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The reaction $~{12}{\rm C}(\nu_\mu,\mu~-) {\rm X}$ has been measured near threshold using a $\pi ~+$ decay-in-flight $\nu_\mu$ beam from the Los Alamos Meson Physics Facility and a massive liquid scintillator neutrino detector (LSND). In the energy region $123.7 < {\rm E}_\nu < 280$ MeV, the measured spectral shape is consistent with that expected from the Fermi Gas Model. However, the measured flux--averaged inclusive cross section ($(8.3 \pm 0.7 {\rm stat.} \pm 1.6 {\rm syst.}) \times 10~{-40} {\rm cm}~2$) is more than a factor of 2 lower than that predicted by the Fermi Gas Model and by a recent random phase approximation calculation.
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