CROSS-SECTIONAL MODEL FOR COLD NEUTRON-SCATTERING IN LIQUID-HE-4

The dynamics of liquid He-4 at all temperatures between 1.0 and 4.2 K is described in terms of a double-differential cross-sectional model f or cold neutron scattering. The major features of the model are as fol lows: decomposition into quasiparticle (phonon-roton) and density comp onents weighted with a temperature-dependent fraction of Bose condensa tion; transition of coherent scattering from a one-phonon Lorentzian p eak at small momentum transfer to a Gaussian shape of elastic scatteri ng by a free nucleus at large momentum transfer; and characterization with fundamental parameters such as excitation energy and its intrinsi c width for phonon and roton. Satisfactory agreement with experimental cross-sectional results, both double-differential and total, is obtai ned, which enables us to apply the present model for the quantitative evaluation of ultra-and very-cold neutron production.