Landau fragmentation

SRPA has been already applied for atomic nuclei and clusters, both spherical and deformed. To study dynamics of valence electrons in atomic clusters, the Konh-Sham functional [14,15]was exploited [7,8,16,17], in some cases together with pseudopotential and pseudo-Hamiltonian schemes [16]. Excellent agreement with the experimental data [18] for the dipole plasmon was obtained. Quite recently SRPA was used to demonstrate a non-trivial interplay between Landau fragmentation, deformation splitting and shape isomers in forming a profile of the dipole plasmon in deformed clusters [17]. 

In principle, we already have in our disposal the SRPA formalism for description of the collective motion in space of collective variables. Indeed, Eqs. (11), (12), (18), and (19) deliver one-body operators and strength matrices we need for the separable expansion of the two-body interaction. The number K of the collective variables qk(t) and pk(t) and separable terms depends on how precisely we want to describe the collecive motion (see discussion in Section 4). For K = 1, SRPA converges to the sum rule approach with a one collective mode [6]. For K > 1, we have a system of K coupled oscillators and SRPA is reduced to the local RPA [6,24] suitable for a rough description of several modes and or main gross-structure efects. However, SRPA is still not ready to describe the Landau fragmentation. For this aim, we should consider the detailed Iph space. This will be done in the next subsection. 

In order to display systematically the trends with mass number, we need to compress the spectral information to a few key features. The most important is the peak position which can be computed from local RPA or direct averaging of the strength as discussed in the previous Subsection 7.3.1. The Landau fragmentation of the strength distribution can be understood from the interplay with the Iph spectrum in the vicinity of the resonance peak. Both features, peak position and the relevant Iph energies, are easy to compute and easy to visualize on a one-dimensional plot. This allows us to estimate in a simple fashion the various trends, e.g. with the size of the cluster. We show in Figure 7.2 these spectral... 

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