The LMA MSW Solution of the Solar Neutrino Problem, Inverted Neutrino Mass Hierarchy and Reactor Neutrino Experiments

In the context of three-neutrino oscillations, we study the possibility of using antineutrinos from nuclear reactors to explore the 10^{-4} {\rm eV^2} < \ms \ltap 8\times 10^{-4} {\rm eV^2} region of the LMA MSW solution of the solar neutrino problem and measure $\ms$ with high precision. The KamLAND experiment is not expected to determine $\ms$ if the latter happens to lie in the indicated region. By analysing both the total event rate suppression and the energy spectrum distortion caused by \bar{\nu}_e oscillations in vacuum, we show that the optimal baseline of such an experiment is L \sim (20 - 25) km. Furthermore, for 10^{-4} {\rm eV^2} < \ms \ltap 5\times 10^{-4} {\rm eV^2}, the same experiment might be used to try to distinguish between the two possible types of neutrino mass spectrum - with normal or with inverted hierarchy, by exploring the effect of interference between the atmospheric- and solar- \Delta m^2 driven oscillations; for larger values of \ms not exceeding 8.0\times 10^{-4} eV^2, a shorter baseline, L \cong 10 km, would be needed for the purpose. The indicated interference effect modifies in a characteristic way the energy spectrum of detected events. Distinguishing between the two types of neutrino mass spectrum requires, however, a high precision determination of the atmospheric \Delta m^2, a sufficiently large \sin^2\theta and a non-maximal \sin^22\theta_{\odot}, where \theta and \theta_{\odot} are the mixing angles respectively limited by the CHOOZ and Palo Verde data and characterizing the solar neutrino oscillations. It also requires a relatively high precision measurement of the positron spectrum in the reaction \bar{\nu}_e + p \to e^{+} + n.