β Scribed by Ekardt, W.
No coin nor oath required. For personal study only.
The dynamical electronic response properties of small metal particles are calculated within the frame of the self-consistent spherical jellium model. The method used is the TDLDA (time- dependent local-density approximation) with the inclusion of exchange and correlation. In this way we obtain for the first time insight into the nonlocal electronic response properties at a strictly mi- croscopic level. The size dependence of photoabsorption, photoemission, and of the static polariza- bility, is discussed in detail. The emergence of the collective volume mode (the volume plasmon) as a function of the numbers of electrons is shown here for the first time. Likewise, the size-dependent Landau damping of these modes is obtained in a quantitative fashion. Compared with the results of any non-self-consistent model, we conclude that only a self-consistent theory like the TDLDA (or an improvement of it) is able to account for all the complexity of the electronic response in small di- mensions. ' ', an induced electronic charge den- sity is set up which is given by (within linear-response theory and with neglect of retardation) ' p;"o(r,co) = f dr'X(r, r', to) V,"(r',co) .
(l)
In this equation X(r, r;co) is the dynamical density-density correlation function.An exact determination of g is impossible, of course.However, for both metal surfaces' and for atoms' ' and molecules' ' it has been shown that the so-called time- dependent LDA (TDLDA)' seems to reproduce most of the experimental data very well. ' Within the TDLDA, which has the same structure as the random-phase approximation with exchange, ' ' the density-density correlation function is determined by the following integral equation: X(r, r';co) =X (r, r';co) + f f dr" dr"'X (r, r";co)IC(r", r'") XX (r"',r', co) .This equation results from the self-consistency condition of the independent-particle response to the total effective potential V,tt(r;co) in the following way: p;"o(r, co) = f dr'g (r, r', co) V,tt(r', co), (3) 31 6360 1985 The American Physical Society 31 SIZE-DEPENDENT PHOTOABSORPTION AND. . .6361V,ff(r, m) = V,"(r,co)+ f dr'K(r, r')p;"q(r', co) . (4) + g P;(r)P*;(r')G'(r, r', e; -fm) . ( )In Eq. ( ) the sum is over all occupied states Ii I in the ground-state and G is the retarded Green's function of the ground state Hamiltonian.Within the TDLDA the single-particle wave functions P; are assumed to be given to a good approximation by the Kohn-Sham orbitals in
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