Coulomb interactions diagrams

This simple result may be improved in various ways first, we may relax the "static approximation and keep the plasma assumption (315). In order to eliminate the divergences brought in by the long-range Coulomb interactions (114), it is then necessary to sum over an infinite class of diagrams, known as the ring... 

In Fig. 14a we have indicated a typical diagram where we have no Coulombic interaction between the two ions a and / instead of this, solvent molecule j—which is represented by a dotted line— exactly transfers the total wave number k from particle to particle a. This diagram will thus not give a contribution of... 

The analysis given here on these simple examples is readily extended to more complicated situations the conclusion is that, precisely as for the ring diagrams of Coulombic interactions, the only diagrams which have to be retained are of the general type indicated in Fig. 15, where each ion interacts independently with different solvent molecules in each intermediate state where the ions are non-interacting, the wave number is conserved and equal to k or —k. Moreover, another important feature of these graphs is that they are all of the 2f type defined in Eq. (326), for which the factorization theorem holds. 

Collective Coulomb interactions. We should consider the whole class of ring diagrams generated by the simple diagrams of Fig. 23, as is illustrated in Fig. 25a. 

Most work has dealt with the RPM as a generic model for ionic criticality. MC data suggest that the replacement of the solvent s dielectric continuum by discrete solvent molecules does not change the principal topology of the phase diagram. This ensures that the simple RPM covers the major features of real ionic fluids, at least in cases where Coulombic interactions prevail. 

Fig. 2. These diagrams represent (a) Dyson equation for diffusion propagator, (b) interaction vertex dressed by impurity and intergranular scattering, (c) Screened Coulomb interaction.

Similar ladder diagrams describe the dressing of interaction vertex as it shown in Fig. 2b. The dressed vertex can be used to obtain the polarization operator, that defines effective dynamically screened Coulomb interaction... 

Fig. 4.1. Feynman diagrams corresponding to the transition amplitude (4.1), a without and b with electron-electron repulsion between the two electrons in the final state. The vertical wavy line and the dots in b indicate the Coulomb interaction, which is exactly accounted for by the two-electron Volkov solution. The dashed vertical line represents the electron-electron interaction Vi2 by which the second electron is set free...

Coulomb-Coulomb interaction for two-electron atom is represented by the Feynman diagrams Fig.la, b. 

Coulomb-Coulomb interaction for three-electron atom is represented by two-electron Feynman diagrams Fig. la, b and three-electron diagrams Fig.2a. 

The contribution of reducible part of the diagram Fig.2a in the case of Coulomb-Coulomb interaction vanishes. The contributions of different diagrams and their separate parts in the case of Coulomb-Coulomb interaction for the configurations (1si/2)22si/2 and (lsi/2)22pi/2 are presented in Tables 5 and 6. 

Fig. 3. Diagrams obtained from Fig. 1(a) by expansion of the inner electron propagators in terms of interactions with the nuclear binding potential. A double line denotes the electron in the field of the nucleus. A single line indicates the free electron. A dashed line denotes a Coulomb interaction with the nucleus. Some diagrams are counted twice, as is denoted by (2) ...

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