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 Na8, Na20 and Na40 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.
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Descourt et al. (2000) studied this question.