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Large momentum part of fermions with large scattering length

Shina Tan
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Abstract

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.

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Shina Tan. 2005-08-13. Large momentum part of fermions with large scattering length. https://doi.org/10.1016/j.aop.2008.03.005

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