Momentum distributions and final-state effects in neutron scattering

A method for analyzing neutron-scattering data at intermediate and high-momentum transfer in liquids and solids is proposed. The aim is to separate the observed dynamic structure factor, S(Q,{ω}), into its impulse-approximation (IA) and final-state (FS) parts. When the separation is made, both the IA and FS effects can be determined from the data. The method is based on a cumulant expansion of the intermediate scattering function, S(Q,t), in powers of t. The expansion parameters are determined by fitting the corresponding S(Q,{ω}) to the data. Using the parameters, the IA and FS function are reconstructed. Variants of the method suitable for systems in which momentum distribution is (1) close to a Gaussian and (2) differs markedly from a Gaussian are proposed. The first variant is applied to recent data of Andersen et al. in normal ⁴He at saturated vapor pressure and T=2.5 K and the kinetic energy, momentum distribution, and the FS broadening function are determined. In the second variant a model momentum distribution is introduced. This is applied to superfluid ⁴He using a model n(k) having a condensate. The model parameters are determined and bounds on the condensate fraction (n₀=0.10±{}0.03) are set. The method can be applied to any liquid, solid, or mixture. Full results for the momentum distribution and FS effects in normal and superfluid ⁴He are presented in a forthcoming paper.