Electron elastic scattering off $A$@C$_{60}$ fullerenes: the ``zeroth-order'' trends

The theoretically revealed trends in electron elastic scattering off endohedral fullerenes A@C$_{60}$ associated with the nature of an encapsulated atom A, its size and spin (A = Ar, Xe, Ba, Cr and Mn) are highlighted. It is shown that placing an atom A inside the C$_{60}$ cage can make electron scattering off A@C$_{60}$ weaker than off the empty C$_{60}$ cage, especially when the encapsulated atom A donates an appreciable part of its electron density to the C$_{60}$ cage, as do Ba, Cr and Mn. It is shown that, for such atoms, $\rm e$ $+$ A@C$_{60}$ scattering can even be weaker than off the isolated atom A itself. In addition, if such encapsulated atom has also a nonzero spin $S$ (Cr's $S=3$, Mn's $S=5/2$), then the C$_{60}$ cage can become ``spin-charged''; this results in a strong electron spin-dependence of $\rm e$ $+$ A@C$_{60}$ scattering. In calculations, (a) electron correlation was ignored, (b) both the encapsulated atom A and C$_{60}$ cage were regarded as non-polarizable targets, and (c) the C$_{60}$ cage was modeled by a spherical annular well. Results, thus, provide the understanding of $\rm e$ $+$ A@C$_{60}$ scattering in a ``zeroth-order'' approximation and, most likely, identify some of the most intrinsic properties of $\rm e$ $+$ A@C$_{60}$ elastic scattering.