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We suggest to use a polarized electron target for improving the sensitivity of the search for the neutrino magnetic moment to the level $\sim 3\cdot10^{-13}\mu_B$ in the processes of neutrino (antineutrino) – electron scattering. It is shown that in this case the weak interaction term in the total cross section is significantly suppressed comparing with unpolarized case, but the electromagnetic term does not depend on electron polarization.

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