It is well known that massive neutrinos have nontrivial electromagnetic properties and at least
magnetic moments of neutrinos should be nonzero. For many years, until 2004, it was believed
that neutrino helicity precession and the corresponding spin oscillations can be induced by the
neutrino magnetic moment interactions with the transversal magnetic field. A new and very in-
teresting possibility for neutrino spin (and spin-flavour) oscillations engendered by the neutrino
interaction with matter background was proposed and investigated in [1] (also mentioned in [2]).
The origin of the new type neutrino spin oscillations $\nu^{-}\Leftrightarrow\nu^{+}$ in the background matter is the
neutrino weak interactions with the transversal matter current $ j_{\perp}$ (determined by the contribution
$G_F j_{\perp}$ to the neutrino evolution Hamiltonian) that generates the corresponding mixing between
neutrino states $\nu_{e}^{-}$ and $\nu_{e}^{+}$. The existence of this effect has been confirmed recently by other authors (see, for instance, [3]). For historical notes reviewing studies and derivation of the discussed
effect see also [4]. In these notes below we give a short flash on the quantum treatment of the
effect that, as an example, result with the exact probability of the spin oscillations between the
electron neutrino states $\nu_{e}^{-}$ and $\nu_{e}^{+}$ in the transversal matter current $ j_{\perp}$.

References
[1] A. Studenikin, Neutrinos in electromagnetic fields and moving media, Phys. Atom. Nucl. 67 (2004)
993.
[2] A. Studenikin, Neutrino in magnetic fields: From the first studies to the new effects in neutrino
oscillations, Frascati Physics Series 34 (2004) 155, hep-ph/0407010.
[3] A. Kartavtsev, G. Raffelt, H. Vogel, Neutrino propagation in media: Flavor-, helicity-, and pair
correlations, Phys. Rev. D 91 (2015) 125020.
[4] A. Studenikin, Neutrino spin and spin-flavour oscillations in transversally moving or polarized matter, J. Phys. Conf. Ser. 888 (2017) 012221, arXiv:1610.06563 [hep-ph]