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 semiquantitatively recent rf experiments on "bound-bound" transitions, predicting effects of varying temperature.