# Single Crystal Phonon Scattering - Si in diamond structure

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

### Experimental data

### 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.