  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.
