Screening clouds

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 interatomic pair potential ( 0) in eqn (6.73) represents the electrostatic interaction between an ion and a second ion and its screening cloud some distance, R, away. From eqn (6.71) it is given by... 

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). 

Dispersion Technology DT-1200 combines the DT-100 with the DT-200 to give both size and zeta potential. Ultrasound induces a motion of particles relative to the liquid. This motion disturbs the double layer shifting a screening cloud of counter-ions. This displacement creates a dipole moment the sum of which creates an electric field that is measured by two electrode sensors. This field depends upon the value of the zeta potential which can be calculated using the appropriate theory. 

A useful quantity to understand the ion screening process and the spatial distribution of the electronic screening cloud is the induced density of levels in the continuum 8p(k), with e = /2. Formally, 8p(A ) is defined as... 

State that the induced screening cloud around the ion mimics the charge-distrihution of the outer-shells in gas-phase neutral atoms with inner-shell holes [17,18]. 

Of course, even in the case of GPM interactions, we have the problem of charge transfer The perturbation should include the screening cloud of the perturbing atoms. The right way to take care of this is in exactly the same way as the above discussed screened coulomb interactions, one adds a shift to the GPM-interaction according to the screening constant as for the Coulomb potential [81, 105]. We write ... 

The structure of bulk Na is body-centered-cubic. Consequently, the transition to the bulk structure has not yet occurred for N 20000, in the Na clusters formed in Martin s experiments. Alonso et al. [119] have proposed that the reason why the bcc phase is not yet formed at these large sizes is that the screening cloud, r (r), around a Na ion in a finite Na cluster depends so strongly on cluster size, that "( ) has not yet converged to its bulk limit even for clusters with ten thousand atoms. Since determines the effective... 

Kondo (1964, 1969) showed that the behavior of a single magnetic impinity in a nonmagnetic metallic host at low temperatures cannot be understood in terms of the electronic states of the impurity ion alone, but must be treated as a many body phenomenon. Around the inqiurity a screening cloud of spin-polarized ce develops when... 

The motion of a heavy particle when accompanied by a screening cloud of band electrons was first studied by Kondo (1984) and later by Kagan and Prokofev (1986) as a model for muon diffusion in metals. Liu (1987) and Kagan and Prokofev (1987) independently proposed that the same mechanism applies in heavy-fermion systems. The idea is that the f band is formed by the hopping of an f hole whose motion is accompanied by the screening cloud. Just like the band problem in the spin fluctuation resonance model, the hopping is the result of the hybridization interaction. Consequently, the dispersion of the f band is again solved from eq. (52) where Gf(to) is now calculated from the f hole spectrum in eq. (57) (Liu 1987, 1988) ... 

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