Nonadiabatic Theory of Inelastic Electron-Hydrogen Scattering

The nonadiabatic theory is applied to the inelastic $S$-wave scattering of low-energy electrons from atomic hydrogen. The zeroth-order (angle-independent) approximation for excitation of the $2s$ level from the ground state is described by the same equation used to describe elastic scattering below the $2s$ threshold, but with more complicated boundary conditions. The solution has been effected by expanding the wave function in terms of separable solutions. With the assumption of reciprocity it is also possible to obtain the $2s-2s$ cross sections. The elastic ($1s-1s$) cross sections are within 1% of the close-coupling results in the triplet case, but are about 20% greater in the singlet case. The inelastic ($1s-2s$) cross sections are reduced about 20% in the triplet case and 20 to 40% in the singlet case, relative to the close-coupling results.