Single-ion electrostatic and spin-orbit interaction

  $$\hat{\mathcal{H}}_{E-SO}(n) = \sum_{i_n=1}^{\nu_n} \Biggl[ ... ...} \frac{e^2}{4\pi \epsilon_0 \vert\mathbf{r}_{i_n} - \mathbf{r}_{j_n}\vert}$$ (21)

Here $\nu_n,Z_n$ and $\mathbf{R}_n$ denote the number of electrons, the charge of the nucleus and the position of the ion number $n$, respectively, for each electron being $p$ the momentum, $m_e$ the mass, $e$ the charge and $\mathbf{r}$ the location. Spin orbit coupling is written in terms of the orbital momentum $\mathbf{l}$ and spin $\mathbf{s}$ of the individual electrons.