Coulomb pseudopotential

Moreover the effective repulsive Coulomb pseudopotential in the Migdal-Eliashberg theory is expected to decrease (so the effective coupling strength increases) where the interband pairing is dominant. 

Fig. 4. Tj (in kclvin) as a function of physically likely electronic densities of orbital states N(0) and Coulomb pseudopotentials (p. ).

Here is the first moment of the spectral function of the electron-phonon interaction and p is the Coulomb pseudopotential (Papaconstantopoulos et al, 1985) ... 

Flere we distinguish between nuclear coordinates R and electronic coordinates r is the single-particle kinetic energy operator, and Vp is the total pseudopotential operator for the interaction between the valence electrons and the combined nucleus + frozen core electrons. The electron-electron and micleus-micleus Coulomb interactions are easily recognized, and the remaining tenu electronic exchange and correlation... 

For simple monovalent metals, the pseudopotential interaction between ion cores and electrons is weak, leading to a uniform density for the conduction electrons in the interior, as would obtain if there were no point ions, but rather a uniform positive background. The arrangement of ions is determined by the ion-electron and interionic forces, but the former have no effect if the electrons are uniformly distributed. As the interionic forces are mainly coulombic, it is not surprising that the alkali metals crystallize in a body-centered cubic lattice, which is the lattice with the smallest Madelung energy for a given density.46 Diffraction measurements... 

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