Creation of electron–positron pairs at excited Landau levels by neutrino in a strong magnetic field

Abstract

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.

Neutrino processesvv̅→e-e+andv→ve-e+in a strong magnetic field

“…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 the approximation of a superstrong field when e − e + are created in the ground Landau level). The next Landau levels can be also excited, as we have shown in our paper [3]. Furthermore, the authors [2] considered the process νν → e − e + without taking account of the magnetic field influence.…”

“…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.…”

“…Some details of calculations can be found in our paper [3]. The probability of the ν → νe − e + process defines its partial contribution into the neutrino opacity of the medium.…”

“…The contribution of the next Landau levels which can be also excited, should be taken into account. In [3], the results are presented of our calculation of the mean neutrino energy losses caused by the process ν → νe − e + in a moderately strong magnetic field, i.e. in the conditions of the Kerr black hole accretion disk.…”

“…This would mean that the conclusion [2] that the contribution of the process ν → νe − e + to the efficiency of the electron-positron plasma production by neutrino exceeds the contribution of the annihilation channel νν → e − e + , and that the first process dominates the energy deposition rate, does not have a sufficient basis. A new analysis of the efficiency of energy deposition by neutrinos through both processes, νν → e − e + and ν → νe − e + , in a hyper-accretion disc around a black hole should be performed, with taking account of our results [3] for the process ν → νe − e + .…”