Time delay of photoionization by endohedrals

In this work, we investigate the time delay of photoelectrons by fullerenes shell in endohedrals. We present general formulas in the frame of the random phase approximation with exchange (RPAE) applied to endohedrals A@C$_{\text{N}}$ that consist of an atom A located inside of a fullerenes shell constructed of N carbon atoms C. We calculate the time delay of electrons that leave the inner atom A in course of A@CN photoionization. Our aim is to clarify the role of the C$_{\text{N}}$ shell, its static potential, and polarization. As concrete examples of A, we have considered Ne, Ar, Kr, and Xe, and as fullerene, we take C$_{60}$. The presence of the C$_{60}$ shell manifests itself in powerful oscillations of the time delay $\tau_{nl}(\omega)$ of an electron that is ionized from a given subshell $nl$ by a photon with the energy $\omega$. Calculations are performed for outer, subvalent, and $d$ subshells.