High-Energy Neutron Scattering from Liquid ${\mathrm{He}}^4$

An experiment is proposed using high-energy neutrons to probe the momentum distribution of helium atoms in liquid helium, and detect the presence of a zero-momentum condensate below $T_{\lambda }$. It is suggested that for momentum transfers to the neutron much larger than a roton momentum, the energy transfer should be equal to the recoil energy of a single helium atom, Doppler-shifted by its initial motion in the helium bath. Thus, if a finite fraction of atoms are initially in the zero-momentum state, they will contribute a peak to the spectrum of scattered neutrons. Corrections due to final-state interactions are discussed briefly and estimated.