  The contact parameter in unitary Fermi Gases governs the short-distance,
high-momentum, and high-energy properties of the system. We perform accurate
quantum Monte Carlo calculations with highly optimized trial functions to
precisely determine this parameter at T=0, demonstrate its universal
application to a variety of observables, and determine the regions of momentum
and energy over which the leading short-range behavior is dominant. We derive
Tan's expressions for the contact parameter using just the short-range behavior
of the ground-state many-body wave function, and use this behavior to calculate
the two-body distribution function, one-body density matrix, and the momentum
distribution of unitary Fermi gases; providing a precise value of the contact
parameter that can be compared to experiments.
