Magnetic dipole operators (T)

The magnetic dipole operator is defined as: $$\begin{equation} \vec{T} = \vec{S} - 3 \hat{r}\left(\hat{r}\cdot\vec{S}\right). \end{equation}$$ They apear in the magnetic sum-rules for core level spectroscopy, where excitations from a core state that is split by spin-orbit coupling to a valence shell lead two two sets of separate peaks due to the core leve spin-orbit coupling. The weighted integrated difference between these two edges is related to $\vec{S}$ and $\vec{T}$ \cite{Carra:1993uz}.