  We analyze charged-current electron-neutrino cross sections on Carbon. We
consider two different theoretical approaches, on one hand the Continuum Random
Phase Approximation (CRPA) which allows a description of giant resonances and
quasielastic excitations, on the other hand the RPA-based calculations which
are able to describe multinucleon emission and coherent and incoherent pion
production as well as quasielastic excitations. We compare the two approaches
in the genuine quasielastic channel, and find a satisfactory agreement between
them at large energies while at low energies the collective giant resonances
show up only in the CRPA approach. We also compare electron-neutrino cross
sections with the corresponding muon-neutrino ones in order to investigate the
impact of the different charged-lepton masses. Finally, restricting to the
RPA-based approach we compare the sum of quasielastic, multinucleon emission,
coherent and incoherent one-pion production cross sections (folded with the
electron-neutrino T2K flux) with the charged-current inclusive
electron-neutrino differential cross sections on Carbon measured by T2K. We
find a good agreement with the data. The multinucleon component is needed in
order to reproduce the T2K electron-neutrino inclusive cross sections.
