Resonant Spontaneous Bremsstrahlung Effect In The Scattering Of Ultrarelativistic Electrons On Nuclei In A Strong Laser Field

The process of resonant spontaneous bremsstrahlung radiation during the scattering of ultrarelativistic electrons with energies of the order $\sim 100\ \text{GeV}$ by the nuclei in strong laser fields with intensities up to $I\sim {{10}^{24}}\ \text{Wc}{\text{m}^{\text{-2}}}$ is theoretically studied. Under resonant conditions, an intermediate electron in the wave field enters the mass shell. As a result, the initial second-order process by the fine structure constant is effectively reduced to two first-order processes: laser-stimulated Compton effect and laser-assisted Mott process. The resonant kinematics for two reaction channels (A and B) is studied in detail. It is shown that in the resonant case there is a characteristic parameter that determines a significant number of absorbed laser photons in the laser-stimulated Compton effect. This parameter is determined by the parameters of the laser installation, the energy of the initial electrons and is proportional to the intensity of the laser wave. An analytical resonant differential cross-section with simultaneous registration of the frequency and the outgoing angle of a spontaneous gamma-quantum is obtained. It is shown that the resonant differential cross-section has the largest value in the region of average laser fields ($I\sim {{10}^{18}}\ \text{Wc}{\text{m}^{\text{-2}}}$) and can be of the order of $\sim {{10}^{18}}$ in units ${{Z}^{2}}\alpha r_{e}^{2}$. With an increase in the intensity of the laser wave, the value of the resonant differential cross-section decreases and for the intensity $I\sim {{10}^{24}}\ \text{Wc}{\text{m}^{\text{-2}}}$ is of the order of $\sim {{10}^{4}}$ in units ${{Z}^{2}}\alpha r_{e}^{2}$. The obtained results reveal new features of spontaneous emission of ultrarelativistic electrons on nuclei in strong laser fields and can be tested at international laser installations.