Electron Scattering from Hydrogen

Kohn's variational principle has been used to calculate $S$-wave elastic scattering of electrons from atomic hydrogen, using up to 50 trial functions of the type introduced by Hylleraas to describe the bound states of two-electron atoms. The phase shifts calculated at several energies up to 10 ev appear to have converged well, leaving residual uncertainties mostly less than one thousandth of a radian. Taking extra pains to include the effect of the long-range force at zero energy, we have also determined very accurate values for the scattering lengths.