Many-body approach of electron elastic scattering on sodium clusters

Electron scattering on metallic clusters, at low and very low energies, is described within the many-body framework of the Dyson equation, taking into account both polarization and exchange effects. A direct solution of the resulting integro-differential equation is presented. Phase shifts and cross sections are calculated for different closed-shell sodium clusters Na-8, Na-20 and Na-40 and compared, when results are available, with previous calculations using different levels of approximations. An extreme sensitivity of the elastic cross sections to the potentials used to describe the electron-cluster interaction was found.