Imaging Delocalized Electron Clouds: Photoionization of ${\mathrm{C}}_{60}$ in Fourier Reciprocal Space

The dynamics of the photoionization of the two outermost orbitals of ${\mathrm{C}}_{60}$ has been studied in the oscillatory regime from threshold to the carbon $K$ edge. We show that geometrical properties of the fullerene electronic hull, such as its diameter and thickness, are contained in the partial photoionization cross sections by examining ratios of partial cross sections as a function of the photon wave number in the Fourier conjugated space. Evaluated in this unconventional manner photoemission data reveal directly the desired spatial information.

Figure 1

Partial photoionization cross sections of the HOMO (filled circles) and $\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}-1$ (open circles) orbitals of ${\mathrm{C}}_{60}$, between 18 and 130 eV photon energy. The dashed and solid curves represent the LDA calculations of Decleva et al. [13] using a full molecular potential. The dotted line represents the total photoionization cross section used for the normalization of the partial cross section. The inset displays two photoelectron spectra of ${\mathrm{C}}_{60}$, taken at different photon energies showing the distinct intensity variation of the photolines of the two outermost orbitals HOMO and $\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}-1$.

Figure 2

Ratio of partial photoionization cross sections for the HOMO and $\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}-1$ (present data: filled black circles, former measurements [6]: open circles). The shaded area represents the various solid state measurements [5, 16, 17], whereas the different curves are the result of the discussed calculations (Decleva et al.: solid line; spherical-jellium model: dashed line; semiempirical: dash-dotted line; coherent part of the semiempirical fit: dotted line).

Figure 3

Schematic representation of the $\pi$-electron distribution of the two outermost valence orbitals of ${\mathrm{C}}_{60}$ (Weaver and Poirier [3] and Bischof in Kuzmany’s paper [21]) along with a cut through a spherical shell potential visualizing the way how coherent and incoherent photoemission from different parts of the fullerene, marked by filled and open circles, may occur. Two characteristic branching ratio oscillation patterns for each process over momentum vector $\mathbf{k}$ are shown at the bottom of the figure. The geometric quantities $R$ and $\Delta$ are connected to the characteristic wavelengths ${\lambda }_R$ and ${\lambda }_{\Delta }$ via $\pi /{\lambda }_{R,\Delta }$.

Figure 4

Fourier transform of the cross section ratio in Fig. 3 for the experimental data (shaded area), the LDA calculation of Decleva et al. [solid line in (a)], the LDA calculation using a spherical-jellium potential [solid line in (b)], and the result of the semiempirical fit (dotted line) [22].