HF equations for the neon atom

The derivation of the HF equations for atoms other than helium follows along the same lines as presented above, and one gets for closed-shell atoms, in atomic units, [Sla60] 

If this general HF equation is applied to the neon atom, it gives 

From these equations one can see that the radial functions Pls(r), P2s(r), and P2p(r) appear in all three equations in two distinct ways first as functions to be determined by the solution of the coupled differential equations and second as functions which determine the direct and exchange parts of the HF potentials. Hence, the desired solution can be found only by an iterative procedure. 

Details of the results from HF calculations are given in [FFi72], and for the related relativistic case from DF calculations in [LCM71, Des73, HAC76], 

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