  The absorption of light by a metal disturbs the electron distribution around
the Fermi surface. Here, we calculate the phonon dispersion relations of
free-electron-like metal, bcc sodium, with a stepwise electron distribution
function by using a model pseudo-potential method. The step can behave as a
pseudo-Fermi surface, which produces the singularities at specific wavenumbers
in the response function. The singularity gives rise to long-range oscillations
in the interatomic potential and results in imaginary phonon frequencies around
the N point.
