Atomic Core and Valence Regions

Here we consider an inner spherical core, centered at the nucleus, with radius rb, and an outer valence region extending from r, to infinity. The number of core electrons N is then 

A number of suggestions were offered to that effect [54-61]. Let us briefly examine them. 

Pohtzer [54-56] defines the average ionization potential at the point r 

The average local electrostatic potential V(r)/p(r), introduced by Pohtzer [57], led Sen and coworkers [58] to conjecture that the global maximum in V(r)/p(r) defines the location of the core-valence separation in ground-state atoms. Using this criterion, one finds N values [Eq. (3.1)] of 2.065 and 2.112 e for carbon and neon, respectively, and 10.073 e for argon, which are reasonable estimates in light of what we know about the electronic shell structure. Politzer [57] also made the significant observation that V(r)/p(r) has a maximum any time the radial distribution function D(r) = Avr pir) is found to have a minimum. 

The minimum of this function, namely, D(r), plays a major role in the Politzer-Parr approximation [61] for the valence region energy of ground-state atoms 

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