The cross section for the elastic scattering reaction nu_e+e- -> nu_e+e- was measured by the Liquid Scintillator Neutrino Detector using a mu+ decay-at-rest nu_e beam at the Los Alamos Neutron Science Center. The standard model of electroweak physics predicts a large destructive interference between the charge current and neutral current channels for this reaction. The measured cross section, sigma_{nu_e e-}=[10.1 +- 1.1(stat.) +- 1.0(syst.)]x E_{nu_e} (MeV) x 10^{-45} cm^2, agrees well with standard model expectations. The measured value of the interference parameter, I=-1.01 +- 0.13(stat.) +- 0.12(syst.), is in good agreement with the standard model expectation of I^{SM}=-1.09. Limits are placed on neutrino flavor-changing neutral currents. An upper limit on the muon-neutrino magnetic moment of 6.8 x 10^{-10} mu_{Bohr} is obtained using the nu_mu and \bar{nu}_mu fluxes from pi+ and mu+ decay.
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