The radiative decay of the massive neutrino in the external electromagnetic fields

The radiative decay of the massive neutrino $\nu_i \rightarrow \nu_j \gamma$ is investigated in the framework of the Standard Model in external electromagnetic fields of various configurations: constant crossed field, constant uniform magnetic field, plane monochromatic wave's field. The effect of significant enhancement of the neutrino decay probability by the external field (electromagnetic catalysis) is discussed. An especially strong enhancement occurs in the case of the ultrarelativistic neutrino decay, since in this case the decay probability does not contain suppression caused by the smallness of the decaying neutrino mass. The ultrarelativistic neutrino decay catalysis is significant even in a relatively weak external field ($F/F_e << 1$, where $F_e$ is the critical Schwinger value). The expression for the photon splitting probability into the neutrino pair $\gamma \rightarrow \nu_i gamma-quanta produced in a volume filled with an electromagnetic field and the neutrino lifetime in a strong magnetic field are presented