GLYPH<c110> RateGLYPH<.notdef>G/ s GLYPH<c109> k n(k) 4 GLYPH<c50> GLYPH<c112> GLYPH<c110> GLYPH<c71> GLYPH<c51>GLYPH<c47>GLYPH<c50> GLYPH<c50> 3/2 ( ) GLYPH<c110> k C a b 0 0.5 1.0 1.5 0 2 0 0.5 1.0 1.5 2.0 2.5 2 4 6 8 0 2 4 6 8 10 12 2 4 6 FIG. 1: Extracting the contact from the momentum distribution and rf lineshape. (a) Measured momentum distribution for a Fermi gas at 1 k$_{F}$ a = − 0 . 08 ± 0 . 10. Here, the wave number k is given in units of k$_{F}$ , and we plot the normalized n ( k ) multiplied by k $^{4}$. The dashed line corresponds to C = 2 . 15 ± 0 . 2, which is obtained by averaging k $^{4}$n ( k ) for k > 1 . 85. (Inset) The measured value for C depends on the rate of the magnetic-field ramp that turns off the interactions before time-of-flight expansion. (b) RF lineshape measured for a Fermi gas at 1 k$_{F}$ a = − 0 . 03 ± 0 . 10. Here, ν is the rf detuning from the single-particle Zeeman resonance, given in units of E$_{F}$ /h . We plot the normalized rf lineshape multiplied by 2 3 / $^{2}$π$^{2}$ν3 / $^{2}$, which is predicted to asymptote to C for large ν . Here, we obtain C = 2 . 13 ± 0 . 2 (dashed line) from an average of the data for ν > 5. Fig. 1a were taken using a magnetic-field sweep rate of approximately 1 . 4 G µs to turn off the interactions for the expansion. In the inset to Fig. 1a, we show the dependence of the measured C on the magnetic-field sweep rate. Using an empirical exponential fit (line in Fig. 1a inset), we estimate that at our typical sweep rate of approximately 1 . 4 G µs our measured C is systematically low by about 10%. We have therefore scaled the contact measured with this method by 1 . 1. The contact is also manifest in rf spectroscopy, where one applies a pulsed rf field and counts the number of atoms that are transferred from one of the two original spin states into a third, previously unoccupied, spin state [12]. We transfer atoms from the | 9 / 2 , − 7 / 2 〉 state to the | 9 / 2 , − 5 / 2 〉 state. It is predicted that the number of atoms transferred as a function of the rf frequency, ν , scales as ν − 3 / 2 for large ν , and that the amplitude of this high frequency tail is C 2 3 / $^{2}$π 2 [13–15]. Here, ν = 0 is the single-particle spin-flip resonance, 4