The process of neutrino production of electron positron pairs in a magnetic field of arbitrary strength, where electrons and positrons can be created in the states corresponding to excited Landau levels, is analysed. The mean value of the neutrino energy loss due to the process ν → νe − e + is calculated. The result can be applied for calculating the efficiency of the electron-positron plasma production by neutrinos in the conditions of the Kerr black hole accretion disc considered by experts as the most possible source of a short cosmological gamma burst. The presented research can be also useful for further development of the calculation technic for an analysis of quantum processes in external active medium, and in part in the conditions of moderately strong magnetic field, when taking account of the ground Landau level appears to be insufficient. * 1 We use natural units c = = kB = 1, me is the electron mass, and e is the elementary charge.

Abstract. The processes of neutrino production of electron-positron pairs, νν → e − e + and ν → νe − e + , in a magnetic field of arbitrary strength, where electrons and positrons can be created in the states corresponding to excited Landau levels, are analysed. The results can be applied for calculating the efficiency of the electron-positron plasma production by neutrinos in the conditions of the Kerr black hole accretion disc considered by experts as the most possible source of a short cosmological gamma burst. IntroductionAn intense electromagnetic field makes possible the processes which are forbidden in a vacuum such as the neutrino production of an electron-positron pair ν → νe − e + . The list of papers devoted to an analysis of this process and the collection of the results obtained could be found e.g. in [1]. In most cases, calculations of this kind were made either in the crossed field approximation, or in the limit of a superstrong field much greater than the critical value of B e = m 2 e /e 4.41 × 10 13 G (we use natural units c =h = k B = 1), when the electrons and positrons are born in states corresponding to the ground Landau level. However, there exist physical situations of the so-called moderately strong magnetic field, p 2 ⊥ ≥ eB m 2 e , when electrons and positrons mainly occupy the ground Landau level, however, a noticeable fraction may be produced at the next levels.The indicated hierarchy of physical parameters corresponds to the conditions of the Kerr black hole accretion disk, regarded by experts as the most likely source of a short cosmological gamma-ray burst. The disc is a source of copious neutrinos and anti-neutrinos, which partially annihilate above the disc and turn into e ∓ pairs, νν → e − e + . This process was proposed and investigated in many details (for the list of references see e.g. [2,3]) as a possible mechanism for creating relativistic, e ∓ -dominated jets that could power observed gamma-ray bursts. In [2], in addition to νν annihilation, the contribution of the magnetic field-induced process ν → νe − e + to the neutrino energy deposition rate around the black hole was also included for the first time. The authors [2] concluded in part, that the process ν → νe − e + could dominate over the basic process νν → e − e + . They used the result for the energy deposition rate in the process ν → νe − e + obtained in [4,5] in the crossed field limit, while in those physical conditions (B to 180 B e , E ν to 25 MeV) the approximation of a crossed field is poorly applicable (as well as

Abstract. The process of neutrino-electron scattering in a dense plasma and magnetic field of arbitrary strength, where electrons can occupy the states corresponding to excited Landau levels, is analyzed. The total probability of this process, summarized over all initial states of the plasma electrons which is only physically meaningful, is calculated. Possible astrophysical applications are discussed.

Abstract. We investigate the process of neutrino-electron scattering in a dense plasma and magnetic field of arbitrary strength, where electrons can occupy the states corresponding to excited Landau levels. We calculate the total probability of this process, summarized over all initial states of the plasma electrons which is only physically meaningful. Possible astrophysical manifestations of the process are briefly discussed.

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