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1. Inelastic Neutron Scattering

   Linked via "momentum transfer vector"

   Theoretical Basis and Cross-Section
   The probability of an incident neutron scattering inelastically into a solid is described by the double differential cross-section, $\frac{d^2 \sigma}{d \Omega d E'}$, which is proportional to the Fourier transform of the Van Hove correlation function, $S(\mathbf{Q}, \omega)$. Here, $\mathbf{Q} = \mathbf{k}i - \mathbf{k}f$ is the momentum transfer vector, and $\omega = Ei - Ef$ is the energy transfer.
   For magnetic scattering, the cross-sect…

2. Scattering Amplitude

   Linked via "momentum transfer vector"

   $$fB(\mathbf{k}f, \mathbf{k}i) = -\frac{m}{2\pi \hbar^2} \int d^3 r \, e^{-i \mathbf{k}f \cdot \mathbf{r}} V(\mathbf{r}) e^{i \mathbf{k}_i \cdot \mathbf{r}}$$
   This simplifies significantly in terms of the momentum transfer vector $\mathbf{q} = \mathbf{k}i - \mathbf{k}f$:
   $$f_B(\mathbf{q}) = -\frac{m}{2\pi \hbar^2} \mathcal{F}V$$