Abstract
We present some general considerations on the properties of a two-component ultracold Fermi gas along the BEC-BCS crossover. It is shown that the interaction energy and the free energy can be written in terms of a single dimensionless function $h(\ensuremath{\xi},\ensuremath{\tau})$, where $\ensuremath{\xi}=\ensuremath{-}{({k}_{F}{a}_{s})}^{\ensuremath{-}1}$ and $\ensuremath{\tau}=T∕{T}_{F}$. The function $h(\ensuremath{\xi},\ensuremath{\tau})$ incorporates all the many-body physics and naturally occurs in other physical quantities as well. In particular, we show that the average rf-spectroscopy shift $\overline{\ensuremath{\delta}\ensuremath{\omega}}(\ensuremath{\xi},\ensuremath{\tau})$ and the molecular fraction ${f}_{c}(\ensuremath{\xi},\ensuremath{\tau})$ in the closed channel can be expressed in terms of $h(\ensuremath{\xi},\ensuremath{\tau})$ and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments.
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