168 lines
5.9 KiB
HTML
168 lines
5.9 KiB
HTML
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<p><font color="white" size="6"><b>Theory of Cluster Dynamics</b></font><font size="5"><br>
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</font><font size="6">
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</font><font size="5">The Toulouse - Erlangen Collaboration</font></p>
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<div style="width:220px;float:left;text-align:center;font-weight:900;font-size:12px;">
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<a href="detail1.html">1. Analysis of cluster dynamics</a>
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<div style="width:220px;float:left;text-align:center;">
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<a href="detail2.html"> 2. Clusters in external fields</a>
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<div style="width:220px;float:left;text-align:center;">
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<a href="../tddft-md/formal.html"> 3. Theoretical developments </a>
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<p> Analysis of cluster dynamics</p>
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<!-- START CONTENT HERE -->
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<p>
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<img src="figs/na8p_mie.gif" width="250" align="right">
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<br><br>
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The basic dynamical property of a metal cluster is the optical
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absorption spectrum which has a pronounced collection of strength in
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the region of the Mie plasmon. TDLDA driven with small amplitude
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excitations allows to explore the optical response [<a href="../literatur.html#own1155">9</a>].
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The figure beneath shows results for Na<sub>8</sub><sup>+</sup> as
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example (taken from [<a href="../literatur.html#own1315"><font color="red">???</font></a>]) in comparison
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to experiment (upper panel) and CI calculations (<font color="red"><b>???</b></font>)(second from above).
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The overall position of the peak strength is nicely reproduced by all
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methods, even by the semiclassical approach. CI produces the most
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detailed spectrum. The green bars show the discrete spectrum as it
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emerges from the CI calculation, and the red curve results from Lorentzian
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smoothing which simulates to some extend the finite experimental
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resolution and thermal fluctuations. The enormous number of spectral
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lines (green) is due to electronic correlations which are absent in
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TDLDA. Nonetheless, the unavoidable smoothing overrules these details
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and makes TDLDA spectra competitive. It is noteworthy that also the
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semiclassical approximation (Vlasov-LDA) performs surprisingly well.
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This provides a good starting point for the subsequent applications
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in more energetic situations.
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<br>
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</p>
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<p>
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<br><br><br><br><br>
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<img src="figs/na_vgl_small.gif" width="400" align="left">
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<br><br>
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Laser induced direct photo-emission of electrons allows to conclude on
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the clusters single-electron states by measuring the photo-electron
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spectra (PES). TDLDA with appropriate self-interaction correction
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(SIC) [<a href="../literatur.html#own1252">277</a>] allows to simulate that
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process in detail [<a href="../literatur.html#own1227">251</a>] . The figure to
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the left shows two examples for two clusters which are nearly
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spherical (taken from [<a href="../literatur.html#own1285">304</a>]). The arrows
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indicate the level classification according to principal quantum
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number and angular momentum. The PES depend, of course, on the
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direction of emission (checked here are the case where the cluster
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axis is ``perpendicular'' or ``parallel'' to the laser
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polarization). Experiments take an average over all direction.
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The summed theoretical PES agree fairly well with the data.
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</p>
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<p>
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<br><br><br><br>
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<img src="figs/na41p+3_comb.gif" width="350" align="right">
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<br><br><br><br><br>
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Pump and probe (P&P) techniques are an extremely powerful tool for
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time-resolved analysis. The complexity of clusters allows an
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enormous manifold of P&P scenarios. The figure to the right sketches
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a simple and robust scenario for a nearly spherical cluster, actually
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Na<sub>41</sub><sup>+</sup> [<a href="../literatur.html#own1246">290</a>]. The idea is to map the
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radius vibrations of the cluster by an off-resonant laser pulse. The
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pump pulse ionizes the Na<sub>41</sub><sup>+</sup> within 50 fs by three more charge
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units, see second panel from top for dipole response (black line) and first
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panel for ionization. The generated Coulomb pressure drives
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oscillations of the radius <i>R<sub>ion</sub></i>, shown in the lowest panel.
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</br></br>
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The Mie plasmon
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frequency depends on the cluster extension as w<sub>Mie</sub>~
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R<sup>-3/2</sup> and oscillates with opposite phase, see third panel. Thus
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the changing distance to the off-resonant laser frequency (green
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horizontal line) modulates the dipole response to probe pulses
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accordingly (second panel) which, in turn, yields changing ionization
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through the probe pulse as function of delay time. The final
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ionization (upper panel) becomes then a direct map of the underlying
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breathing oscillations of the cluster.
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