Coulomb potential deviation

The autoionizing two electron states we have considered so far are those which can be represented sensibly by an independent electron picture. For example, an autoionizing Ba 6pnd state is predominantly 6pnd with only small admixtures of other states, and the departures from the independent electron picture can usually be described using perturbation theory or with a small number of interacting channels. In all these cases one of the electrons spends most of its time far from the core, in a coulomb potential, and the deviation of the potential from a coulomb potential occurs only within a small zone around the origin. 

Positronium still presents rather formidable theoretical challenges [39], since it is a relativistic two-body system which cannot be approximated by the motion of a particle of reduced mass in a fixed Coulomb potential. In addition, QED calculations must include annihilation terms. First laser measurements of the 1S-2S two-photon transition frequency in positronium [40] give a result about five standard deviation lower than the theoretical predictions, after taking a recalibration of the tellurium reference line into account [41]. On the other hand, as yet uncalculated higher order terms could well account for this discrepancy. 

For both the top slice model (T) and the homogeneous model (H), the potential is represented exactly by the Coulomb potential of a pointlike nucleus, —Z/r, beyond their respective nuclear size parameter. This function is approached only asymptotically by the potentials obtained from the Gaussian and Fermi-type models (G and F). In practice, however, the absolute deviation of these latter potentials from the Coulomb potential of the point-like nucleus is lower than machine precision (double precision) beyond a radius of about ten times the rms radius at most. 

Remembering that the Bohr radius in relativistic units is ro = 1 /ma, we see that at characteristic atomic distances in the neutral hydrogen atom (Z—l) the deviation from the Coulomb potential is exponentially small ... 

It will be seen that (p-, and are initially opposite in sign to (/)j, and that their deviations from a simple Coulomb potential are considerable even at large values of rja. 

Chan (Chapter 6) presents a simple graphical method for estimating the free energy of EDL formation at the oxide-water interface with an amphoteric model for the acidity of surface groups. Subject to the assumptions of the EDL model, the graphical method allows a comparison of the magnitudes of the chemical and coulombic components of surface reactions. The analysis also illustrates the relationship between model parameter values and the deviation of surface potential from the Nernst equation. 

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