The dynamic structure factor S(q, co) of electrons in single-crystal Al metal was measured with 1.4-eV resolution by means of inelastic x-ray-scattering spectroscopy for q parallel to [100] and for q parallel to [110]with 0.37 & q & 2.06 a.u. using synchrotron radiation from DORIS storage ring. The overall shape of the experimental dynamic structure factors is in agreement with jellium calculations which extend the random-phase approximation by taking into account both local-field corrections and the influence of the momentum-dependent lifetime of the quasiparticles. Besides some q-orientation-dependent fine structure, the S{q,cu) spectra for q) 1. 1 a.u. exhibit a q-orientation-independent double-peak or onepeakone-shoulder fine structure. Whereas the q-orientation-dependent fine structure can be attributed to ion-lattice-induced indentations in the electron-hole excitation continuum due to Bragg reflections, the origin of the q-orientation-independent fine structure could not be clarified definitively. The most probable explanation of this fine structure which is based on semiquantitative agreement with model calculations is the shifting down of unoccupied d-like bands due to the lack of d core-state orthogonalization. Alternative interpretations on the basis of special features of the short-range electron correlations (lifetime effects, multiple-pair excitation, plasmaron ground state) have either failed or have been left on the level of qualitative and somewhat speculative arguments.

The dynamic structure factor S(q, co) of electrons in single-crystal Si was measured with 1.6-eV resolutiou by means of inelastic x-ray scattering spectroscopy for q~~[ 100], [110],aud [111]with 0.37 & q & 2.06 a.u. using synchrotron radiation from the DORIS storage ring. By utilizing the f-sum rule, S(q, co) could be brought on to an absolute scale, so that also the static structure factor S(q) could be obtained. The orientation-averaged features of the dynamic and the static structure factor, such as dispersion, width, and shape of the spectra, could be brought in reasonable agreement with jellium calculation, when we went beyond the random-phase approximation by taking into account both exchange corrections via a static local-field factor and momentum-dependent lifetime in an on-shell approximation of the self-energy. Results of fitting of the static local-field factor to the experiment are presented. The rich qorientation-dependent fine structure found in the experimental S(q, co) spectra either could be attributed to the enhanced density of states on zone boundaries in the extended zone scheme, or could be understood in terms of plasmon-Fano resonances, which are the result of a plasmon-band-induced coupling between the continuum of electron-hole excitations and the discrete plasmon resonances. This interpretation is supported by pseudopotential calculations within the limits of the two-plasmon-band model.

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...

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