  We present a new combinatorial method for the calculation of the nuclear
level density. It is based on a Monte Carlo technique, in order to avoid a
direct counting procedure which is generally impracticable for high-A nuclei.
The Monte Carlo simulation, making use of the Metropolis sampling scheme,
allows a computationally fast estimate of the level density for many fermion
systems in large shell model spaces. We emphasize the advantages of this Monte
Carlo approach, particularly concerning the prediction of the spin and parity
distributions of the excited states, and compare our results with those derived
from a traditional combinatorial or a statistical method. Such a Monte Carlo
technique seems very promising to determine accurate level densities in a large
energy range for nuclear reaction calculations.
