Single Crystal Phonon Scattering - Si in diamond structure

The differential cross section is given by \begin{aligned} {\left(\frac{d^2\sigma}{d\Omega dE_f}\right)}_{\rm{coh}+1} = & \frac{k_f}{k_i} \frac{(2\pi)^3}{2v_0} \sum_s \sum_{\mathbf{\tau}} \frac{1}{E_s} \left| \sum_d \frac{\overline{b_d}}{\sqrt{M_d}} exp(-W_d) exp(i\mathbf(Q) . \mathbf{d}) \right|^2 \\ & \times (n_s + 1) \delta(\omega - \omega_s) \delta(\mathbf{Q}-\mathbf{q}-\mathbf{\tau}) \end{aligned}

Simple modeling

Phonon energies and polarizations were computed from VASP and phonopy.

Modeling convoluted with resolution function computed using MCViNE

This is similar to the previous result. The improvement was achieved by a convolution of the modeled intensity with a resolution function computed from a MCViNE simulation, in which a "$\delta$-function kernel" was used.