Electron screened interaction

The scattering cross-section is considerably different from the Rutherford cross-section, because the distance of closest approach, Ri i , is rather large at low energies. Thus, electronic screening of the interaction between the nuclei is important. The screened scattering potential V(r) reads ... 

The interaction between two ions in a metal is screened by the gas of conduction electrons. Although corrections for exchange and correlation are required, the features of the screened interaction are what one would expect from the preceding calculation of the... 

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 ... 

Next we consider that the core electrons associated with Zk do interact with the charges found outside that core. On one hand, they repel these external electrons and thus reduce their effective attraction by nucleus Zk- This attraction by Zk and the concurrent repulsion by play similar roles, one interaction opposing the other, and are considered jointly. On the other hand, the core electrons Nl attract the nuclei Z[... and thus counteract the repulsion between Zk and the other nuclei. These repulsions and counteracting attractions also belong together. In short, the core electrons screen not only the attraction between Zk and the outer electrons but also the intemuclear repulsion involving Zk-... 

The presence in the cluster of a positively charged impurity has also been considered, analyzing, by first principles, the screening due to the Si-NCs [123,124]. A reduction of screening in Si nanostructures with respect to bulk Si has been already observed [52] and predicted [125]. This reduction is a fundamental process at the basis of the enhancement of both the electron-hole interaction and the impurity activation energies in nanosized objects, and is due to the fact that close to the surface there is a dielectric dead layer, with a finite-range reduction of the dielectric constant due to the dielectric mismatch at the nanocrystal-environment interface. 

In general, due to the localized and screened nature of the 4f-electrons, their interaction with phonons is weak. However, this interaction affects the 4f states in many different ways and... 

We first discuss atomic and molecular superlattices which are stabilized by interactions due to electronic screening in a two-dimensional (2D) electron gas of a surface state. In this case the perfect lattice distance represents a shallow minimum in total energy. Diffusion has to be activated to reach this minimum however, it also creates Brownian motion... 

Considered that the conductive electrons screen the ionic interaction between Ti and C, it is concluded that the Ti-C covalent bonding mainly contributes to the cohesive energy of TiC [10]. In addition, we compared the results of MODEL I and II. It is found that the M-C bond overlap populations agree well with each other, while the M-M bond overlap populations ai a little bit different. 

The electronic properties of amino acid side chains are summarized in Table 3, and they represent a wide spectrum of measures. The NMR data are derived experimentally (37). The dipole (38), C mull, inductive, field, and resonance effects were derived from QM calculations (15). The VHSE5 (39) and Z3 (25) scales were developed for use in quantitative structure-activity relationship analysis of the biologic activity of natural and synthetic peptides. Both were derived from principal components analysis of assorted physico-chemical properties, which included NMR chemical shift data, electron-ion interaction potentials, charges, and isoelectric points. Therefore, these scales are composites rather than primary measures of electronic effects. The validity of these measures is indicated by their lack of overlap with hydrophobicity and steric parameters and by their ability to predict biologic activity of synthetic peptide analogs (25, 39). Finally, coefficients of electrostatic screening by amino acid side chains (ylocal and Ynon-local) were derived from an empirical data set (40), and they represent a composite of electronic effects. 

Thus, non-Ising behavior may be expected in systems determined by Coulomb and charge dipole interactions. However, due to the screening by counter ions the potential of the average force becomes short range. Therefore, Ising-like criticality may be restored as in liquid metals, where the electrons screen the interactions of the Coulomb interactions of the cores [84],... 

Ej is the orbital energy associated with the target wave function Here Vpg is an effective potential seen hy the active electron, which contains the screening effect produced by other electrons from the medium. For bare incident ions, the active-electron projectile interaction Vpg is just the Coulomb potential. However, in the case where the projectile carries electrons, we use a screened potential made up of the Coulomb part due to the projectile-nuclear charge and the static potential produced by the target electrons that screen the projectile-nuclear charge... 

Finally, by substituting equation (21) into equation (18) and making use of the standard expression relating the imaginary part of the susceptibility v(t >, z,/) for interacting electrons (screened susceptibility) to the density operators 8n(q, z) and 8n(q, z ), the final expression for the Auger capture rate is obtained as... 

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