The resonant trident process (Oleinik's resonances) in the field of a strong electromagnetic wave and ultrarelativistic initial and final particles has been theoretically studied. Resonant kinematics and resonant differential and total rates are obtained. Published in Quantum Research. The results obtained can be used to describe experiments at high-intensity lasers centers, as well as in astrophysics near neutron stars and supernovae.
When ultrarelativistic electron beams collide with a strong electromagnetic wave, the nonlinear Compton effect (a first-order process with respect to the fine structure constant) mainly occurs when a gamma quantum and an electron are present in the final state. At the same time, in such a collision of electrons with an electromagnetic wave, a second-order process can take place according to the fine structure constant. This is the so-called trident process, when there are three particles in the final state: an electron and an electron-positron pair. It is important to note that the trident process can proceed in a resonant way (Oleinik resonances). In this case, the intermediate virtual gamma quantum becomes real (the laws of conservation of energy and momentum are fulfilled for it). Because of this, the original trident process effectively splits into two first-order processes: the nonlinear Compton effect and the nonlinear Breit-Wheeler process. The resonant infinity is eliminated by the Breit-Wigner procedure. In this case, the resonance width is determined by the total probability of a nonlinear Breit-Wheeler process on an intermediate gamma quantum. It is extremely important to emphasize that the probability of a resonant trident process can significantly (by several orders of magnitude) exceed the corresponding non-resonant trident process. Therefore, the theoretical and experimental study of the resonant trident process is very relevant.
In our article, the resonant trident process is theoretically studied for the ultrarelativistic energies of initial and final particles in the field of a strong (up to the critical Schwinger field) circularly polarized wave. In this problem, there is a symmetry between an electron and a positron pair. Because of this, the case of equal energies of an electron and a positron pair is considered.
The kinematics of the resonant trident process has been studied in detail. It is shown that there are two characteristic quantum energies in this process: the characteristic Compton effect energy and the characteristic Breit-Wheeler energy. The characteristic energies are proportional to the intensity and inversely proportional to the frequency of the wave. In the field of optical frequencies and not very high laser intensities, the characteristic energy is of the order of magnitude about 100 GeV. For the electromagnetic field of X-ray frequencies (for example, near neutron stars and supernovae), the characteristic energies are of the order of magnitude much smaller. The energies of the initial electrons, which exceed the characteristic energies, have the greatest contribution to the probability of a resonant process. There are two qualitatively different cases in this problem. In the first case, the resonant trident process is determined by the characteristic energy of the Compton effect, and in the second case, by the characteristic energy of the Breit-Wheeler process. In the first case, the energy of the final electron uniquely determines the energies and outgoing angles of the electron-positron pair. In the second case, the energy of the positron (electron) of the pair uniquely determines the energy and outgoing angle of the final electron. Thus, in these cases, there is a quantum entanglement of the final particle states.
Analytical expressions are obtained for the partial rate distributions of the resonant trident process over the energy of the final electron, as well as the positron (electron) of the pair. These partial differential rates were integrated near the resonant particle outgoing angles, taking into account the resonant width. It is shown that the differential rates are several orders of magnitude higher than the corresponding rates of the non-resonant trident process.
The total rates of the resonant trident process (integrated by the energies of the final particles and summed over all possible numbers of absorbed photons of the wave at the first and second vertices) are obtained. It is shown that these total resonant rates significantly depend on the energy of the initial electrons, as well as on the frequency and intensity of the electromagnetic wave. At the same time, the resonant total rates significantly exceed the corresponding non-resonant rates of the trident process.
The results obtained can be used in modern laser facilities to produce high-energy positron beams with specified parameters, as well as to explain the processes of quantum electrodynamics near neutron stars, black holes and supernovae.
This paper "Characteristic features of the resonant trident process in the field of a strong monochromatic electromagnetic wave" was published in Quantum Research .
Roshchupkin SP, Shakhov MV. Characteristic features of the resonant trident process in the field of a strong monochromatic electromagnetic wave. Quantum Res. 2026(1):0001, https://doi.org/10.55092/qr20260001.
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Characteristic features of the resonant trident process in the field of a strong monochromatic electromagnetic wave
11-May-2026