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In the BCS limit density profiles for unpolarized trapped fermionic clouds ofatoms are largely featureless. Therefore, it is a delicate task to analyze themin order to quantify their respective interaction and temperaturecontributions. Temperature measurements have so far been mostly considered inan indirect way, where one sweeps isentropically from the BCS to the BEC limit.Instead we suggest here a direct thermometry, which relies on measuring thecolumn density and comparing the obtained data with a Hartree-Bogoliubovmean-field theory combined with a local density approximation. In case of anattractive interaction between two-components of $^{6}$Li atoms trapped in atri-axial harmonic confinement we show that minimizing the error within such anexperiment-theory collaboration turns out to be a reasonable criterion foranalyzing in detail measured densities and, thus, for ultimately determiningthe sample temperatures. The findings are discussed in view of various possiblesources of errors.

Unravelling Interaction and Temperature Contributions in Unpolarized Trapped Fermionic Atoms in the BCS Regime