-function singularity at $p = 0$. Similarly, the Fermi liquid character of He$^{3}$ is associated with a sharp discontinuity in the Fermi surface at the Fermi momentum $p_{F}$. Using the Wide Angular Chopper Spectrometer at the Spallation Neutron Source, we recently carried out a deep inelastic neutrons scattering study of dilute He$^{3}$ + He$^{4}$ solutions confined in mesoporous MCM-41 in order to investigate the effects of confinement on the non-classical momentum distribution of an isotopic helium solution. The Bose condensate fraction, Fermi surface, average isotopic kinetic energies, and related work in the literature will be discussed.