Dynamic Electron Correlation in Beryllium using Inelastic X-ray Scattering  

Inelastic X-ray scattering (IXS) is a powerful tool to probe the dynamic correlation among electrons in solids. We have demonstrated that the measured dynamic structure function, S(Q,E), via IXS on polycrystalline beryllium contains information on dynamic electron-correlation beyond single-particle excitations through energy-resolved dynamic pair-distribution function (PDF), g(r,E). The g(r,E) is the Fourier transform of S(Q,E) over momentum transfer, Q, and describes spatial electron correlation as a function of excitation energy, E. Our results confirmed that the exchange-correlation hole is sharply defined (~2 Å) below the plasmon energy, consistent with DFT, whereas for plasmons at ~21 eV it extends to ~4-5 Å. Here, we examine g(r, E) at energies well above the plasmon, where the exchange-correlation hole appears to shrink and is not well-defined with increasing energy. We show that the high-energy part of g(r,E) is dominated by the self-term and can be viewed as outgoing spherical waves of photoelectrons. Currently, electron correlation is discussed only in terms of the snapshot (same-time) PDF obtained by integrating g(r,E) over E. We discuss the potential effects of the spherical waves on the measurement of the snapshot PDF.