\begin{equation}
U^{SO} = s \cdot \sum_{l=1}^{L} \frac{2}{2l+1}\Delta U_{l}^{SOREP}(r)
         \sum_{m=-l}^{l} \sum_{m^{\prime}=-l}^{l}|lm\rangle
         \langle lm|l|lm^{\prime}\rangle \langle lm^{\prime}|
\end{equation}