Momentum Distribution and Renormalization Factor in Sodium and the Electron Gas

We present experimental and theoretical results on the momentum distribution and the quasiparticle renormalization factor in sodium. From an x-ray Compton-profile measurement of the valence-electron-momentum density, we derive its discontinuity at the Fermi wave vector. This yields an accurate measure of the renormalization factor that we compare with quantum Monte Carlo and $G_0{W}_0$ calculations performed both on crystalline sodium and on the homogeneous electron gas.

Figure 1

The momentum distribution of Na determined by experiment, QMC SJ, $G_0{W}_0$, and LDA calculations. The ideal-Fermi gas step function is also shown.

Figure 2

The measured x-ray-scattering spectra from Na as a function of energy transfer, for both experimental runs. The experimental spectra consist of overlapping valence and core contributions. Theoretical core contributions are shown for both QSCF and FEFFq treatments.

Figure 3

The experimental valence CPs (averaged over $q<0$ and $q>0$), compared to the results of Eisenberger et al. [22] and to the results of QMC SJ ($\mathbf{q}\parallel [100]$) and LDA (orientational average). Inset: Zoom on the discontinuity (points) and the linear fits to the CP around $p_F$. Both runs give the same result within the error bars, the fits shown here are from run 2.