  We present a novel analytical approach for the calculation of the mean
density of states in many-body systems made of confined indistinguishable and
non-interacting particles. Our method makes explicit the intrinsic geometry
inherent in the symmetrization postulate and, in the spirit of the usual Weyl
expansion for the smooth part of the density of states in single-particle
confined systems, our results take the form of a sum over clusters of particles
moving freely around manifolds in configuration space invariant under elements
of the group of permutations. Being asymptotic, our approximation gives
increasingly better results for large excitation energies and we formally
confirm that it coincides with the celebrated Bethe estimate in the appropriate
region. Moreover, our construction gives the correct high energy asymptotics
expected from general considerations, and shows that the emergence of the
fermionic ground state is actually a consequence of an extremely delicate large
cancellation effect. Remarkably, our expansion in cluster zones is naturally
incorporated for systems of interacting particles, opening the road to address
the fundamental problem about the interplay between confinement and
interactions in many-body systems of identical particles.
