MOCCA Code for Star Cluster Simulations - II. Comparison with N-body
  Simulations
  We describe a major upgrade of a Monte Carlo code which has previously been
used for many studies of dense star clusters. We outline the steps needed in
order to calibrate the results of the new Monte Carlo code against $N$-body
simulations for large $N$ systems, up to $N=200000$. The new version of the
Monte Carlo code (called MOCCA), in addition to the features of the old
version, incorporates the direct Fewbody integrator (Fregeau et al. 2004) for
three- and four-body interactions, and a new treatment of the escape process
based on Fukushige & Heggie (2000). Now stars which fulfil the escape criterion
are not removed immediately, but can stay in the system for a certain time
which depends on the excess of the energy of a star above the escape energy.
They are called potential escapers. With the addition of the Fewbody integrator
the code can follow all interaction channels which are important for the rate
of creation of various types of objects observed in star clusters, and ensures
that the energy generation by binaries is treated in a manner similar to the
$N$-body model.
  There are at most three new parameters which have to be adjusted against
$N$-body simulations for large $N$: two (or one, depending on the chosen
approach) connected with the escape process, and one responsible for the
determination of the interaction probabilities. The values adopted for the free
parameters have at most a weak dependence on $N$. They allow MOCCA to reproduce
$N$-body results with reasonable precision, not only for the rate of cluster
evolution and the cluster mass distribution, but also for the detailed
distributions of mass and binding energy of binaries. Additionally, the code
can follow the rate of formation of blue stragglers and black hole - black hole
binaries.
