We study the prospects for observing superfluidity in a spin-polarized atomic gas of 6 Li atoms, using state-of-the-art interatomic potentials. We determine the spinodal line and show that a BCS transition to the superfluid state can indeed occur in the (meta)stable region of the phase diagram if the densities are sufficiently low. We also discuss the stability of the gas due to exchange and dipolar relaxation and conclude that the prospects for observing superfluidity in a magnetically trapped atomic 6 Li gas are particularly promising for magnetic bias fields larger than 10 T. PACS numbers: 03.75.Fi, 32.80.Pj, 42.50.Vk Ultracold atomic gases have received much attention in recent years, because of their novel properties. For instance, these gases are well suited for high-precision measurements of single-atom properties and for the observation of collisional and optical phenomena that reflect the (Bose or Fermi) statistics of the constituent particles. Moreover, a large variety of experimental techniques are available to manipulate the atomic gas samples by means of electromagnetic fields, which offers the exciting possibility to achieve the required conditions for quantum degeneracy and to study macroscopic quantum effects in their purest form.At present, most experimental attempts towards quantum degeneracy have been performed with bosonic gases and have been aimed at the achievement of Bose-Einstein condensation. In particular, most of the earlier experiments used atomic hydrogen [1,2]. These experiments provided crucial ingredients for the recent attempts with alkali vapors, for which the experimental advances towards the degeneracy regime were so rapid that Bose-Einstein condensation has actually been reported now for the isotopes 87 Rb [3] and 7 Li [4].In view of these exciting developments it seems timely to investigate theoretically also the properties of spinpolarized atomic 6 Li, since 6 Li is a stable fermionic isotope of lithium that can be trapped and cooled in much the same way as its bosonic counterpart. Therefore, magnetically trapped 6 Li promises to be an ideal system to study degeneracy effects in a weakly interacting Fermi gas, thus providing valuable complementary information on the workings of quantum mechanics at the macroscopic level. Moreover, using a combination of theoretical analysis and experimental results [5][6][7], accurate knowledge of the interparticle (singlet and triplet) potential curves of lithium have recently been obtained, which lead to the prediction of a large and negative s-wave scattering length a of 24.6 3 10 3 a 0 (a 0 is the Bohr radius) for a spin-polarized 6 Li gas. This is important for two reasons: First, the fact that the scattering length is negative implies that at the low temperatures of interest [L ¿ r V , where L ͑2ph 2 ͞mk B T͒ 1͞2 is the thermal de Broglie wavelength of the atoms and r V is the range of the interaction] the effective interaction between the lithium atoms is attractive, and we expect a BCS-like phase transition to a superfluid state ...