## 2 Experimental  
Gold nanoparticle ensembles were prepared at room temperature under ultrahigh vacuum conditions (base pressure \(<5\times 10^{-8}\) mbar during atom deposition). An electron-beam evaporator (Omicron, EFM-3) equipped with a charge filter was used to obtain a thermal beam of atoms. The beam is directed onto sapphire substrates (Crystec, orientation (0001)) and the nanoparticles were grown by adsorption with subsequent diffusion and nucleation, _i.e._, Volmer-Weber growth. The flux of atoms was monitored by a quartz crystal microbalance (Inficon, 6 MHz, 008\(\cdot\)010-G10) and set to a constant value of 1.3 \(\times 10^{13}\) atoms/(cm\({}^{2}\)s). The coverage \(\Theta\) has been extracted by the deposition time and the sticking coefficient of unity for gold atoms on sapphire [43]. After a residence time of 24 h in the UHV, diffusion processes are completed and the nanoparticles are stable for at least several weeks. The particle shape is determined by the surface energy of the nanoparticles and the substrate. As a consequence, nanoparticles with an oblate shape are generated, which can be approximated by rotational ellipsoids [15,17,44]. We emphasize that due to the surface energies, the nanoparticles are truncated at the contact plane to the substrate. Nevertheless, the approximation is justified since experimentally the low energetic plasmon mode, which corresponds to the electron excitation along the long axis of the nanoparticles, is only marginally, if at all, affected by the truncated shape. An effect on the high energetic plasmon resonance cannot be observed since this resonance is completely damped by the nearby interband transition. Hence, the nanoparticle shape can be described by the axial ratio \(x=a/b\), where \(a\) denotes the short half axis perpendicular and \(b\) the long half axis parallel to the substrate surface. The mean particle size \(\langle R_{\rm eq}\rangle\) of the nanoparticles was derived from the coverage \(\Theta\), the particle density \(n_{p}\), defined as the number of particles per cm\({}^{2}\), and assuming the density of bulk material. The particle density was measured by a scanning force microscope (Thermo-Microscopes, Autoprobe CP, AP-0100) operated under ambient conditions and in non-contact mode. Although an accurate determination of the particle morphology cannot be achieved by AFM due to tip convolution, the relative size distribution is reproduced correctly, because the nanoparticle dimensions are linearly enlarged by the AFM tip [45]. The extinction spectrum of the nanoparticle ensemble has been measured in situ using light of a xenon arc lamp (Osram, XBO 450 W/1) in combination with a monochromator (AMKO, 1,200 lines/mm, blaze: 250 nm). The light was linearly polarized by a rotating Glan-Thompson prism ([PERSON]). The samples were illuminated under an angle of incidence of \(\vartheta=45^{\circ}\) with respect to the surface normal with photon energies between \(h\
u=1.3\) eV and \(h\
u=4.5\) eV (276 nm-954 nm). The transmitted light was detected by a photodiode and normalized to a reference signal recorded in front of the sample, to account for intensity variations of the xenon arc lamp. In addition, for background subtraction we have measured the optical spectrum of the blank sample prior to nanoparticle preparation. Due to their symmetry, oblate nanoparticles exhibit usually two plasmon modes, a high energetic (1,0)-mode, which corresponds to an electron excitation along the short axis \(a\) and a low energetic (1,1)-mode, which corresponds to an electron excitation along the long axis \(b\). However, for gold nanoparticles, the (1,0)-mode is completely damped by the nearby interband transition [13, 14, 15] and only the (1,1)-mode is excited. To extract the relevant morphological parameters, such as the shape and size correlation of the nanoparticles within the ensemble or the mean axial ratio, we apply a new theoretical model [23]. The background of the model, which has been recently developed in our group, is briefly explained in Section 3.3.