  Quasi-one-dimensional (quasi-1d) two-component Fermi gases with effectively
attractive and repulsive interactions are characterized for arbitrary
interaction strength. The ground-state properties of the gas confined in highly
elongated harmonic traps are determined within the local density approximation.
For strong attractive effective interactions the existence of a molecular
Tonks-Girardeau gas is predicted. The frequency of the lowest breathing mode is
calculated as a function of the coupling strength for both attractive and
repulsive interactions.
