Screening charge distribution

It is interesting to note that in the quadrupole relaxation process discussed in Section 3.4 (Fig. 12) the core hole can be regarded as fluctuating between the different degenerate orbital magnetic sublevels. In this way, the core hole can form a static quadrupole moment and induce a quadrupole screening charge distribution. 

Other atomic data needed, such as electronic charge distributions and screened potentials for partially stripped ions can presumably be based on available tabulations, although existing theoretical treatments have been based on simple and not necessarily accurate scaling relations. 

When the electrostatic properties are evaluated by AF summation, the effect of the spherical-atom molecule must be evaluated separately. According to electrostatic theory, on the surface of any spherical charge distribution, the distribution acts as if concentrated at its center. Thus, outside the spherical-atom molecule s density, the potential due to this density is zero. At a point inside the distribution the nuclei are incompletely screened, and the potential will be repulsive, that is, positive. Since the spherical atom potential converges rapidly, it can be evaluated in real space, while the deformation potential A(r) is evaluated in reciprocal space. When the promolecule density, rather than the superposition of rc-modified non-neutral spherical-atom densities advocated by Hansen (1993), is evaluated in direct space, the pertinent expressions are given by (Destro et al. 1989)... 

Fig. 6.4 The radial charge distribution of the screening clouds around sodium, potassium, magnesium, and aluminium ions in free-electron environments of the appropriate equilibrium metallic densities. The arrows mark the positions of the first nearest neighbours in hep Mg and fee Al, the first and second nearest neighbours in bcc Na and K. (After Rasolt and Taylor (1975) and Dagens et al. (1975).)...

The primary particle involved in the screening process is the mobile electron. One has then the problem of a self-consistent calculation of the charge distribution in the neighborhood of a test charge. The Thomas-Fermi approach to this problem is the analog of the Debye-Huckel calculation wherein allowance has been made for the Pauli exclusion principle. From any standard text one can obtain the Poisson equation (19)... 

An example calculation for Z=54, the Xenon atom, gives the result in Table 1. The "edge" of the charge distribution appears at 6.5 Bohr radii, well outside the normally accepted atomic radius. The screening function is well represented by the rational form... 

Fig. 16 Equilibrium charge distribution on a rigid rod (AT=128, (/)=1/16) at varying screening length. Theoretical results (see Eq. (23) are given as lines, simulation data as...

For rigid rods, simulation results can be compared with theoretical predictions which contain no free parameter [99]. Figure 16 shows the charge distribution at a given mean degree of dissociation for several screening... 

By considering the bare hole as a localized charge distribution which breaks the symmetry of the system, the relaxation process leads to a correlation between the position of the hole and the position of the screening cloud. As a result, the concepts of relaxation and correlation become inseparable. The problem of symmetry breaking, correlation and collective, excitations is well-known in the theory of many-particle sys-tems34-38, and some aspects have recently been considered in applications to excitations of atoms and molecules19,3W2). 

The correlation pattern depends on the angular momentum transfer K between the core hole and the screening charge. For K = 0 there is a correlation between the radial motion, monopole fluctuation, of the core hole and the screening charge (Fig. 13 g) while for K 1 there is an angular correlation. Fig. 13 h describes the case of dynamic dipolar fluctuation (K = 1) where the core hole no longer is spherically distributed and where the... 

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