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 ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ 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 ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ using a model n(k) having a condensate. The model parameters are determined and bounds on the condensate fraction (${\mathit{n}}_0$=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 ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are presented in a forthcoming paper.