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Using arguments based on sum rules, we derive a general result for the average shifts of rf lines in Fermi gases in terms of interatomic interaction strengths and two-particle correlation functions.
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Integrating ∂ ( E / V ) / ∂ g 12 − 1 = − g 12 2 n 2 \partial(E/V)/\partial g_{12}^{-1}=-g_{12}^{2}n^{2} with respect to g ¯ \bar{g} we recover immediately the low-energy result, E int / V = g 12 n 2 E_{\rm int}/V=g_{12}n^{2}
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M. Bartenstein, A. Altmeyer, S. Riedl, R. Geursen, S. Jochim, C. Chin , J. H. Denschlag, R. Grimm, A. Simoni, E. Tiesinga, C. J. Williams, and P. S. Julienne, Phys. Rev. Lett. 94
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One can calculate the total weight at frequencies ∼ < ϵ F {\raisebox{-2.15277pt}{$\stackrel{{\scriptstyle<}}{{\sim}}$}}\epsilon_{\rm F} energy using an effective low-energy Hamiltonian with renormalized couplings. The correlation function for the low energy excitations of the system is given by the Hartree approximation, and so the average shift of transitions with energies ∼ < ϵ F \raisebox{-2.15277pt}{$\stackrel{{\scriptstyle<}}{{\sim}}$}\,\epsilon_{\rm F} is again given by Eq. ( 11
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