Bremsstrahlung Emission from Low-Energy Electrons on Atoms

General expressions are given for the bremsstrahlung cross section resulting from electron-neutral-atom collisions at energies comparable to or lower than the excitation energies of the atom and for the bremsstrahlung emission from an electron-neutral-atom gas. These quantities have been evaluated for oxygen and nitrogen, and appear to be consistent with shock-tube data. Electron scattering is treated by Hartree-Fock equations which contain neutral-atom bound orbitals and a semiempirical polarization potential. Elastic-scattering data are fitted by the adjustment of a single parameter in the polarization potential. The bremsstrahlung cross section is derived from a distorted-wave theory. The dipole-acceleration form of the matrix element is used for numerical convenience. Because each angular-momentum state has different direct and exchange potentials, the conventional bremsstrahlung formula must be generalized. Approximate analytical expressions for the bremsstrahlung cross section are also obtained from the dipole-length form of the matrix element. From two sorts of resonance phenomena exhibited by the bremsstrahlung cross section—one associated with maxima and minima in the elastic scattering, and one with the relative proportion of $p$-wave $s$-wave scattering—it may be concluded that an accurate treatment of the electron scattering is necessary for the reliable prediction of bremsstrahlung.