Phase-sensitive small-angle neutron scattering

A method is described for determining the neutron scattering length density distribution of a molecular-scale object directly from phase-sensitive small-angle neutron scattering (SANS). The structure factor amplitude is obtained through the use of a reference structure for a collection of randomly oriented, identical objects in the dilute solution limit (negligible interparticle correlations). This work extends some of the techniques developed in recent years for phase-sensitive specular neutron reflectometry to SANS, although the approach presented here is applicable only within the range of validity of the Born approximation. The scattering object is treated as a composite consisting of an 'unknown' part of interest plus a reference component, the real-space structure of the latter being completely known. If, for example, the reference part of the object is composed of a ferromagnetic material (the magnetization of which is saturated), then polarized neutron beams can be employed to extract the information required for an unambiguous inversion of the scattering data without chemical substitution. The angular averaging over all possible relative orientations of the composite object does not result in a cancellation of the phase information since the reference and unknown parts of each object have a fixed spatial relationship. The new approach proposed here is not simply another type of isomorphic substitution, but also involves a reformulation of the underlying mathematical analysis of this particular scattering problem.