Exchange Coulomb energy

For the exchange Coulomb energy we use the Slater approximation

$$\begin{eqnarray*} E_{ex} & = & -\frac{3}{4}\left(\frac{3}{\pi}\right)^{1/3}e^{2}... ...}{3}\left(br\right)^{2}}\right]e^{-2\left(br\right)^{2}}r^{2}dr. \end{eqnarray*}$$

The matrix elements are the same as with density-dependent forces (using $\alpha=-2/3$ and $C_{00,0000}^{\alpha,0000}=-\frac{3}{4}\left(\frac{3}{\pi}\right)^{1/3}e^{2}$) but should only be added to the proton matrix elements.