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We investigate two-component attractive Fermi gases with imbalanced spinpopulations in trapped one dimensional configurations. The ground stateproperties are determined within local density approximation, starting from theexact Bethe-ansatz equations for the homogeneous case. We predict that theatoms are distributed according to a two-shell structure: a partially polarizedphase in the center of the trap and either a fully paired or a fully polarizedphase in the wings. The partially polarized core is expected to be a superfluidof the FFLO type. The size of the cloud as well as the critical spinpolarization needed to suppress the fully paired shell, are calculated as afunction of the coupling strength.Comment: Final accepted versio

Attractive Fermi Gases with Unequal Spin Populations in Highly Elongated Traps