Photoionization of atoms and ions from endohedral anions

We study the interconnection between the results of two qualitatively different approximate calculations of photoionization cross sections, $\sigma_{n\ell}$, for neutral atoms ($A$) or their cations ($A^+$), centrally confined inside a fullerene-anion shell, $C_{N}^{q}$ , where $q$ represents the negative excess charge on the shell. One of the approximations, frequently employed in previous studies, assumes a uniform excess negative charge distribution over the entire fullerene shell, by analogy with a charged metallic sphere. The other approximation, not previously discussed in the literature, considers the quantum states of the excess electrons on the shell, determined by specific $n$ and $\ell$ values of their quantum numbers. Remarkably, both methods yield photoionization cross sections for the encapsulated species that are close to each other. Consequently, we find that the photoionization of the encapsulated atoms or cations inside a $C_{N}^{q}$ anion is minimally influenced by the quantum states of the excess electrons on the fullerene shell. Furthermore, we demonstrate that the aforementioned influence decreases even further with an increasing size of the confining fullerene shell. All this holds true at least under the assumption that the confined atom or cation is compact, i.e., its electron density remains primarily within itself rather than being drawn into the fullerene shell. This remarkable finding results from Hartree-Fock calculations combined with a popular modeling of the fullerene shell, where it is modeled by an attractive spherical annular potential.