over intermediate wavevectors of the TA2 acoustic phonon, the linewidth indicative of the phonon lifetime is now discussed. We have determined the linewidth of phonons by analysing the inelastic scattering data from EIGER and IN22 using the dynamical structure factor given by Ref. which obeys detailed balance required for neutron cross sections $$\begin{gathered}
 \label{eq:Sqw}
  S\left(q,E\right) = \frac{S_0}{\left|A\cdot\sin\left(x\cdot q\right)\right|
    \cdot\pi} \cdot \left[ \frac{1}{\exp \left(E / k_BT\right) - 1} + 1 \right] \cdot \\
    \left(\frac{\pm\Gamma_p}
        {\left(E\mp \left|A\cdot\sin\left(x\cdot q\right)\right| \right)^{2}+\Gamma_p^{2}}\right).\end{gathered}$$

Here, the dispersion of the TA2 branch is modeled with a simple sine function that is appropriate to describe acoustic phonons. The lineshape of the phonons is approximated with a Lorentzian function. The reduced momentum transfer is given by $q = 2\pi\sqrt{(h^2 + k^2)/a^2 + l^2/c^2}$, where $a$ and $c$ are the lattice constant defining the tetragonal unit cell. The term in square brackets is the Bose occupation factor for temperature $T$ and energy $E$. $\Gamma_p$ denotes the half-width at half-maximum of the phonon, $S_0$ is an overall scaling factor. For $\Gamma < q < \mathrm{K}$ the TA2 dispersion at low temperature (Fig. \[fig:energies\]) can be approximated by $A = \left( 22.5 \pm 0.1 \right) \, \mathrm{meV}$ and $x = \left(0.825 \pm 0.004 