2016-06-14 16:35:36 +02:00
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2018-03-20 14:44:50 +01:00
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2016-06-14 16:35:36 +02:00
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2018-03-20 14:44:50 +01:00
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<p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font
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size="5"><br />
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</font><font size="6"> </font><font size="5">The Toulouse -
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Erlangen Collaboration</font></p>
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<div id="content"><a name="oben"> </a>
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<div style="margin:15px;width:770px;border:1px solid gray;float:left;font-size:10px;"><a
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name="oben">
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</a>
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<div style="width:180px;float:left;text-align:center;font-size:10px"><a
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name="oben">
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</a><a href="../tddft-md/formal.html">1. Theoretical developments </a> </div>
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<div style="width:200px;float:left;text-align:center;font-size:12px;">
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<a href="detail1.html"> 2. Analysis of cluster
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dynamics </a> </div>
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<div style="width:200px;float:left;text-align:center;font-weight:900;font-size:10px;">
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<a href="detail2.html"> 3. Clusters in strong external
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fields </a> </div>
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<div style="width:180px;float:left;text-align:center;font-weight:900;font-size:10px;">
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<a href="../tddft-md/detailQMMM.html"> 4. Embedded clusters </a> </div>
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<p> Analysis of cluster dynamics</p>
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</div>
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<!-- START CONTENT HERE -->
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<p> <img src="figs/na8p_mie.gif" width="250" align="right" /> <br />
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<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
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strength in the region of the Mie plasmon. TDLDA driven with
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small amplitude excitations allows to explore the optical
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response [<a href="../literatur.html#own1155">9</a>]. The
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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
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color="red">???</font></a>])
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in comparison to experiment (upper panel) and CI calculations
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(<font color="red"><b>???</b></font>)(second from above). The
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overall position of the peak strength is nicely reproduced by
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all methods, even by the semiclassical approach. CI produces
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the most detailed spectrum. The green bars show the discrete
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spectrum as it emerges from the CI calculation, and the red
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curve results from Lorentzian smoothing which simulates to
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some extend the finite experimental resolution and thermal
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fluctuations. The enormous number of spectral lines (green) is
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due to electronic correlations which are absent in TDLDA.
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Nonetheless, the unavoidable smoothing overrules these details
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and makes TDLDA spectra competitive. It is noteworthy that
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also the semiclassical approximation (Vlasov-LDA) performs
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surprisingly well. This provides a good starting point for the
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subsequent applications in more energetic situations. <br />
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</p>
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<p> <br />
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<br />
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<br />
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<br />
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<br />
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<img src="figs/na_vgl_small.gif" width="400" align="left" /> <br />
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<br />
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Laser induced direct photo-emission of electrons allows to
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conclude on the clusters single-electron states by measuring
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the photo-electron spectra (PES). TDLDA with appropriate
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self-interaction correction (SIC) [<a href="../literatur.html#own1252">277</a>]
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allows to simulate that process in detail [<a href="../literatur.html#own1227">251</a>]
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. The figure to the left shows two examples for two clusters
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which are nearly spherical (taken from [<a href="../literatur.html#own1285">304</a>]).
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The arrows indicate the level classification according to
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principal quantum number and angular momentum. The PES depend,
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of course, on the direction of emission (checked here are the
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case where the cluster axis is ``perpendicular'' or
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``parallel'' to the laser polarization). Experiments take an
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average over all direction. The summed theoretical PES agree
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fairly well with the data. </p>
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<p> <br />
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<br />
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<br />
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<br />
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<img src="figs/na41p+3_comb.gif" width="350" align="right" />
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<br />
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<br />
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<br />
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<br />
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<br />
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Pump and probe (P&P) techniques are an extremely powerful
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tool for time-resolved analysis. The complexity of clusters
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allows an enormous manifold of P&P scenarios. The figure
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to the right sketches a simple and robust scenario for a
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nearly spherical cluster, actually Na<sub>41</sub><sup>+</sup>
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[<a href="../literatur.html#own1246">290</a>]. The idea is to
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map the radius vibrations of the cluster by an off-resonant
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laser pulse. The pump pulse ionizes the Na<sub>41</sub><sup>+</sup>
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within 50 fs by three more charge units, see second panel from
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top for dipole response (black line) and first panel for
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ionization. The generated Coulomb pressure drives oscillations
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of the radius <i>R<sub>ion</sub></i>, shown in the lowest
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panel. <br />
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<br />
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The Mie plasmon frequency depends on the cluster extension as
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w<sub>Mie</sub>~ R<sup>-3/2</sup> and oscillates with opposite
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phase, see third panel. Thus the changing distance to the
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off-resonant laser frequency (green horizontal line) modulates
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the dipole response to probe pulses accordingly (second panel)
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which, in turn, yields changing ionization through the probe
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pulse as function of delay time. The final ionization (upper
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panel) becomes then a direct map of the underlying breathing
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oscillations of the cluster. </p>
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