Regge Oscillations in Electron-Atom Total Scattering Cross Sections?

In quantum scattering, the presence of a sufficiently narrow resonance allows the collision partners to form a long-lived intermediate complex which rotates as it decays to preserve the total angular momentum. Here we consider a system trapped in such a resonance state and allow it to decay at zero scattering angle, which through the optical theorem can be related to the total cross section (TCS). If the complex has a large angular life, it will return to forward scattering %$\theta=0^{\circ}$ many times. For the resonance to contribute to the TCS requires: (i) Several rotations of the complex (Regge trajectory stays close to real axis) and (ii) Coherent addition of forward scattering sub-amplitudes (real part of Regge pole is close to an integer). Our analysis is based on the recent complex angular momentum approach [1] used to explain low energy oscillations in proton-H collision. Specifically, we want to establish whether similar oscillations can also be observed in electron-atom scattering. To this end, we present a detailed analysis of Regge trajectories and their contributions to the TCS for the model Thomas-Fermi potential. \begin{enumerate} \bibitem{1} J. H. Macek {\it et al.}, Phys. Rev. Lett. {\bf 93}, 183203 (2004). \end{enumerate}