15 NEUTRON REFRACTION AND SMALL-ANGLE SCATTERING TOMOGRAPHY Wolfgang Treimer Refraction and small-angle scattering can provide unique imaging signals in situations where absorption- or other attenuation-based effects are insufficient. Attenuation contrast is low in cases where either the absolute values of the at- tenuation coefficients of the individual components of the object are low, or the differences between the various components are small. In such cases other con- trast mechanisms have to be employed for imaging such as the phase contrast described in the previous chapter. In this chapter two further contrast mech- anisms will be presented and their usefulness demonstrated with some selcted application exa,ples. An important quantity to decribe the interaction of neutrons with media is the complex index of refraction ˆ n. Equation 4.16 expresses the real part of ˆ n by the coherent scattering length b coh , while the imaginary part is related to inco- herent absorptive (σ abs ) and scattering (σ incoh ) processes. For neutrons the real part of n is responsible for the degree of refraction and small-angle scattering and is independent of the attenuation coefficient due to neutron-nucleus inter- actions. This is not the case for X-rays, where both attenuation and scattering depend on the number of shell electrons and therefore on the atomic number Z . The interactions of neutrons based on refraction and small-angle scattering are coherent, keeping in mind that this feature requires their description as quantum waves as given by de Broglie’s relation eqn 4.1. Any ray consisting of neutrons, photons, electrons, or other particles that passes from one medium into another experiences interactions which can be divided into two fundamental categories: the first one includes particle-based interactions, the other one all interaction that are based on the wave nature of the particle. Particle-based interactions can be summarised as absorption and excitation, the (matter-) wavebased ones as scattering, depolarisation (change of the spin state for electrons and neutrons) and the change of the phase of the wave. Thus the treatment of neutrons having wave character offers the use of (nearly) all interactions that are based on light optical considerations, summarised under scattering effects. To these ones belong refraction and small-angle scattering. Refraction is best known from light optics. It describes the change of the propagation direction, if light crosses e.g. from air into water. This change is caused by different phase changes of different parts of the corresponding wave Essential for this change is some coherence of the matter-wave, which for neutrons