  We theoretically investigate the ground state of trapped neutral fermions
with population imbalance in the BCS-BEC crossover regime. On the basis of the
single-channel Hamiltonian, we perform full numerical calculations of the
Bogoliubov-de Gennes equation coupled with the regularized gap and number
equations. The zero-temperature phase diagram in the crossover regime is
presented, where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state
governs the weak-coupling BCS region of a resonance. It is found that the FFLO
oscillation vanishes in the BEC side, in which the system under population
imbalance turns into a phase separation (PS) between locally binding superfluid
and fully polarized spin domains. We also demonstrate numerical calculations
with a large particle number O(10^5), comparable to that observed in recent
experiments. The resulting density profile on a resonance yields the PS, which
is in good agreement with the recent experiments, while the FFLO modulation
exists in the pairing field. It is also proposed that the most favorable
location for the detection of the FFLO oscillation is in the vicinity of the
critical population imbalance in the weak coupling BCS regime, where the
oscillation periodicity becomes much larger than the interparticle spacing.
Finally, we analyze the radio-frequency (RF) spectroscopy in the imbalanced
system. The clear difference in the RF spectroscopy between BCS and BEC sides
reveals the structure of the pairing field and local ``magnetization''.
