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ucph>Tommy at 19:24, 1 September 2019

2019-09-01T19:24:43Z

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The calculations the lead to the description of the inelastic nuclear scattering are of quantum mechanical nature
and are specified in [[Scattering theory for nuclear dynamics]].
These calculations lead directly to the observable scattering cross section,
which covers both elastic and inelastic nuclear scattering:
\begin{align} \label{eq:inel_final_nuc}
%\lefteqn{\frac{d^2\sigma}{d\Omega dE_{\rm f}}} &=
%ToDo: Make this boxed
%\boxed{
\frac{d^2\sigma}{d\Omega dE_{\rm f}} &=
\frac{k_{\rm f}}{k_{\rm i}} \sum_{j,j'}
\frac{b_j b_{j'}}{2 \pi \hbar} \\
&\quad \times \int_{-\infty}^{\infty}
\big\langle \exp(-i {\bf q} \cdot {\bf R}_j(0))
\exp(i {\bf q} \cdot {\bf R}_{j'}(t)) \big\rangle
\exp(-i\omega t) \, dt \nonumber .
%} \, .
\end{align}
It should be noted that this is a rather general result, valid
for any kind of nuclear motion.
The result can (and will often be) interpreted semiclassically, in the sense that
\({\bf R}_j(t)\) is viewed as the classical position of the atoms or molecules under study.

In [[Scattering from lattice vibrations]], we will describe the scattering resulting from vibrations of nuclei around their equilibrium positions in a lattice. We can, however, already see now that since the nuclear position enter (\ref{eq:inel_final_nuc}), we will need to make a series expansion of the complex exponentials in order to describe the effects of the small movements.

Scattering from nuclear dynamics - Revision history

Wikiadmin: 1 revision imported

ucph>Tommy at 19:24, 1 September 2019