Large momentum part of a strongly correlated Fermi gas

It is well known that the momentum distribution of the two-component Fermi gas with large scattering length has a tail proportional to 1/k41/k4 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/k41/k4 tail and various physical quantities, including the pressure at thermal equilibrium and the rate of change of energy in a dynamic sweep of the inverse scattering length.