VQLUME S4, NUMBER 9 PHYSICAL REVIEW LETTERS 4 MARCH 198S High-Momentum-Transfer Inelastic Neutron Scattering from Liquid Helium-3 P. E. Sokol(') Department of Physics, University of Illinois at Urbana Cha-mpaign, Urbana, Illinois 61801 and K. Skold The Studsvik Science Research Laboratory, S-61182 Nykoping, Sweden and D. L. Price and R. Kleb Materials Science and Technology Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received 9 August 1984) The inelastic scattering of neutrons by liquid He at 0.2 K saturated vapor pressure has been mea- 0 ] 0 sured for momentum transfers in the range 10 A & Q & 16 A . The observed scattering func- tion is well described, within statistical uncertainties, by a Gaussian centered at the recoil energy. The average kinetic energy per atom, obtained from the width of the scattering function, is 8. 1+I 3 K. PACS numbers: 67.50.Dg, 61.12. Fy Liquid He at low temperatures is a degenerate Fer- mi liquid of considerable experimental and theoretical interest. One of the unique features of degenerate Fermi systems is that the single-particle momentum distribution n (p) has a discontinuity at the Fermi en- ergy EF if the interaction between the particles is not too strong. A direct observation of n (p) would be of great help in evaluating theoretical calculations of the ground state in the liquid. In the absence of a direct observation of the shape of n (p), information on the moments, one of which gives the average kinetic ener- gy per atom, is of great use since they may be com- pared to theoretical calculations. Information about n(p) can be obtained from in- elastic neutron scattering experiments. At sufficiently large values of the momentum transfer 0, only single-particle scattering is observed. The dynamic structure factor S(Q, E) may then be calculated using the impulse approximation (IA) and is given by $202 h 2 S(Q, E) =„'I n(p)8 E — — Q p d p, (1) where M is the mass of the particles constituting the scattering system. Recent measurements' on liquid and solid 4He have shown that the IA is valid for momentum transfers above 10 A ' and that the single-particle momentum distribution may be ob- tained from the observed S(Q, E). Analogous experi- ments using x rays have been made to study n (p) of electrons in metals and have observed the discontinui- ty at the Fermi surface. 2 We report here the first neutron scattering measure- ments on liquid He at high momentum transfer. The experiment was carried out with the low-resolution medium-energy chopper spectrometer (LRMECS) at the Intense Pulsed Neutron Source at Argonne. LRMECS is a time-of-flight spectrometer with a chopper before the sample to monochromatize the pulsed white beam from the spallation neutron source. The chopper-source phasing was chosen such that neu- trons of energy 260 meV were selected. Time-of-flight spectra for scattered neutrons were observed at four- teen scattering angles between 58. 8' and 116. 4', corre- sponding to momentum transfers in the range 10 A-1 to 16 A ' for neutrons scattered from freely recoiling 3He atoms. The large neutron-absorption cross section of the 3He nucleus complicates the experiment, because to correctly remove the scattering from the cell we must be able to do an empty-cell run without observing scattering from the parts of the cell obscured by the sample. The optimal configuration in this case is to FIG. 1. Cell geometry used in this work; the inset illus- trates how the cadium slats prevent scattering from the back of the cell from reaching the detectors. Qc 1985 The American Physical Society 909