Modeling A@C$_{60}$ atoms: diffuse versus square-well confining pseudo-potentials

An empirical model approximating the C$_{60}$ cage potential by a square-well confining potential has played an important role in providing the initial understanding of photoionization spectra of A@C$_{60}$ endohedral atoms [1]. However, the square-well potential is discontinuous at its boarders. A more realistic confining potential must be diffuse, obviously. However, it is not at all clear \textit{apriori} to what degree replacement of a square-well potential by a diffuse potential may alter predictability of the model. In particular, should a large array of predicted data and phenomena made on the basis of a square-well potential model be re-studied with an eye on a more realistic diffuse potential boarders of C$_{60}$? It will be shown in this presentation, with H@C$_{60}$ and Xe@C$_{60}$ as case studies, that both the square-well and diffuse confining potentials lead to practically identical calculated data for A@C$_{60}$ photoionization spectra. Moreover, the latter are largely insensitive to the degree of diffuseness of the potential, in reasonable limits. Hence, either of said potentials is equally suitable for mimicking the C$_{60}$ cage.\\[4pt] [1] V. K. Dolmatov, Adv. Quant. Chem. \textbf{58}, 13 (2009).