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We investigate the single-particle properties at T=0 of a trapped superfluidgas of Fermi atoms with a Feshbach resonance. A tunable pairing interactionassociated with the Feshbach resonance leads to the BCS-BEC crossover, wherethe character of superfluidity continuously changes from the BCS-type to a BECof composite bosons. In this paper, we extend our previous work for a uniformsuperfluid Fermi gas [Y. Ohashi and A. Griffin, Phys. Rev. A {\bf 67}, 063612(2003)] to include the effect of a harmonic trap. We directly solve theBogoliubov-de Gennes coupled equations, and find self-consistent values for thespatially-dependent local density $n({\bf r})$ as well as the composite BCSorder parameter ${\tilde \Delta}({\bf r})$. Using these results, we calculatethe single-particle density of states in the crossover region, and from thisdetermine the true single-particle energy gap ($E_{\rm g}$) of the trappedFermi superfluid at T=0. This is associated with the in-gap (or Andreev) statesin the low density region at the edge of the trap. We calculate thelaser-induced current $I(\omega)$, as measured in recent rf-spectroscopyexperiments. We show how the high-energy part of $I(\omega)$ gives informationabout ${\tilde \Delta}(r=0)$ at the center of the trap. We emphasize that thenarrow "unpaired atom" peak in the rf-data gives information about $E_g$ andthe low-energy in-gap states of a Fermi superfluid. While our calculations arelimited at T=0, we use them to discuss the recent Innsbruck data and the LDAcalculations of T\"orm\"a and co-workers.Comment: 47 pages, 22 figure

Single-particle excitations in a trapped gas of Fermi atoms in the BCS-BEC crossover region