Distortion and preservation of Giant resonances in Endohedral Atoms A@C$_{60}$

It is demonstrated in this Letter that the effect of the fullerene shell upon atomic Giant resonance decisively depends upon energy of photoelectrons, by which the resonance decay. According to the earlier prediction, the Giant resonance in Xe is strongly modified in the endohedral Xe@C$_{60}$ being transformed from a single broad and powerful maximum in Xe into four quite narrow, but with almost the same total oscillator strength. On the contrary, here the $4d$ Giant resonances in ions Ce$^{3+}$ (the electronic structure that Ce has, when stuffed into fullerene), in Ce$^{4+}$, and Eu are considered. In none of them the $4d$ Giant resonance in endohedrals is affected essentially. This is because the decay of the Giant resonances in these endohedrals proceeds by emission of fast photoelectrons that are almost unaffected by the C$_{60}$ shell. The results obtained give at least qualitative explanation to the fact that relatively recent observation of $4d$ Giant resonance in Ce@C$_{82}^+$, where the Giant resonance was observed as a maximum without noticeable structure.