  Using anyon-fermion mapping method, we investigate the ground state
properties of hard-core anyons confined in a one-dimensional harmonic trap. The
concise analytical formula of the reduced one-body density matrix are obtained.
Basing on the formula, we evaluated the momentum distribution, the natural
orbitals and their occupation distributions for different statistical
parameters. The occupation and occupation fraction of the lowest natural
orbital versus anyon number are also displayed. It is shown that the ground
state properties of anyons interplay between Bosons and Fermions continuously.
We can expect that the hard-core anyons of larger statistical parameter exhibit
the similar properties to the hard-core Bosons although anyon system satisfy
specific fractional statistics.
