Photoionization of spherical fullerenes: Dependence of the strength and lifetime of plasmon resonances on the number of carbon atoms

The time-dependent local density approximation is used to calculate the total and subshell-differential photoionization cross sections of a number of spherical carbon fullerenes C$_{N}$. For each system the core comprised of $N$ number of C$^{4+}$ ions is smeared into a classical jellium hull before treating the correlated motion of 4$N$ valence electrons quantum mechanically in the Kohn-Sham formalism [1]. Results show two collective plasmon resonances in each fullerene system as expected from previous studies on C$_{60}$ [2]. The peak values and the lifetimes of these resonances, however, exhibit diverse variations as a function of $N$. In general, while the maximum value of the low-energy plasmon (LEP) increases as the second power of $N$, deviations from such simple scaling are found for the high-energy plasmon (HEP). On the other hand, the lifetime of the LEP suggests a near linear increase with $N$ but for the HEP the variation of the lifetime with $N$ shows non-monotonic behavior.\\[4pt] [1] Madjet et al., \textit{J. Phys.} B \textbf{41}, 105101 (2008);\\[0pt] [2] Scully et al., \textit{Phys. Rev.Lett.} \textbf{94}, 065503 (2005).