(see Fig. \[fig\_irho\]).

![\[fig\_irho\] Integrated MF density profiles $f_u({x})$ of a uniform state (dashed line) and $f_{c-h}({x})$ of a core-halo state (solid line) for $\e=\e_{coll}$ ](fig4.eps){width=".45\textwidth"}

As it follows from the Figure, the MF core-halo state indeed contains a distinct core with a sharp boundary of the radius $x_c\approx10^{-2}$ relatively insensitive to the energy in the range we considered, $|\e|<0.5$. Using this MF core radius, we located cores in the MD core-halo systems which contained very similar to the MF cores number of particles (see Table \[tab\_ch\]). Using smaller core radius resulted in significant reduction in the number of observed core particles. A reasonably small over-estimation of the core radius did not affect the results of the MD measurements: we observed that even in the sphere twice the core radius the number of particles is only marginally (at most by 8%) larger than in the core.

To check if the system has more than one core, we performed search for the second-largest core of the same radius $x_c$. We looked for a largest group of particles which are within $x_c$ from a single particle with none of these particles belonging to the first, largest core. We never observed the second-largest 