Modes of Atomic Motions in Liquid Helium by Inelastic Scattering of Neutrons

Abstract

The wavelength distribution of ${4.03}_{9}$A neutrons scattered inelastically by specimens of liquid helium has been measured at 30 angles of scattering in the range 10\ifmmode^\circ\else\textdegree\fi{} to 140\ifmmode^\circ\else\textdegree\fi{}. At each angle of scattering there is a discrete peak which shows little broadening, and little if any excess scattering outside this peak. The changes in energy and momentum corresponding to the change in wavelength of the scattered neutrons have been calculated for each angle of scattering. The dispersion curve in the liquid is similar in form to that predicted theoretically but there are differences in detail. For momentum changes ($\ensuremath{\hbar}Q$) in the range $0.26 {\mathrm{A}}^{\ensuremath{-}1}\ensuremath{\le}Q\ensuremath{\le}0.6 {\mathrm{A}}^{\ensuremath{-}1}$, the measurements fall on a straight line which has a slope given by the velocity of sound. The maximum and the minimum of the curves occur at 1.10 ${\mathrm{A}}^{\ensuremath{-}1}$ and 13.7\ifmmode^\circ\else\textdegree\fi{}K and at 1.91 ${\mathrm{A}}^{\ensuremath{-}1}$ and 8.65\ifmmode^\circ\else\textdegree\fi{}K, respectively. Beyond the minimum the curve starts to rise with a slope equal to or less than the phonon branch and then falls below this, suggesting the possible existence of a second maximum. The relative partial differential cross section for the production of a single phonon excitation is low at low momenta, has a maximum in the region of 2.0 ${\mathrm{A}}^{\ensuremath{-}1}$ and then decreases rapidly to low values in the region of 2.68 ${\mathrm{A}}^{\ensuremath{-}1}$. The position of the maximum may be compared with 2.05 ${\mathrm{A}}^{\ensuremath{-}1}$, the maximum in the total differential cross-section curve and 1.91 ${\mathrm{A}}^{\ensuremath{-}1}$, the minimum of the dispersion curve, respectively. The widths and mean energy change of neutrons scattered through 80\ifmmode^\circ\else\textdegree\fi{} have been measured at 13 temperatures in the range 1.78\ifmmode^\circ\else\textdegree\fi{}K to 4.21\ifmmode^\circ\else\textdegree\fi{}K. Scattering at this angle corresponds to the production of excitations at the minimum of the dispersion curve. The mean energy change decreases rapidly from a value of ${8.6}_{5}$\ifmmode^\circ\else\textdegree\fi{}K at 1.1\ifmmode^\circ\else\textdegree\fi{}K to 5.6\ifmmode^\circ\else\textdegree\fi{}K at the $\ensuremath{\lambda}$ temperature where there is a marked change in slope and only a much slower decrease above the $\ensuremath{\lambda}$ temperature to 4.9\ifmmode^\circ\else\textdegree\fi{}K at 4.2\ifmmode^\circ\else\textdegree\fi{}K. The widths of the spectra increase rapidly from a value of 1\ifmmode^\circ\else\textdegree\fi{}K at 1.1\ifmmode^\circ\else\textdegree\fi{}K to 11\ifmmode^\circ\else\textdegree\fi{}K at the $\ensuremath{\lambda}$ temperature where there is also a marked change in slope and only a much slower increase to about 15\ifmmode^\circ\else\textdegree\fi{}K at 4.2\ifmmode^\circ\else\textdegree\fi{}K. The measured widths are compared with theoretically calculated widths.