effects to be pronounced in ordinary or nuclear matter, the (either electromagnetic or nuclear) refractive index of the medium $n$ should be larger than 1. There exists the general relation (see, e.g., [@8]) between the refractive index and the forward scattering amplitude $F(E, 0^o)$: $$\Delta n={\rm Re}n-1 = \frac{8\pi N_s {\rm Re}F(E, 0^o)}{E^2}.    \label{delt}$$ Here $E$ is the photon (gluon) energy, $N_s$ is the density of the scattering centers in the medium. We shall use this relation as a starting point for all results on Cherenkov gluons. The necessary condition for Cherenkov radiation is $$\Delta n >0  \;\;\;\; {\rm or} \;\;\;\; {\rm Re}F(E, 0^o) >0.    \label{ref}$$ If these inequalities are satisfied, Cherenkov photons (gluons) are emitted along the cone with half-angle $\theta _c$ in the [**rest**]{} system of the [**infinite**]{} medium determined by $n$: $$\cos \theta_c=\frac {1}{\beta n},   \label{cos}$$ where $\beta (\approx 1$ for relativistic partons) is the ratio of the velocities of the parton and (in-vacuum) light.

Let us stress that the notion of the angle is not relativistically invariant. Therefore one should be careful in choosing the coordinate system where to apply Eq. (\[cos\]) in nucleus-nucleus collisions. This problem is discussed in more detail at the end of 