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Description
The probability amplitudes of a photon emission from the vacuum accompanied by a created electron-positron pair or from a single-electron (positron) state in the presence of a constant electric field were considered earlier by Nikishov [Zh. Eksp. Teor. Fiz. 59, 1262 (1970)]. However, these amplitudes present a satisfactory description of the phenomenon of the emission in the case of not so strong field when the effect of the pair creation is tini. In the case of a strong field, one has to use a perturbation theory with respect to the radiative interaction for average values, which is quite different from the technique suitable for calculating amplitudes. Following a nonperturbative formulation of strong-field QED developed in our earlier works, we consider photon emission accompanying vacuum instability under the action of a quasi-constant strong electric field of finite duration T. We construct closed formulas for the total probabilities and study the photon emission by an electron and for the photon emission accompanying an electron-positron pair creation from a vacuum. We study angular and polarization distribution of the emission as well as emission characteristics in a high-frequency approximations with respect of 1/T. We see that the emission accompanying the pair creation from vacuum is distinguished by the fact of the cylindrical symmetry. It is a further development of the locally constant field approximation proposed in [Phys. Rev. D 95, 076013 (2017)].