Dispersion relations and the elastic scattering of electrons by helium atoms

Abstract

The elastic scattering of electrons by helium is analysed in terms of a dispersion relation for the forward scattering intensity. The zero energy scattering length obtained from this relation agrees well with that derived from application of effective range formulae to observed data on total cross sections and to drift velocity and microwave probe data. It also agrees well with results of exchange-adiabatic calculations. At energies below the excitation threshold these calculations give total and differential cross sections which agree well with observed results except at small scattering angles at energies of 10 eV and below. The dispersion relation gives results agreeing with the calculated at zero scattering angle suggesting that the observed distributions are in error. At energies above the excitation threshold the dispersion relation shows that Born’s first approximation is still considerably in error (by a factor of 2) at zero scattering angle at energies of 300 eV. Experimental data between 100 and 300 eV are consistent with extrapolation to the values given by the dispersion relation for the forward scattered intensity.