  In this paper, we indicate a possibility of utilizing the intense chromium
source ($\sim 370 PBq$) in probing the neutrino nature in low energy neutrino
experiments with the ultra-low threshold and background real-time Borexino
detector located near the source ($\sim 8 m$). We analyze the elastic
scattering of electron neutrinos (Dirac or Majorana, respectively) on the
unpolarized electrons in the relativistic neutrino limit. We assume that the
incoming neutrino beam is the superposition of left-right chiral states. Left
chiral neutrinos may be detected by the standard $V A$ and non-standard scalar
$S_L$, tensor $T_L$ interactions, while right chiral ones partake only in the
exotic $V + A$ and $S_R, T_R$ interactions. Our model-independent study is
carried out for the flavour (current) neutrino eigenstates. We compute the
expected event number for the standard $V-A$ interaction of the left chiral
neutrinos using the current experimental values of standard couplings and in
the case of left-right chiral superposition. We show that the significant
decrement in the event number due to the interference terms between the
standard and exotic interactions for the Majorana $\nu_e$'s may appear. The $90
\%$ C. L. sensitivity contours in the planes of corresponding exotic couplings
are also found. The presence of interferences in the Majorana case gives the
stronger constraints than for the Dirac neutrinos, even if the neutrino source
is placed outside the detector.
