Review of the progress in model theoretical studies of $e + A@{\rm C}_{60}$ electron scattering

A series of recent semi-empirical theoretical studies of electron scattering off endohedral atoms $A$@C$_{60}$ [1-4] have identified interesting measurements as well as more rigorous calculations of $e + A@{\rm C}_{60}$ scattering to perform. This report provides the interested researchers with a review of the most significant findings of works [1-4] on $e + A@{\rm C}_{60}$ scattering. First, we demonstrate features of $e + A@{\rm C}_{60}$ elastic scattering of slow electrons [1, 2] and low-frequency bremsstrahlung [1] when both the atom $A$ and the cage C$_{60}$ are ``frozen'' [1, 2]. Then [3], we ``unfrozen'' the atom $A$ but keep the C$_{60}$ cage ``frozen'' and demonstrate novel effects of dynamical polarization of the atom $A$ under the ``frozen'' C$_{60}$ confinement on $e + A@{\rm C}_{60}$ scattering. Finally, we demonstrate the combined effect of both the dynamical polarization of the encapsulated atom and the static polarization of C$_{60}$ on the scattering process [4].\\ $[1]$ V. K. Dolmatov et.al., PRA \textbf{91}, 062703, 2015. $[2]$ M. Ya. Amusia and L. V. Chernysheva, JETP Lett. \textbf{100}, 503 (2015). $[3]$ V. K. Dolmatov, M. Ya. Amusia, and L. V. Chernysheva, PRA \textbf{92}, 042709 (2015). $[4]$ M. Ya. Amusia and L. V. Chernysheva, arXiv:1512.00211, 2015.