Abstract
A perturbation method is developed for calculating the oscillating frequencies of collective modes of trapped superfluid Fermi gases from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensation (BEC). Based on the complete and orthogonal eigenfunction set obtained recently and a series expansion of the equation of state beyond the mean-field approximation, the corrections of eigenfrequencies and eigenfunctions of all collective modes are given systematically, which are valid for various superfluid regimes in the BCS-BEC crossover beyond the mean-field approximation. Expressions of frequency correction of the collective modes for both spherical and axial symmetric traps excited near the BCS, BEC, and unitarity limits are provided explicitly, and their dependence on interatomic interaction strength and anisotropic trapping parameter is also discussed in detail.
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