Bremsstrahlung at Low-Energy Electron–Nucleus Collisions in the Quantizing Magnetic Field. I. Distant Collisions

We analytically calculate the spectral power of bremsstrahlung from a slow electron colliding with motionless nuclei in a strong quantizing magnetic field, in which the energy of the Coulomb interaction between particles at a distance of the order of the Larmor radius exceeds the mechanical energy of the system in absolute value. In this case, the electron motion becomes quasibound in sufficiently close collisions. In this part of research, we consider bremsstrahlung at low frequencies, which is stipulated by distant flybys without quasibound motion: an electron can spread over many Landau levels as a result of the collision, but keeps the direction of its motion along the magnetic field. We prove that the transition from the classical to quantum cyclotron gyration of an electron does not manifest itself in the spectral emission power of the waves with arbitrary polarization at the considered frequencies. This property stems from the fact that the low-frequency emission is due to the longitudinal motion and electric drift in the crossed Coulomb and magnetic fields which remain quasiclassical. Thus, we confirm that the bleaching of the photosphere of a magnetic white dwarf, which was discovered in the classical consideration with respect to collisional absorption of the extraordinary wave (polarized across the external magnetic field), is also preserved in the quantum limit—for stars of this spectral type with the strongest magnetic field.