0 1 GLYPH<Multiply> 10 6 2 GLYPH<Multiply> 10 6 3 GLYPH<Multiply> 10 6 4 GLYPH<Multiply> 10 6 5 GLYPH<Multiply> 10 6 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Attractive fermions 1 4 π η/s µ/T FIG. 11: The ratio η/s as a function of µ/T as µ/T gets very large.. The horizontal line is 1 / 4 π . The filling fractions are shown for several µ/T up to log z$_{c}$ . From these plots, it appears that f is diverging at k = 0 as z approaches z$_{c}$ , suggestive of condensation to a superfluid. Let us refer to the maximum density then as the critical density The scaling function c is shown in Figure 15. The limiting value is which is considerably less than for a free boson with c = 1. The function b decreases to zero at T/µ → 0, and the limiting value is n$_{c}$ ≈ 1 . 24 m k$_{B}$T 2 π ℏ 2 ⇐⇒ T$_{c}$ ≈ 0 . 81 T$_{F}$ (88) c ( z$_{c}$ ) ≈ 0 . 35 (89) b ( z$_{c}$ ) ≈ 0 . 94 (90) 31 The energy per particle scaling functions ξ and ˜ ξ are shown in Figures 16, 17.