The dynamics of the photoionization of the two outermost orbitals of 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

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... veal directly the desired spatial information. Fullerenes, in particular C 60 [1], are a very specific form of matter which causes surprising behavior even in such matured fields as scanning tunneling microscopy [2] and photoelectron emission [3], both well established tools for the structural analysis of matter. Because of its spherical symmetry a sample of C 60 molecules provides all structural information independently from any particular orientation, either in crystalline form or in the gas phase [4] . This made it promising to look for such information in the dynamics of the photoionization cross sections of C 60 and other fullerenes, particularly because theoretical considerations based on the acceleration form of the dipole operator showed that spatial regions with a large gradient in the potential of an illuminated target contribute dominantly to photoionization. The path differences of electron continuum waves emanating from these regions of steep potential gradient should lead to characteristic oscillatory patterns in the cross sections from which spatial properties of the target should be reconstructed. Evidence for an oscillating behavior of the partial cross sections in fullerenes was first obtained from photoemission experiments on solid C 60 by Benning et al. [5] . These early measurements showed a photon energy dependent oscillation in the intensity of the photolines of the two highest occupied molecular orbitals [(HOMO) and HOMO ÿ 1] in the photon energy range between 24 and 100 eV whose origin was unknown. It has been attributed to a particular band structure in the continuum influenced by the special symmetries of the C 60 bound states [5] . Only after the first gas phase measurements revealed similar oscillations [6] it became clear that this effect was not related to the electronic properties of condensed matter. However, also quantum chemical approaches based on individual electronic orbitals treating C 60 as a big molecule failed to explain the origin of the oscillations. Xu, Tan, and Becker [7] explained the oscillations with an empirical refraction model where a valence electron inside the fullerene, modeled as a sphere of radius R, feels a constant potential. At the fullerene edge the potential drops suddenly to zero. This causes refraction which leads to an oscillating photoionization cross section. The refraction model assumed that the oscillation is of geometrical origin and a property of the entire valence electron density rather than due to individual quantum orbitals. Experimental data on other fullerenes [8] confirmed the original C 60 experiments concerning the single frequency character of the oscillations. However, theoretical work [9] providing a general framework for geometry-based oscillations in photoionization cross sections for systems with delocalized electrons described by a jellium potential [10] predicted four oscillation frequencies when applied to C 60 , connected to the diameter 2R of C 60 , to the thickness of the electron hull, and to sidebands related to 2R [11]. Previous experiments did not reach far enough in photon energy to clarify if these frequencies do exist. Here, we report on new experimental data taken in smaller steps and at higher photon energies, as well as on new calculations designed to interpret as many features of the fullerene photoabsorption cross section as possible in structural terms. The measurements for the partial cross sections were performed at the undulator beam line BW3 of the Hamburg Synchrotron Radiation Laboratory HASYLAB at DESY [12]. This undulator delivers intense photon beams of 10 12 photons per sec, monochromatized by a SX 700 monochromator. The photon beam is crossed with an effusive beam of C 60 molecules produced by a resistively heated crucible inside a vacuum chamber containing two time-of-flight (TOF) electron spectrometers for the energy and angular resolved detection of the C 60 photoelectrons [6, 8] . In order to keep the resolution of the electron spectra virtually the same for the whole energy range between 20 and 290 eV appropriate retardation voltages had to be applied before the electrons entered the drift tubes of the TOF spectrometers. The inset of Fig. 1 shows two of such spectra taken at a photon energy of 22 eV and 37 eV, respectively. A crucial point for the measurements is the calibration of the photon flux over the whole energy range VOLUME 89, NUMBER 12 P H Y S I C A L