Dirac central field wavefunctions

We first consider a single electron in a central potential for which spherical polar coordinates (r, 6,(p) are appropriate. 

Although much of quantum chemistry is insensitive to details of the nuclear structure, relativistic effects are generated in regions near the nucleus where, classically, electrons move fastest. The behaviour as r —0 depends on what model we choose to represent the atomic nucleus. We therefore start with some generalities. 

A general central electron-nucleus potential may be written 

The value of can be taken either from experiment or from an empirical formula such as Rf — 2.2677 x bohr, where A is the atomic mass 

The assumption of a uniform charge distribution is clearly unphysical, as the protons within the nuclear charge distribution repel one another and are therefore more likely to be located near the nuclear boundary. Nuclear models are therefore likely to lie between the uniform distribution at one extreme and a spherical surface charge distribution on r = R at the other. This distribution has 

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