  The transition from the weakly interacting BCS regime to the strongly
interacting unitary regime is explored for ultracold trapped Fermi gases
assuming a normal mode description of the gas instead of the conventional
Cooper pairing. The Pauli principle is applied ``on paper'' by using specific
normal mode assignments. Energies, entropies, critical temperatures, and an
excitation frequency are studied and compared to existing results in the
literature. These normal modes have been derived analytically for N identical,
confined particles from a first-order L=0 group theoretic solution of a
three-dimensional Hamiltonian with a general two-body interaction. In previous
studies, normal modes were able to describe the unitary regime obtaining ground
state energies comparable to benchmark results and thermodynamics quantities in
excellent agreement with experiment. In a recent study, the behavior of the
normal mode frequencies was investigated for Hamiltonians with a range of
interparticle interaction strengths from BCS to unitarity in the first test of
this approach beyond the unitary regime, and a microscopic basis of the large
excitation gaps and universal behavior at unitarity was proposed. Based on the
success of these earlier studies, the current paper continues to explore the
ability of normal modes to describe superfluidity along the BCS to unitarity
transition. The results confirm earlier conclusions that the physics of
superfluidity can be described using normal modes across a wide range of
interparticle interaction strengths and offer an alternative to the two-body
pairing models commonly used to describe superfluidity along this transition.
