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Neutrino magnetic moments in low-energy neutrino scattering on condensed matter systems

The cross sections of elastic neutrino scattering on electrons and nuclei in the regime of low-energy transfer are known to be very sensitive to neutrino electromagnetic properties. In particular, the magnetic moment of the neutrino can be effectively searched using liquid or solid detectors with a very low energy threshold. We present the formalism that incorporates the neutrino magnetic moment contribution in the theoretical treatment of the low-energy elastic neutrino scattering on a condensed-matter target. The concept of the dynamic structure factor is employed to describe the collective effects in the target. The differential cross section for tritium antineutrino scattering on the superfluid $^4$He is calculated numerically. We find that the neutrino magnetic moment of the order of $10^{-11}μ_B$ strongly affects the cross section. Our results can be used in the search of neutrino magnetic moments in future low-energy neutrino scattering experiments with liquid or solid targets.