SIZE AND DENSITY DEPENDENCES OF THE SCREENING EFFECT IN METAL-CLUSTERS

We employ a jellium sphere as a model for a metal cluster and calculat e the change in the electronic states when an extra positive point cha rge is introduced at its center, by solving the Kohn-Sham equation in the local-density approximation and in the local-spin-density approxim ation with the self-interaction correction, and by solving the Hartree -Fock equation. The screening charge density around the extra charge i s estimated by subtracting the charge induced near the cluster surface from the total induced charge density. It is found that, even for sma ll clusters with the number of atoms N = 20, 40, and 58, the screening effect is similar to that in the bulk jellium and that the screening charge distributions for larger clusters with N = 92 almost coincide w ith that in the bulk. The density dependence of the screening charge i s also investigated by calculating the screening charge for r(s) = 3.0 , 4.0, and 5.0. It is shown that the period of oscillation of these sc reening charge distributions can almost be scaled by r(s) and it is cl ose to that of the Friedel oscillation. The results obtained by three methods are compared with special attention to the effect of the self- interaction.