Photoionization of atoms and cations confined in fullerene anions: A@(C_N)^q

We study the interconnection between results of two distinct semi-empirical approximations for photoionization cross sections, σ_nℓ, of atoms or their cations confined inside a fullerene anion (C_N)^q, where q represents the negative excess charge on C_N. One of the approximations, frequently used (see, e.g., [1,2]), simply assumes a uniform spread of the charge q over the outer surface of C_N. The other approximation, introduced in this work, considers the quantum states of the excess electrons on the shell, determined by specific n and ℓ values of their quantum numbers. We find, at least in all case studies we have performed for this research, that the calculated σ_nℓ’s of the thus confined atoms/cations is insignificantly influenced by the quantum states of the excess electron(s) in the (C_N)^q anion. Furthermore, we demonstrate that the influence is generally decreasing with increasing size of (C_N)^q. These findings assume that the electron density of the atom/cation remains primarily within the atom/cation itself rather than being noticeably drawn into the fullerene shell. We chose hydrogen as well as helium atoms and ions for our case study. Both discussed herein approximations employ a popular modeling of the fullerene shell represented by an attractive spherical annular potential with a subsequent use of the Hartree-Fock approximation to the structure and photoionization of the thus confined atoms or cations.

[1] V. K. Dolmatov and S. T. Manson, Photoionization of atoms encapsulated in endohedral ions A@C60±z, Phys. Rev. A 73, 013201 (2006).

[2] A. Thuppilakkadan et.al., "Modifications in the angular photoemission time delay in Ar@C^q=−1₆₀ ...", Phys. Rev. A 107, 052804 (2023).