On possible multiple occurrences of the breakdown of the dipole and dipole-quadrupole approximations in angle-differential spectra of fullerene anions, C$_{n}^{-}$

TL;DR

This study investigates the limitations of dipole and dipole-quadrupole approximations in describing the angle-differential photodetachment spectra of fullerene anions, revealing breakdowns at relatively low photon energies and increasing with fullerene size.

Contribution

It introduces a model-based analysis showing the potential failure of common approximations in fullerene anions' spectra at certain energies, highlighting the need for more advanced theories.

Findings

Breakdowns occur at photon energies of a few tens of eV.

Breakdowns start at lower energies for larger fullerenes.

Frequency of breakdowns increases with fullerene size.

Abstract

We provide the initial insight into the angle-differential photodetachment spectra of fullerene anions beyond the dipole approximation by utilizing a broadly used modelling of C$_{n}$. In the model, the C$_{n}$ cage is approximated by a spherical attractive potential of a certain inner radius, thickness and depth which binds an external electron, thereby turning into a C$_{n}^{-}$ anion. It is demonstrated in the framework of the utilized model, which a single-electron model in its essence, that the dipole and dipole-quadrupole approximations might get broken down in the angle-differential photodetachment spectra of fullerene anions, C$_{n}^{-}$, at a great number of photon energies of only a few tens of eV. Moreover, the breakdown occurrences are shown to start developing at lower photon energies, and the frequency of the occurrences grows with increasing size of C$_{n}^{-}$. The findings are demonstrated by direct calculations of angle-differential photodetachment cross sections of the C$_{60}^{-}$, C$_{240}^{-}$, C$_{540}^{-}$ and C$_{1500}^{-}$ anions. It is not clear beforehand how electron correlation might affect the predicted anomalies in the C$_{n}^{-}$ angle-differential photodetachment spectra, so that the verification(s) of the predicted breakdowns by means of more sophisticated theories is urged.