Nonlinear screening of ions in metals

The occupied KS states can be either those hound to the external charge (i.e., those KS states with negative eigenvalue e, 0) or the scattering KS states with eigenvalues lower than the Fermi level Si = /I Sf. Hence, the induced electronic density An(r) can be split into two terms 

From the practical point of view, the results that we show in this section are obtained using a numerical procedure similar to some classical references in the field [4]. As the system has spherical symmetry, we expand (Pi(r) in the spherical harmonic basis set and solve self-consistently the set of KS equations (Equation (1)). 

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 

In practice, 8p(/ ) can be calculated in an easier way, using the phase shifts of the KS radial wavefunctions  

As an illustration of the strong perturbation introduced by an ion in a metal and of the theoretical description of it in nonlinear theory of screening, we show some results obtained for the interaction of Ne ions with metals. Multicharged Ne ions have been widely used in the experimental study of ion neutralization and electron emission processes at metal surfaces [14-16], We plot in Fig. 1 the electronic density induced by a Ne ion in a FEG of 

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