The application of variational methods to atomic scattering problems II. Impact excitation of the 2s level of atomic hydrogen-distorted wave treatment

The cross-section for excitation of the 2 S level of atomic hydrogen by electrons is calculated using the distorted wave method with full allowance for exchange. The distorted wave functions used in the calculations are determined by Hulthèn’s variational method. The initial wave functions, representing the motion of an electron in the field of a normal atom with allowance for exchange, are taken to be those calculated by Massey & Moiseiwitsch (1950). The final wave functions, representing the motion of an electron in the field of a hydrogen atom in the 2 S state, have been obtained by a modification of the same method. Exchange effects are found to be less important in determining the forms of these wave functions. The cross-sections obtained are considerably smaller than those calculated by the Born-Oppenheimer method, in which the electron wave functions are undistorted plane waves. This is largely because the symmetrical cross-section, which has the greater weight in determining the mean cross-section, is much greater than the antisymmetrical according to the Born-Oppenheimer method, but the reverse is true if distortion is allowed for. In no case does the distorted wave method give results exceeding the theoretical upper limit, whereas with plane waves this limit is exceeded at certain electron energies by the symmetrical cross-section.