We discuss the complicated resonance structure of the endohedral atom photoionization cross section. Very strong enhancement and interference patterns in the photoionization cross-section of the valent and subvalent subshells of noble gas endohedral atoms A@C60 are demonstrated. It is shown also that the atomic Giant resonance can be either completely destroyed or remains almost untouched depending on the velocity of photoelectrons that are emitted in the resonances decay process. These effects are results of dynamic modification of the incoming beam of radiation due to polarization of the fullerenes electron shell and reflection of photoelectrons be the fullerenes shell static potential. We have considered the outer np- and subvalent ns-subshells for Ne, Ar, Kr and Xe noble gas atoms. The modification of the Giant resonances is considered for a whole sequence of endohedrals with atoms and ions Xe, Ba, La, Ce+, Ce+4, Eu. The polarization of the fullerene shell is expressed via the total photoabsorption cross section. The photoelectron reflection from the static potential is taken into account in the frame of the so-called bubble potential that is a spherical -type potential.
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