  We consider the sensitivity of future neutrino experiments in the low energy
region, such as BOREXINO or HELLAZ, to a solar electron antineutrino signal. We
show that, if neutrino conversions within the Sun result in partial
polarization of initial solar neutrino fluxes, then a new opportunity arises to
observe the electron antineutrinos and thus to probe the Majorana nature of the
neutrinos. This is achieved by comparing the slopes of the energy dependence of
the differential neutrino electron scattering cross section for different
neutrino conversion scenarios. We also show how the \nu_e -> \bar{\nu}_e
conversions may take place for low energy solar neutrinos while being
unobservable at the Kamiokande and Super-Kamiokande experiments.
