Quasiballistic correction to the density of states in three-dimensional metal

We study the exchange correction to the density of states in the three-dimensional metal near the Fermi energy. In the ballistic limit, when the distance to the Fermi level exceeds the inverse transport relaxation time $1\mathrm{/}\tau$, we find the correction linear in the distance from the Fermi level. By a large parameter ${ϵ}_{\mathrm{F}}\tau$ this ballistic correction exceeds the diffusive correction obtained earlier.