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We present a theoretical interpretation of a recent experiment presented inref. \cite{Zwierlein06} on the density profile of Fermi gases with unbalancedspin populations. We show that in the regime of strong interaction, theboundaries of the three phases observed in \cite{Zwierlein06} can becharacterized by two dimensionless numbers $\eta\_\alpha$ and $\eta\_\beta$.Using a combination of a variational treatment and a study of the experimentalresults, we infer rather precise bounds for these two parameters.Comment: 4 pages, 2 figure

Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations