Diffuse versus square-well confining potentials in modelling $A$@C$_{60}$ atoms

TL;DR

This study compares diffuse and square-well potentials in modeling endohedral atoms within C60, finding that photoionization spectra are largely unaffected by the potential's diffuseness or discontinuity, and proposes improved parameter sets.

Contribution

It demonstrates that realistic diffuse potentials yield similar spectra to square-well models and provides optimized parameters for better experimental agreement.

Findings

Photoionization spectra are insensitive to potential diffuseness.

Spectra are unaffected by the potential's discontinuity.

New parameters improve agreement with experimental data.

Abstract

Attention: this version-$2$ of the manuscript differs from its previously uploaded version-$1$ (arXiv:1112.6158v1) and subsequently published in 2012 J. Phys. B \textbf{45} 105102 only by a removed typo in Eq.(2) of version-$1$; there was the erroneous factor "2" in both terms in the right-hand-side of the Eq.(2) of version-$1$. Now that the typo is removed, Eq.(2) is correct. A perceived advantage for the replacement of a discontinuous square-well pseudo-potential, which is often used by various researchers as an approximation to the actual C$_{60}$ cage potential in calculations of endohedral atoms $A$@C$_{60}$, by a more realistic diffuse potential is explored. The photoionization of endohedral H@C$_{60}$ and Xe@C$_{60}$ is chosen as the case study. The diffuse potential is modelled by a combination of two Woods-Saxon potentials. It is demonstrated that photoionization spectra of $A$@C$_{60}$ atoms are largely insensitive to the degree $\eta$ of diffuseness of the potential borders, in a reasonably broad range of $\eta$'s. Alternatively, these spectra are found to be insensitive to discontinuity of the square-well potential either. Both potentials result in practically identical calculated spectra. New numerical values for the set of square-well parameters, which lead to a better agreement between experimental and theoretical data for $A$@C$_{60}$ spectra, are recommended for future studies.