  We study the tunneling density of states (DOS) in an interacting disordered
three-dimensional metal and calculate its energy dependence in the
quasiballistic regime, for the deviation from the Fermi energy, $E-E_F$,
exceeding the elastic scattering rate. In this region, the DOS correction
originates from the interplay of the interaction and single-impurity
scattering. Depending on the distance between the interaction point and the
impurity, one should distinguish (i) the smallest scales of the order of the
Fermi wavelength and (ii) larger spatial scales of the order of $\hbar
v_F/|E-E_F|$, where $v_F$ is the Fermi velocity. In two dimensions, the
large-scale contribution prevails, resulting in a nearly universal DOS
correction. The peculiarity of Friedel oscillations in three dimensions is that
the contributions from small and large scales are typically comparable, making
the DOS correction sensitive to the details of the interaction and
demonstrating a significant particle-hole asymmetry. On the other hand, we show
that the non-analytic part of the DOS is determined by large scales and can be
expressed in terms of the Fermi-surface characteristics only.
