  The one-particle density matrices for hard core bosons in a one-dimensional
harmonic trap are computed numerically for systems with up to 160 bosons.
Diagonalization of the density matrix shows that the many-body ground state is
not Bose-Einstein condensed. The ground state occupation, the amplitude of the
lowest natural orbital, and the zero momentum peak height scale as powers of
the particle number, and the corresponding exponents are related to each other.
Close to its diagonal, the density matrix for hard core bosons is similar to
the one of noninteracting fermions.
