The application of variational methods to atomic scattering problems V. The zero energy limit of the cross-section for elastic scattering of electrons by hydrogen atoms

Abstract

Calculations have been made using the central-field, exchange and exchange-polarization approximations. In agreement with previous work it is found that the wave functions are profoundly modified by inclusion of exchange. The exchange radial equations are solved by numerical integration and by variational methods; consideration of the form of the equations for moderately large radial distances suggests an improved two-parameter trial function which is found to give satisfactory results. Polarization, i. e. the inclusion of the interelectronic distance r 12 in the trial function, is much more important for the symmetric than for the anti-symmetric case. A symmetric exchange-polarization trial function is obtained which appears more satisfactory than those previously employed. It may be hoped that the final result for the zero-energy elastic scattering cross-section, Q (0) = 5·76 x 10 -15 cm 2 , is correct to within about 15%.