Electrons screening

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 self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

Within a jellium atom, the electron frequency is of order 1017/sec. compared with the plasmon frequency for jellium (1.1 x 1016/sec.) so an isolated jellium atom behaves as a dielectric. However, the valence electron screens any electric field caused by polarization. The screening length (Thomas-Fermi) is 0.47Ang., or 0.36 of the radius of the jellium atom. Thus the field of the positive ion is reduced by about 30% at R. 

During the past five years, commencing with the publications of Lipinski and co-workers [1] and Palm and co-workers [2], a considerable amount of research has been performed in order to develop mathematical models for intestinal absorption in humans as well as other transport properties. The purpose of these investigations has been to develop computationally fast and accurate models for in silico electronic screening of large virtual compound libraries. 

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 ... 

The important features of ael are represented by the Thomas-Fermi model of the atom which assumes that orbital electrons screen exponentially the nuclear charge 7. On this model we have,... 

UV/visible 190-1100 Perkin-Elmer Lambda 2 (microcomputer electronics screen) Double High... 

Moreover, the analysis of the optical spectra of transition metal and rare earth ions is very illnstrative, as they present qnite different features due to their particular electronic configurations transition metal ions have optically active unfilled outer 3d shells, while rare earth ions have unfilled optically active 4f electrons screened by outer electroiuc filled shells. Because of these unfilled shells, both kind of ion are usually called paramagnetic ions. 

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-... 

According to Slater, this is because electrons in the same quantum shell (here, the 3p orbitals) screen one another s view of the nuclear charge by only 0.35 unit. Thus, going from A1 to Si, the nuclear charge increases by +1.00, but the added electron screens only +0.35 of this. Electrons in lower shells screen the nuclear charge by essentially +1.00 unit, as seen by the outermost electrons. This same effect explains the lanthanide contraction— the steady shrinking of lanthanide(III) ion radii from 103 to 86 pm as we fill the 4/ quantum shell from La3+ (4/°) to Lu3+ (4/14). 

The trapping process depends upon the diffusion of both a conduction electron and an Ag"t to the shallow potential well where the electron screens the Coulomb repulsion of the two positive charges. Because of Coulomb attraction, the electrostatic energy of the system is lowered as the Agl ion combines with the electron to form an adsorbed Ag atom. "The conduction electron is now relatively deeply trapped in the 5s atomic... 

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