content_image/341904.jpg content_image/341907.jpg content_image/341909.jpg content_image/341908.jpg
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where v is the average speed and ℓ$_{free}$ the mean free path. The mean free path is ℓ$_{free}$ = 1 / $_{(}$√$_{2}$$_{nσ}$$_{) where}$ σ is the total cross-section. The √$_{2 comes from the ratio}$ of the mean speed to the mean relative speed[28]. In the unitary limit, formally S = 1 + i IM = − 1, which implies the scattering amplitude M = 2 i/ I . (See section IV.) The cross-section in eq. (7) gives σ = m $^{2}$/k I 2 in 2 dimensions, where I = m/ 4[20]. Thus, in the unitary limit 

where k is a single particle momentum. This gives 

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