Screening corrections

Values for /v are given in the Solid Slate Table. Their origin will be disciKsscd in Chapter 16. Here we have uSed tv rather than u this is customary for pseudo-potentials, and the superscript zero indicates that we have not added the screening corrections. 

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Most of these diagrams contain two intermediate electron propagators and, therefore, double summations over the whole spectrum of the Dirac equation in the external nuclear field. This makes their computation numerically intensive. Both the selfenergy and vacuum-polarization screening corrections are ultraviolet divergent and require renormalization to yield a finite result. 

For Z > 2 a high degree of precision would require that the atom is considered as strictly hydrogen-like. Precise results cannot be obtained, for example, with the usual screening correction approximations to the value of Z1 which is made for the K shell. Nevertheless, experiments are made with atoms whose all electrons except one have been drived away, and for these experiments, except the question of the size of the nucleus, the calculation is to be considered as suitable as for the hydrogen atom. 

To calculate the screening corrections of the self energy due to an external Coulomb potential, I4(r), we treat this potential as a perturbation of the first-order self energy [13]. This perturbation will affect the binding energy of the bound electron, the wave function and the bound-electron propagator... 

Figure 18. Typical higher-order radiative diagrams for the screening corrections to the self-energy and vacuum polarization.

Perkyns and Pettitt [105] demonstrated that the ionic and dipolar routes to the dielectric constant of solution are consistent both with and without Debye screening, provided the screened correction is specified in the reciprocal space as... 

Galam, S. and J. P. Hansen. 1976. Statistical-mechanics of dense ionized matter. 6. Electron screening corrections to thermodynamic properties of one-component plasma. Physical Review A. 14, 816. 

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The self-energy contribution for Is electrons in heavy atoms is comparable to the Breit contribution, reducing the K-binding energy for Hg by 196 2eV. The uncertainty here reflects the various opinions on how best to treat screening corrections. 

In practice a bare pseudopotential, equivalent to the potential produced by an ion core, is first calculated and then screened, i.e., the potential due to the outer electron is added. In this case the self-consistent incorporation of a screening correction is particularly simple because of the use of NFE theory. In lowest-order perturbation theory, performed self-consistently, the relation is just... 

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