Dispersion relation analysis for electron-atom scattering at zero energy

Abstract

The dispersion relations are expressions which relate the real and the imaginary parts of the scattering amplitude. The importance of the dispersion relations in collision theory lies in that they can be used to derive rigorous formulae for quantities directly related to the measured values; and can therefore serve as a criterion for the analysis of experimental data. This is done by connecting an integral over the total cross section with the scattering length, the consistency and accuracy of total cross section measurements can be assessed. The most extensive application so far, of the dispersion relations has been to the electron scattering by hydrogen (Gerjuoy and Krall, 1960) and helium (Lawson et al. 1966, Bransden and McDowell 1969, 1970). Part of the problem addressed in the following account is that of accurately calculating the Born exchange contribution at zero energy for electron scattering by helium and lithium in the forward direction using various wavefunctions. The corresponding dispersion relations have also been discussed.