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The T2K off-axis near detector, ND280, is used to make the first differentialcross-section measurements of electron neutrino charged current interactions atenergies ~1 GeV as a function of electron momentum, electron scattering angleand four-momentum transfer of the interaction. The total flux-averaged $\nu_e$charged current cross-section on carbon is measured to be$1.11\pm0.09~(stat)\pm0.18~(syst)\times10^{-38} cm^2/nucleon$. The differentialand total cross-section measurements agree with the predictions of two leadingneutrino interaction generators, NEUT and GENIE. The NEUT prediction is$1.23\times10^{-38} cm^2/nucleon$ and the GENIE prediction is$1.08\times10^{-38} cm^2/nucleon$. The total $\nu_e$ charged currentcross-section result is also in agreement with data from the Gargamelleexperiment.

Measurement of the Inclusive Electron Neutrino Charged Current Cross Section on Carbon with the T2K Near Detector