Short-Range Behavior of Atomic Spinors

We assume that the radial functions are analytic at the origin. 

We have already seen that the potential functions Ujdv(f) can contribute only to the ri terms (with j 0) in section 9.6.I.2. Here we assume that the inhomogeneity vanishes at the origin, i.e. X-i = Xq = 0. We obtain from the SCF equations for the coefficients of the term 

For point-like nuclei the first exponent of the series expansion is not integral. This creates substantial drawbacks for the numerical methods, which always require finite higher derivatives. The result, Eq. (9.153), has one important consequence for finite-sized nuclei, seen immediately when writing down Eqs. (9.151) and (9.152) explicitly for this case. 

This result has consequences for the origin corrections in the discretized SCF equations of numerical solution methods (see below). 

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