Temperature and final state effects in radio frequency spectroscopy experiments on atomic Fermi gases

We present a simple and systematic characterization of the radio frequency (RF) spectra of homogeneous, paired atomic Fermi gases at general temperatures, $T$, in the presence of final state interactions. The spectra, consisting of possible bound states and positive as well as negative detuning ($\nu$) continua, satisfy exactly the zeroth- and first-moment sum rules at all $T$. We show how to best extract the pairing gap and how to detect the $\nu <0$ continuum arising from thermally excited quasiparticles, not yet seen experimentally. We explain semi-quantitatively recent RF experiments on ``bound-bound'' transitions, predicting effects of varying temperature.