  We investigate the single-particle properties at T=0 of a trapped superfluid
gas of Fermi atoms with a Feshbach resonance. A tunable pairing interaction
associated with the Feshbach resonance leads to the BCS-BEC crossover, where
the character of superfluidity continuously changes from the BCS-type to a BEC
of composite bosons. In this paper, we extend our previous work for a uniform
superfluid 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 the
Bogoliubov-de Gennes coupled equations, and find self-consistent values for the
spatially-dependent local density $n({\bf r})$ as well as the composite BCS
order parameter ${\tilde \Delta}({\bf r})$. Using these results, we calculate
the single-particle density of states in the crossover region, and from this
determine the true single-particle energy gap ($E_{\rm g}$) of the trapped
Fermi superfluid at T=0. This is associated with the in-gap (or Andreev) states
in the low density region at the edge of the trap. We calculate the
laser-induced current $I(\omega)$, as measured in recent rf-spectroscopy
experiments. We show how the high-energy part of $I(\omega)$ gives information
about ${\tilde \Delta}(r=0)$ at the center of the trap. We emphasize that the
narrow "unpaired atom" peak in the rf-data gives information about $E_g$ and
the low-energy in-gap states of a Fermi superfluid. While our calculations are
limited at T=0, we use them to discuss the recent Innsbruck data and the LDA
calculations of T\"orm\"a and co-workers.
