Neutrino-electron scattering in a magnetic field with allowance for polarizations of electrons

We present an analytic formula for differential cross section (DCS) of neutrino-electron scattering (NES) in a magnetic field (MF) with allowance for longitudinal polarizations of initial and final electrons (IAFE). The DCS of NES in a MF is sensitive to the spin variable of the IAFE and to the direction of the incident and scattered neutrinos (IASN) momenta. Spin asymmetries and field effects in NES in a MF enable us to use initial electrons having a left-hand circular polarization (LHCP) as polarized electron targets in detectors for detection of low-energy neutrinos or relic neutrinos and for distinguishing neutrino flavor (NF). In general, gas consisting of only electrons having a LHCP and gas consisting of only electrons having a right-hand circular polarization (RHCP) are heated by neutrinos asymmetrically. The asymmetry of heating (AH) is sensitive to NF, MF strength, energies (Landau quantum numbers and third components of the momenta) of IAFE, final electron chemical potential, the final temperature of gas consisting of only electrons having a LHCP (RHCP), polar angles of IASN momenta, the difference between the azimuthal angles of IASN momenta, the angle {phi}, and IASN energies. In the heating process of electrons by neutrinos the dominant role belongs to electron neutrinos compared with the contribution of muon (tauon) neutrinos. Electrons having a LHCP in NES in a MF are heated by {nu}{sub e} and {nu}{sub {mu}}({nu}{sub {tau}}) unequally when both the IASN fly along or against the MF direction. For magnetars and neutrinos of 1 MeV energy, within the considered kinematics, the AH in an electron neutrino-electron scattering is 2.23 times that in a muon neutrino-electron scattering or in a tauon neutrino-electron scattering.