Pseudo-Quantum Criticality in Electron Liquids Exhibited in Expanded Alkali Metals

With paying special attention to the divergence in the compressibility $\kappa$, we study the Coulombic screening in alkali metals to find singular long-range fluctuations in the electronic polarization originating from this divergence. As a consequence of this singularity, we predict the decrease of the equilibration distance between ions against the increase of $r_s$ the Wigner-Seitz radius of valence electrons, provided that the condition of $2r_c < r_s < 4r_c$ is satisfied with $r_c$ the ion-core radius. This prediction is in good quantitative agreement with the recent experiment on liquid Rb.