  This work explains a delayed-coincidence method to perform MeV-scale neutrino
spectroscopy with electron-neutrino capture on gallium. An electron-neutrino
possessing energy greater than 407.6 keV can be captured on gallium and produce
a daughter germanium nucleus at its first excited state with a mean lifetime of
114 ns. The released electron and gammas before the first excited state of Ge
can generate a prompt signal representing the solar neutrino energy and the
gamma from the deexcitation of the first excited state, 175 keV, can give a
delayed signal. The cross-section of this electron-neutrino capture process is
evaluated and is comparable with electron-neutrino capture on chlorine. A
possible implementation with a liquid scintillator is discussed to exploit the
delayed coincidence. The detection scheme is more feasible than using 115In,
etc, but need a larger target. The proposed method can be helpful for the
MeV-scale solar neutrino spectroscopy and for solving the gallium anomaly.
