  Ultracold atomic gases with short-range interactions are characterized by a
number of universal species-independent relations. Many of these relations
involve the two-body Tan contact. Employing the canonical ensemble, we
determine the Tan contact for small harmonically trapped two-component Fermi
gases at unitarity over a wide range of temperatures, including the zero and
high temperature regimes. A cluster expansion that describes the properties of
the N-particle system in terms of those of smaller subsystems is introduced and
shown to provide an accurate description of the contact in the high temperature
regime. Finite-range corrections are quantified and the role of the Fermi
statistics is elucidated by comparing results for Fermi, Bose and Boltzmann
statistics.
