  We use boson-fermion mapping to show that the single-particle momentum
distribution in a one-dimensional gas of hard point-like bosons (Tonks gas)
inside a harmonic trap decays as $p^{-4}$ at large momentum $p$. The relevant
integrals expressing the one-body density matrix are evaluated for small
numbers of particles in a simple Monte Carlo approach to test the extent of the
asymptotic law and to illustrate the slow decay of correlations between the
matter-wave field at different points.
