4 and Discovery Projects DP0984522 and DP0984637. which may be due to reduced pairing at the finite tem- perature ( T/T$_{F}$ = 0 . 10 ± 0 . 02 at unitarity). At 1 / ( k$_{F}$ a ) = -0.2 the temperature will be lower following the adia- batic magnetic field sweep [34] while at 1 / ( k$_{F}$ a ) = +0.3 the temperature will be higher but pairing takes place at much higher temperatures. At T ≪ T$_{C}$ ( ≃ 0 . 2 T$_{F}$ ) , phonons dominate the excitations and the contact should increase as ( T/T$_{F}$ ) 4 [35]. In the relevant temperature window, we estimate this increase to be only 0 . 1% which could easily be negated by normal single-particle excita- tions localized at the cloud edge. At 1 / ( k$_{F}$ a ) = +0.3 the data depart from a straight line displaying the downward curvature consistent with the first order term in Eq. (2). A similar upward curvature is seen at 1 / ( k$_{F}$ a ) = -0.2. Our simple relation Eq. (2) is seen to accurately describe S ( k ) on both sides of the Feshbach resonance demon- strating the wide applicability of the Tan relations. In summary, we have shown that the structure fac- tor of a strongly interacting ultracold Fermi gas follows a universal law which is a direct consequence of Tan’s relation for the pair correlation functions. Our measure- ments provide one of the first demonstrations of a broadly applicable exact result for Fermi gases in the BEC-BCS crossover. This work opens the way to a complete tem- perature and interaction dependent map of the contact through the BEC-BCS crossover and may provide a new means for obtaining the equation of state. This work is supported by the Australian Research Council Centre of Excellence for Quantum-Atom Optics Figure 3. Universal dependence of the static structure fac- tor of a strongly interacting Fermi superfluid. Measured and calculated static structure factor versus k$_{F}$ /k for 1 / ( k$_{F}$ a ) = +0.3, 0.0, and -0.2. Bragg momentum k is fixed while k$_{F}$ is varied by changing the mean trapping frequency ¯ ω . Vertical error bars are due to atom number fluctuations and uncer- tainties in measuring the center of mass and horizontal error bars are due to atom number fluctuations and uncertainties in ¯ ω . Solid lines are the zero temperature theory and the dashed line is a straight line fit to the 1 / ( k$_{F}$ a ) = 0 data yielding a slope of 0 . 75 ± 0 . 03 . 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 1.00 1.10 1.20 1.30 1.40 S ( k ) k$_{F }$ / k 1/ k$_{F }$a + 0.30 - 0.20  0.00 [1] H. Heiselberg, Phys. Rev. A 63 , 043606 (2001). [2] T.-L. Ho, Phys. Rev. Lett. 92 , 090402 (2004). [3] H. Hu, P.D. Drummond, and X.-J. Liu, Nat. Phys. 3 , 469 (2007). [4] S. Jochim et al. Science 302 , 2101 (2003). [5] M. Greiner, C. A. Regal, and D. S. Jin, Nature 426 , 537 (2003). [6] M. W. Zwierlein et al. , Nature 435 , 1047 (2005). [7] J. Kinast et al. , Science 307 , 1296 (2005). [8] G. B. Partridge et al. Phys. Rev. Lett. 95 , 020404 (2005). [9] S. Nascimbène et al. Nature 463 , 1067 (2010). [10] N. Navon S. Nascimbène, F. Chevy and C. Salomon, Sci- ence 328 , 729 (2010). [11] S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 80 , 1215 (2008). [12] S. Tan, Ann. Phys. 323 , 2952 (2008). [13] S. Tan, Ann. Phys. 323 , 2971 (2008). [14] S. Tan, Ann. Phys. 323 , 2987 (2008). [15] R. Combescot, S. Giorgini, and S. Stringari, Europhys. Lett. 75 , 695 (2006). [16] H. Hu, X.-J. Liu, and P. D. Drummond, Europhys. Lett. 74 , 574 (2006). [17] E. Braaten, and L. Platter, Phys. Rev. Lett. 100 , 205301 (2008). [18] S. Zhang and A. J. Leggett, Phys. Rev. A 79, 023601 (2009). [19] F. Werner, L. Tarruell, and Y. Castin, Eur. Phys. J. B 68 , 401 (2009). [20] J. T. Stewart, J. P. Gaebler, T. E. Drake, and D. S. Jin, Phys. Rev. Lett. 104 , 235301 (2010). [21] L. Luo et al. , Phys. Rev. Lett. 98 , 080402 (2007). [22] G. E. Astrakharchik, J. Boronat, J. Casulleras, and S. Giorgini, Phys. Rev. Lett. 93 , 200404 (2004). [23] X.-J. Liu, H. Hu, and P. D. Drummond, Phys. Rev. Lett. 102 , 160401 (2009). [24] D. Pines, and P. Nozières, The Theory of Quantum Liq- uids, Vol. I (Benjamin, New York, 1966). [25] J. Stenger et al. , Phys. Rev. Lett. 82 , 4569 (1999). [26] F. Zambelli, L. P. Pitaevskii, D. M. Stamper-Kurn, and S. Stringari, Phys. Rev. A 61 , 063608 (2000). [27] D.M. Stamper-Kurn et al. , Phys. Rev. Lett. 83 , 2876 (1999). [28] J. Steinhauer, R. Ozeri, N. Katz, and N. Davidson, Phys. Rev. Lett. 88 , 120407 (2002). [29] G. Veeravalli, E. Kuhnle, P. Dyke, and C. J. Vale, Phys. Rev. Lett. 101 , 250403 (2008). [30] C. H. Schunck, Y. Shin, A. Schirotzek, and W. Ketterle, Nature 454 , 739 (2008). [31] J. T. Stewart, J. P. Gaebler, and D. S. Jin, Nature 454 , 744 (2008). [32] J. Fuchs et al. , J. Phys. B: At. Mol. Opt. Phys. 40 , 4109 (2007). [33] A. Brunello et al. Phys. Rev. A 64 , 063614 (2001). [34] L. D. Carr, G. V. Shlyapnikov, and Y. Castin, Phys. Rev. Lett. 92 , 150404 (2004). [35] Z. Yu, G. M. Bruun, and G. Baym, Phys. Rev. A 80 , 023615 (2009).