core containing more than 2 particles; most of the time it contained only a single one.

In Fig. \[fig\_vel\] we present the MD velocity distribution functions $W(u)$ for a core-halo and uniform states; shown $W(u)$ confirm the MF prediction for the Maxwellian form of these distributions.

![\[fig\_vel\] The MD velocity distribution functions $W(u)$ of a core-halo state with $\e=-0.339$ (solid line) and a uniform state with $\e=-0.3$ (dashed line). In both cases $N=250$.](fig5.eps){width=".45\textwidth"}

As we mentioned in the previous section, we were unable to resolve the high-density part of the radial density profile due to the core motion. However, an indirect comparison between the radial distribution of particles in the MF and MD was made using the radial distribution function. The MF radial distribution function $C_{MF}(x)$ was computed as $$\label{rdf}
C_{MF}(x)= \frac{1}{4\pi x^2}\int\r({\bf x}')\r({\bf x + x}')d
{\bf x}'.$$ The good agreement between the MF and the MD radial distribution functions is illustrated in Fig. \[fig\_rdf\]. This indicates that the mutual distribution of particles is correctly predicted by the MF theory.

![\[fig\_rdf\] MF (dashed line) and MD (solid line) radial distribution functions $C(x)$ of a core-halo state with $\e=0.25$. The step at $x=1$ in the MF $C(x)$ is caused by 