The Unitary Fermi Gas in a Harmonic Trap and its Static Response

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We use harmonically trapped systems to find the leading gradient corrections of the supefluid local density approximation (SLDA) - a density functional theory (DFT) describing the unitary Fermi gas (UFG). We find the leading order correction to be negative, and predict the q² coefficient of the long-range static response c = 1.5(3) - a factor of two smaller than predicted by mean-field theory - thereby establishing a new and experimentally measurably universal constant.