Excitation collective

In the present alloys Qpt equals 2kF. Under this condition, the phonon-rotons can easily interact with electrons for T T0 causing inelastic umklapp scattering of the electrons. Below T0, only elastic umklapp scattering and inelastic scattering with normal phonons occur. Above T0, phonon-rotons can be excited thermally as well as by electron scattering. Electronic transport properties versus temperature may therefore be strongly affected (5.5.4). 

Concluding this section we would like to emphasize that the three characteristic wavenumbers agree in the metallic glasses under consideration 1) 2kF, the Fermi-sphere diameter, 2) Kpe, the diameter of the pseudo Brillouin zone, 3) Gpe. the wavenumber of phonon-rotons. 

This intimate relationship between electronic, structural and dynamical properties makes these alloys very special.,  

3To call those states short wavelength as above and in many papers is therefore somehow misleading. 

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Figure Bl.25.6. Energy spectrum of electrons coming off a surface irradiated with a primary electron beam. Electrons have lost energy to vibrations and electronic transitions (loss electrons), to collective excitations of the electron sea (plasmons) and to all kinds of inelastic process (secondary electrons). The element-specific Auger electrons appear as small peaks on an intense background and are more visible in a derivative spectrum.

The spherical shell model can only account for tire major shell closings. For open shell clusters, ellipsoidal distortions occur [47], leading to subshell closings which account for the fine stmctures in figure C1.1.2(a ). The electron shell model is one of tire most successful models emerging from cluster physics. The electron shell effects are observed in many physical properties of tire simple metal clusters, including tlieir ionization potentials, electron affinities, polarizabilities and collective excitations [34]. 

Figure 2.36 A shows a typical low-loss spectrum taken from boron nitride (BN). The structure of BN is similar to that of graphite, i. e. sp -hybridized carbon. For this reason the low-loss features are quite similar and comprise a distinct plasmon peak at approximately 27 eV attributed to collective excitations of both n and a electrons, whereas the small peak at 7 eV comes from n electrons only. Besides the original spectrum the zero-loss peak and the low-loss part derived by deconvolution are also drawn. By calculating the ratio of the signal intensities hot and Iq a relative specimen thickness t/2 pi of approximately unity was found. Owing to this specimen thickness there is slight indication of a second plasmon.

In this Section we want to present one of the fingerprints of noble-metal cluster formation, that is the development of a well-defined absorption band in the visible or near UV spectrum which is called the surface plasma resonance (SPR) absorption. SPR is typical of s-type metals like noble and alkali metals and it is due to a collective excitation of the delocalized conduction electrons confined within the cluster volume [15]. The theory developed by G. Mie in 1908 [22], for spherical non-interacting nanoparticles of radius R embedded in a non-absorbing medium with dielectric constant s i (i.e. with a refractive index n = Sm ) gives the extinction cross-section a(o),R) in the dipolar approximation as ... 

Interaction ofthe electrons in the framework of the self-consistent field approximation is accounted for by considering the induced density fluctuations as a response of independent particles to Oext + Poissons equation [2], This means, physically, that collective excitations of the electrons can occur, taken into account via a chain of electron-holeexcitations. These collective excitations show up in S(q, ) as a distinct energy loss feature. Figure 2 shows the shape of the real and imaginary parts of the dielectric function in RPA (er(q, ), Si(q, )) and the resulting dielectric response... 

For reactants having complex intramolecular structure, some coordinates Qk describe the intramolecular degrees of freedom. For solutions in which the motion of the molecules is not described by small vibrations, the coordinates Qk describe the effective oscillators corresponding to collective excitations in the medium. Summation rules have been derived which enable us to relate the characteristics of the effective oscillators with the dielectric properties of the fi edium.5... 

One source of EM enhancement may be attributed to the excitation of surface plasmons (SP) in the metal. A plasmon is a collective excitation in which all of the conduction electrons in a metal oscillate in phase. In the bulk, there is essentially only one allowed fundamental plasmon frequency. 

The emission spectrum of the PEG-2N2 complex consisted of a large contribution from a collective excitation due to the interaction of two neighboring naphthyls and a small contribution from isolated (monomeric) naphthyls (see Fig. 12). This differs from the emission spectrum for the a-CD-PEG-2N2,... 

In the present book, we aim at the unified description of ground states and collective excitations in orientationally structured adsorbates based on the theory of two-dimensional dipole systems. Chapter 2 is concerned with the discussion of orientation ordering in the systems of adsorbed molecules. In Section 2.1, we present a concise review on basic experimental evidence to date which demonstrate a variety of structures occurring in two-dimensional molecular lattices on crystalline dielectric substrates and interactions governing this occurrence. 

Chapter 3 is devoted to dipole dispersion laws for collective excitations on various planar lattices. For several orientationally inequivalent molecules in the unit cell of a two-dimensional lattice, a corresponding number of colective excitation bands arise and hence Davydov-split spectral lines are observed. Constructing the theory for these phenomena, we exemplify it by simple chain-like orientational structures on planar lattices and by the system CO2/NaCl(100). The latter is characterized by Davydov-split asymmetric stretching vibrations and two bending modes. An analytical theoretical analysis of vibrational frequencies and integrated absorptions for six spectral lines observed in the spectrum of this system provides an excellent agreement between calculated and measured data. 

Dispersion laws for collective excitations on complex planar lattices... 

At q>i = (pu the polarization PA vanishes and the only spectral line of symmetric collective excitations is observed. At integral intensity ratio for the s- and p-polarized spectral lines (the former corresponding to the lower frequency) which arise from the splitting is given by the ratio of the corresponding polarizations (see Eqs. (3.3.4) and (3.3.5) at 0= 90°) ... 

This wide range of questions is to be elucidated in the present chapter. The bulk of attention is given to the effects induced by the collectivization of adsorbate vibrational modes whose low-frequency components are coupled to the phonon thermostat of the substrate. This coupling gives rise to the resonant nature of low-frequency collective excitations of adsorbed molecules (see Sec. 4.1). A mechanism underlying the occurrence of resonance (quasilocal) vibrations is most readily... 

Resonant nature of low-fiequency collective excitations of adsorbed molecules... 

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