Abstract
Oscillating electric field is chosen to investigate the electron-positron pair production process by using a quantum kinetic theory and the effective mass model [Phys. Rev. Lett. 112, 050402 (2014)]. The particle yield exhibits a characteristic oscillatory structure which is related to the multi-photon thresholds. The true peak positions are typically slightly above the naive threshold estimate, which is defined as frequency shift. During the numerical calculations, we find the frequency shift can be affected by the system parameters under adiabatic closing the external field, it is worthwhile to study in detail. In this paper, we investigate the frequency shift and the sub-band effect in electron-positron pair production with oscillating electric field. First, a quantum kinetic theory and the effective mass are presented to obtain the frequency shift, the results are fitted very well. And we find the frequency shift and the sub-band effect can be influenced by pulse duration, photon number, and strength of the external field. The frequency shift becomes evident as increases of photon number and the external field strength. The sub-band width is relatively lower at longer pulse duration, higher photon number region, and weaker external field. The results shown in the paper are helpful for understanding multi-photon pair production process in the strong field.
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