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

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.