We consider a problem of electron motion in different media and magnetic field. It is shown that in case of nonmoving medium and constant homogenious magnetic field the electron energies are quantized. We also discuss the general problem of eigenvectors and eigenvalues of a given class of Hamiltonians. We examine obtained exact solutions for the particular case of the electron motion in a rotating neutron star with account for matter and magnetic field effects. We argue that all of these considerations can be usefull for astrophysical applications.
The modified Dirac equation for the neutrino in a material medium and its solution for a nonuniform motion of the medium with a velocity gradient along a certain direction are examined in the present paper. This formulation of the problem is analogous to the problem of electron motion in a constant uniform magnetic field. This is manifested through a similar character of particle wave functions that in both cases describe the states with circular orbits. A new mechanism of confinement of low-energy neutrinos in fast-rotating dense astrophysical objects is predicted based on this property of the wave functions. As an example of their application, a process of spin light ( SL ν ) of neutrino is examined in this configuration of matter.
In this erratum we revise the results given in the paper concerning the limits on the neutrino charge radii obtained from the analysis of the COHERENT data, that were affected by an incorrect treatment of the antineutrino contribution. In the paper we took into account the fact that neutrinos and antineutrinos have opposite charge radii, but we did not notice that also the weak neutral current couplings change sign from neutrinos to antineutrinos. Indeed, both the electromagnetic vector current and the V − A weak neutral current change sign under a CP transformation that changes left-handed neutrinos into righthanded antineutrinos. Therefore the relative sign of the weak neutral current and charge radius contributions does not change from neutrinos to antineutrinos. This correction leads to significant changes of the limits on the neutrino charge radii obtained from the analysis of the COHERENT data.A revised version of our paper with the correct results and discussion is available as the last version of arXiv:1810.05606. Here we present: 1) the corrected version of Table II that contains the numerical results of the analysis of the COHERENT data, 2) the corrected version of Fig. 2 that illustrates the effects of the diagonal charge radii, and 3) the corrected versions of Figs. 3 and 6 that show the allowed regions in the hr 2 ν e i-hr 2 ν μ i plane. The corrections to the text of the paper are as follows: (i) In the abstract the words "especially that of ν μ " must be removed. (ii) Equation (18) and the surrounding text "This is important for the diagonal charge radii that contribute coherently with weak interactions in the cross section (14). Since …[Eq. (18)]…neutrinos and antineutrinos contribute with different signs to the shift of sin 2 ϑ W in Eq. (1)." must be replaced with "However, also g p V and g n V change sign for antineutrinos. Therefore, the diagonal charge radii of neutrinos and antineutrinos generate the same shift of sin 2 ϑ W in Eq. (1)". (iii) The words "whereas the allowed range of hr 2 ν μ i increases by about 30% in the free R n approach" at the end of the text in page 6 must be removed.
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