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When the atoms are prepared in the spin-stretched state and the molecules in the spin-stretched component of the first rotationally excited state, they collide inelastically with a rate coefficient of $k_2 = (6.6 \\pm 1.5) \\times 10^{-11}$ cm$^{3}$/s at temperatures near 100~$\\mu$K. We attribute this to rotation-changing collisions. 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