It is demonstrated that in photoabsorption by endohedral atoms some atomic Giant resonances are almost completely destroyed while the others are totally preserved due to different action on it of the fullerenes shell. As the first example we discuss the 4d10 Giant resonance in Xe@C60 whereas as the second serves the Giant autoionization resonance in Eu@C60. The qualitative difference comes from the fact that photoelectrons from the 4d Giant resonance has small energies (tens of eV) and are strongly reflected by the C60 fullerenes shell. As to the Eu@C60, Giant autoionization leads to fast photoelectrons (about hundred eV) that go out almost untouched by the C60 shell. As a result of the outgoing electrons energy difference the atomic Giant resonances will be largely destroyed in A@C60 while the Giant autoionization resonance will be almost completely preserved. Thus, on the way from Xe@C60 Giant resonance to Eu@C60 Giant autoionization resonance the oscillation structure should disappear. Similar will be the decrease of oscillations on the way from pure Giant to pure Giant autoionization resonances for the angular anisotropy parameters. At Giant resonance frequencies the role of polarization of the fullerenes shell by the incoming photon beam is inessential. Quite different is the situation for the outer electrons in Eu@C60, the photoionization of which will be also considered.
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