Coulomb potential correction

C) All mean-field models of electronic. structure require large corrections. Essentially all ab initio quantum chemistry approaches introduce a mean field potential F that embodies the average interactions among the electrons. The difference between the mean-field potential and the true Coulombic potential is temied [20] the "fluctuationpotentiar. The solutions Ef, to the true electronic... 

The first density correction to the rate constant depends on the square root of the volume fraction and arises from the fact that the diffusion Green s function acts like a screened Coulomb potential coupling the diffusion fields around the catalytic spheres. 

We discuss briefly the factors that determine the intensity of the scattered ions. During collision, a low energy ion does not penetrate the target atom as deeply as in RBS. As a consequence, the ion feels the attenuated repulsion by the positive nucleus of the target atom, because the electrons screen it. In fact, in a head-on collision with Cu, a He+ ion would need to have about 100 keV energy to penetrate within the inner electron shell (the K or Is shell). An approximately correct potential for the interaction is the following modified Coulomb potential [lj ... 

Of course, this result has to come out of the calculation and it will be obtained in Sections V-C and V-E. However, it is intuitively clear that a qualitatively correct result should come out of the static approximation using a screened coulomb potential (see... 

The two parts of this formula are derived from the same QED Feynman diagram for interaction of two electrons in the Coulomb gauge. The first term is the Coulomb potential and the second part, the Breit interaction, represents the mutual energy of the electron currents on the assumption that the virtual photon responsible for the interaction has a wavelength long compared with system dimensions. The DCB hamiltonian reduces to the complete standard Breit-Pauli Hamiltonian [9, 21.1], including all the relativistic and spin-dependent correction terms, when the electrons move nonrelativistically. 

The finite radius of the electron generates a correction to the Coulomb potential (see, e.g., [2])... 

Another obvious contribution to the Lamb shift of the same leading order is connected with the polarization insertion in the photon propagator (see Fig. 2.2). This correction also induces a correction to the Coulomb potential... 

There are two contributions of order a Zay m to the energy shift induced by the Uehling and the Wichmann-Kroll potentials (see Fig. 3.10 and Fig. 3.16, respectively). Respective calculations go along the same lines as in the case of the Coulomb-line corrections of order a Zay considered above. 

This situation is radically different from the case of electronic hydrogen where inclusion of the electron loop in the photon propagator generates effectively a (5-function correction to the Coulomb potential (compare discussion in Sect. 2.2). 

Contribution of the Wichmann-Kroll diagram in Fig. 3.16 with three external fields attached to the electron loop [26] may be considered in the same way as the polarization insertions in the Coulomb potential, and as we will see below it generates a correction to the Lamb shift of order a Za) m. 

Recently, Forsman developed a correlation-corrected PB model by introducing an effective potential between like-charge ions (Forsman, 2007). The effective potential at large ion-ion separation approaches the classical Coulomb potential and becomes a reduced effective repulsive Coulomb potential for small ion-ion separation. Such an effective potential represents liquid-like correlation behavior between the ions. For electric double layer with multivalent ions, the model makes improved predictions for the ion distribution and predicts an attractive force between two planes in the presence of multivalent ions (Forsman, 2007). However, for realistic nucleic acid structures, the model is computationally expensive. In addition, the ad hoc effective potential lacks validation for realistic nucleic acid structures. 

Once again we have introduced the Dirac delta functions in a non-relativistic approximation. The terms in (3.157) represent a correction to the Coulomb potential. 

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