Fourier analysis of subshell photoionizations: Pristine C$_{60}$ and atoms endohedrally confined in C$_{60}$

Theory and experiment have confirmed oscillations in the photoionization from two highest occupied orbitals of free C$_{60}$ [1]. It is however not known if the oscillations from inner orbitals also show the same spectral ``morphology''. We found using a Fourier analysis approach that the oscillation spectacularly alters by the centrifugal barrier created by a high angular momentum inner electron [2]. Theory has also predicted oscillations in the photo cross section of atoms confined in C$_{60}$. Most of the studies however modeled the confining shell by a simplistic one-active-electron potential. A method has recently been established that treats the C$_{60}$ electrons in a sophisticated multi-electron frame which we use to perform calculations of closed-shell atoms in C$_{60}$. Employing the Fourier analysis we unravel the unique interplay between specific ionization modes that induces oscillations in the cross section of the confined atom. [1] Ruedel et al., Phys. Rev. Letts. \textbf{89}, 125503 (2002); [2] McCune et al., J. Phys. B FTC \textbf{41}, 201003 (2008).