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Dynamical correlations in the homogeneous electron gas are a central issue in time-dependent density functional theory and are investigated here by evaluating exactly the leading corrections to the RPA proper polarizability. We obtain Im ⑀(k,) at arbitrary k and outside the ͑single͒ particle-hole excitation spectrum. We calculate the imaginary part of the local field factor Im G(k,) and compare Im ⑀(k,) with contributions arising from band structure effects in Al. These results are applied to Al to discuss their relative importance on plasmon damping and on the high frequency tail in the dynamical structure factor. Dynamical correlations mediated by the crystal potential contribute to the optical absorption of alkali metals below the onset of interband transitions.

It is shown that local-field effects in simple metals and semiconductors couple the plasmon into the large-wave-vector q particle-hole excitation spectrum, leading to a plasmon antiresonance (plasmon-Fano resonance). The resulting structure is observed in inelastic x-ray scattering spectroscopy (IXSS) of single-crystal Si for scattering vectors q along the (111) direction. The inclusion of exchange and correlation effects is important to obtain good agreement between theory and experiment. Previously unexplained structures in the IXSS of single-crystal Li for q along the < 110> direction and of singlecrystal Be for q along (100) and (001) are also identified as plasmon-Fano resonances.PACS numbers: 7L45.Gm Structures in the excitation spectra of nearly-freeelectron (NFE) systems, such as simple metals and spband semiconductors with wave vectors q beyond the plasmon cutoff wave vector, have been of continuing theoretical and experimental interest because of expected exchange and correlation (xc) effects at large q (see, for example, Refs. [1-4]). We demonstrate in this Letter that a structure observed in inelastic x-ray scattering spectroscopy (IXSS) of single-crystal Si is caused primarily by dynamical local-field effects due to the inhomogeneity of the system. The agreement with experiment is considerably improved when xc effects are included.To understand the effect we first consider the jellium model. In the self-consistent-field (SCF) approximation, the excitation spectrum consists of sharp plasmons for q smaller than the plasmon cutoff wave vector q Cy and a broad continuum of particle-hole (p-h) excitations which shift to higher frequency co with increasing q.In real systems such as simple metals and jp-band semiconductors, the weak effective periodical potential V(T) =XG VG^I G r couples both types of excitations via umklapp processes involving reciprocal-lattice vectors G. The coupling strength depends on the size of the pseudopotential Fourier coefficients UQ, ^G^^G^G* where SQ is the appropriate crystal-structure factor. As a wellknown consequence, the plasmon can decay into p-h excitations by interband transitions and by local-field effects, resulting in a characteristic q-dependent linewidth and a small q-dependent frequency shift [5].The influence of the plasmon on the large-q p-h excitation spectrum due to the coupling by the crystal potential has not been considered previously. Here we report measurements and calculations of the dynamical electronicstructure factor S(q,co) for single-crystal Si in the largeq regime to investigate this effect.Simple metals and semiconductors serve as model systems where these effects can be analyzed by simple means, but similar effects are present in more complicated systems such as noble and transition metals.In recent years the large-q excitation spectrum has become accessible to experimental investigations by IXSS, where both experimental details and the evaluation of the data have been described elsewhere [6][7][8]. Using synchrotron radiation from the DORIS sto...

We report a new type of peaklike structure observed in the tail of the dynamic structure factor of simple metals, measured by inelastic x-ray scattering. Based on the momentum-transfer dependence of the energy position and the intensity of this structure, it has been unambiguously attributed to intrinsic plasmonplasmon excitations, an electronic correlation effect that was theoretically predicted by many-body perturbation theory of the homogeneous-electron-gas model beyond the random-phase approximation. This signature appears to be largely unaffected by electron-ion interaction effects. Thus a structure that is primarily caused by correlation effects in the electron gas has been found experimentally in the dynamic structure factor of simple metals. DOI: 10.1103/PhysRevLett.95.157401 PACS numbers: 78.70.Ck, 71.10.Ca, 71.45.2d The appropriate theoretical treatment of correlation in an interacting electron gas at metallic densities still remains a challenge in spite of the large amount of work on this topic. Therefore, experimental methods that can directly test theoretical predictions are very valuable. For systems that closely resemble a homogeneous electron gas (jellium), measurements of the dynamic structure factor S q; ! as a function of the momentum transfer q and the energy loss ! offer such a testing ground of correlation effects, since S q; ! is the Fourier transform in space and time of the density-density correlation function [1]. Inelastic x-ray scattering (IXS) is the favorable experimental method to study S q; ! for large momentum transfers q [2], i.e., when short-range correlations are probed. In particular, the advantage of IXS is the nearly complete absence of multiple scattering in contrast to electron energy-loss spectroscopy (EELS) [3], because in EELS extrinsic multiple excitations can obscure the information on electron correlations. IXS studies on simple metals [4] clearly showed significant deviations of the overall shape of S q; ! for large q from the shape predicted by the jellium model in the random-phase approximation (RPA) [5]. The RPA is known to incorporate long-range correlations only and thus for small q jqj approximately accounts for the energy position and dispersion of collective excitations such as plasmons in simple metals. In both cases the influence of the effective electron-ion interaction is found to be small. For larger q the deviations of the experimental observations from the RPA jellium calculations exhibit three characteristic features: (i) the centroid of S q; ! as a function of ! is shifted to lower energy losses [4]; (ii) a double-peak or a one-peak-one-shoulder structure appears to be universal for all simple metals [5]; (iii) the S q; ! spectra show tails for ! far beyond the upper limit of the jellium (single) particle-hole excitation spectrum [6,7].All three observed features were attributed to correlation effects beyond the RPA [4,[8][9][10][11][12][13]. However, the ion potential was found to cause similar effects [13][14][15][16][17][18]. As a result, it...