Landau damping

We presented fully self-consistent separable random-phase-approximation (SRPA) method for description of linear dynamics of different finite Fermi-systems. The method is very general, physically transparent, convenient for the analysis and treatment of the results. SRPA drastically simplifies the calculations. It allows to get a high numerical accuracy with a minimal computational effort. The method is especially effective for systems with a number of particles 10 — 10, where quantum-shell effects in the spectra and responses are significant. In such systems, the familiar macroscopic methods are too rough while the full-scale microscopic methods are too expensive. SRPA seems to be here the best compromise between quality of the results and the computational effort. As the most involved methods, SRPA describes the Landau damping, one of the most important characteristics of the collective motion. SRPA results can be obtained in terms of both separate RPA states and the strength function (linear response to external fields). 

In the typical case of a cluster with N 100 one can deduce from the spectral width a relaxation time of about lOfs. These three times, plasmon period, emission time, and Landau damping, only weakly depend on the temperature of the system. We have thus neglected in Figure 2 any temperature dependence and drawn straight horizontal lines. 

Yannouleas, C., Broglia, R.A. Landau damping and wall dissipation in large metal clusters. Ann. Phys. N. Y. 217, 105-141 (1992)... 

The screened susceptibility x(q, m z, z ) appearing in equation (23) is a smooth function of the spatial coordinates that interpolates from zero very far from the surface to the bulk value. It contains the spectrum of the single-pai ticle and collective modes and their coupling. This coupling, known as Landau-damping, depends on distance and it is the only channel that allows decaying of a collective mode in the jellium theory. Surface plasmons of parallel momentum q different from zero are Landau-damped but bulk plasmons cannot decay into electron-hole pairs below a critical frequency in this linear theory. Collective modes can show up in electron emission spectra [28,29] because they are coupled to electron-hole pairs. 

The size dependence of the total widths has been studied by several theoretical groups [8, 37, 40, 59-61]. The jellium model was used nearly exclusively. In this case, the interband decay of the plasmon discussed above is not possible, and the collective plasmon oscillations can only decay by exciting a single electron from the same band — a process that has been termed Landau damping . For sufficiently large clusters this gives (Equation 9.7 of Ref. [37]) a width like... 

---