We report on a calculation of cross sections for charged-current quasielastic antineutrino scattering off $^{12}$C in the energy range of interest for the MiniBooNE experiment. We adopt the impulse approximation (IA) and use the nonrelativistic continuum random phase approximation (CRPA) to model the nuclear dynamics. An effective nucleon-nucleon interaction of the Skyrme type is used. We compare our results with the recent MiniBooNE antineutrino cross-section data and confront them with alternate calculations. The CRPA predictions reproduce the gross features of the shape of the measured double-differential cross sections. The CRPA cross sections are typically larger than those of other reported IA calculations but tend to underestimate the magnitude of the MiniBooNE data. We observe that an enhancement of the nucleon axial mass in CRPA calculations is an effective way of improving on the description of the shape and magnitude of the double-differential cross sections. The rescaling of $M_{A}$ is illustrated to affect the shape of the double-differential cross sections differently than multinucleon effects beyond the IA.
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