  It is well known that the momentum distribution of the two-component Fermi
gas with large scattering length has a tail proportional to $1/k^4$ at large
$k$. We show that the magnitude of this tail is equal to the adiabatic
derivative of the energy with respect to the reciprocal of the scattering
length, multiplied by a simple constant. This result holds at any temperature
(as long as the effective interaction radius is negligible) and any large
scattering length; it also applies to few-body cases. We then show some more
connections between the $1/k^4$ tail and various physical quantities, in
particular the rate of change of energy in a DYNAMIC sweep of the inverse
scattering length.
