Singular behavior in electron-atom scattering at small momentum transfer

At fixed energy, the electron-atom differential cross section is commonly believed to be an analytic function of the momentum transfer squared K-2 around K-2 = 0. We negate this by demonstrating the presence of nonanalytic terms of the form root K-2 coming from second-order long-range terms. This result, combined with a Regge pole representation, yields a new generalized Lassettre expansion to evaluate optical oscillator strengths through the extrapolation of apparent generalized oscillator strengths to K-2 + 0. Electron-H scattering demonstrates our new formula over a wide range of impact energies.