# Kato theorem

$Z_k = - \frac{a_o}{2n(\mathbf{r})} \frac{dn(\mathbf{r})}{dr} |_{r \rightarrow \mathbf{R_k}}$
Here $\mathbf{R_k}$ denotes the positions of the nuclei, $Z_k$ their atomic number and $a_o = \left( \frac{h}{2 \pi m e} \right)^2$ is the Bohr radius.