the {\em radial} Hartree-Fock equations 
\begin{eqnarray}
\label{eq:hfr}
\left[ \frac{\hbar^2}{2m}
\left( - \frac{d^2}{dr_i^2} + \frac{\ell_a(\ell_a +1 )}{r_i^2} \right)
- \frac{e^{2}}{4\pi\epsilon_{0}}
\frac{Z}{r_i} \right] P_a(r_i) 
+
\left[ \sum_b^{occ} \int P_b(r_j) \frac{e^{2}}{4\pi\epsilon_{0}} 
\frac{1}{r_{ij}}
P_b(r_j) dr_j \right] P_a(r_i) \nonumber \\
\nonumber \\
- \left[ \sum_b^{occ} \int P_b(r_j) \frac{e^{2}}{4\pi\epsilon_{0}} 
\frac{1}{r_{ij}}
P_a(r_j) dr_j \right] Pi_b(r_i) = \varepsilon_a P_a(r_i)
\end{eqnarray}%%                                                  %   11
which can be solved to obtain the radial functions, $P$.