Upper Bound on Total Electron Scattering Cross Sections in Hydrogen

Dispersion relations for electron-hydrogen scattering are combined with existing scattering length calculations. The sign of the scattering length is shown to give an upper bound on ∫σ(k)dk where σ(k) is the total cross section for scattering of electrons of incoming momentum k. Recent calculations of the scattering length are used to determine this limit. An experiment by Fite et al. satisfies this bound, agreeing with the recent calculations of the scattering length.