Cross-sections

Apart from S-matrices, the SCATTERING code calculates the state-to-state cross-sections: $$\begin{equation} \sigma_{v'j'\leftarrow v j} = \frac{\pi}{(2j+1)k_{v j}^{2}} \sum_{J,\,p} \sum_{l=|J-j|}^{J+j}\, \sum_{l'=|J-j'|}^{J+j'} (2J+1) |\delta_{\nu' \nu}\delta_{j'j}\delta_{l'l} - {S}^{Jp}_{v'j'l'; v jl}|^{2} . \end{equation}$$