On the behavior of scattering phases in collisions of electrons with multi-atomic objects

We have studied the energy dependence of several first scattering phases with multi-atomic object. As concrete examples representing the general trends endohedrals Ne@C$_{60}$ and Ar@C$_{60}$ are considered. It appeared that the presence of an inner atom, either Ne or Ar, qualitatively affects the scattering phases, in spite of the fact that the fullerene consists of 60 carbon atoms, while the atom staffed inside is only one. Calculations are performed in the one-electron Hartree–Fock (HF) and random phase approximation with exchange (RPAE) for the inner atom while the fullerenes shell is substituted by static potential without and with the polarization potential. It appeared that the total endohedral scattering phase is simply a sum of atomic, Ne or Ar, and fullerenes C$_{60}$ phases, contrary to the intuitive assumption that the total phases on C$_{60}$ and Ne@C$_{60}$ or Ar@C$_{60}$ has to be the same.