Evaluation of cold-neutron scattering cross sections for liquid 4He at temperatures between 1 and 4.2 K

Cold neutron scattering from liquid 4He at temperatures between 1.0 and 4.2K is evaluated in terms of a simple cross-section model. The model is developed to illustrate some fundamental excitations in superfluid and normal 4He, such as phonon-roton (quasiparticle) excitations at low temperatures T≤Tλ, density ones at all T and also recoil scattering from a free 4He atom for high incident neutron energies E0. This enables us to apply the present model for a wide range of E0, say, from 0.1 μeV to 10 eV. The temperature dependence of the cross-section model is examined with some experimental results, both double-differential and total, and found to be in satisfactory agreement for various T and E0. On the basis of these results, a discussion is given of ultra-cold neutron production in superfluid 4He.