Partial Cross Sections and Angular Distributions

Photoionization cross sections are among those fundamental quantities of nature which provide direct insight into the orbital or, more generally, electronic structure of atoms, molecules, and solids. Therefore, since the discovery of the photoeffect by H. Hertz in 1887,(1) the determination of cross section data was one of the primary goals of photoionization studies. Starting from simple photoyield measurements, the determination of photoionization cross sections has become more and more sophisticated. A first step toward a more highly differentiated analysis was the energy dispersion of the emitted electrons via electron spectrometers [photoelectron spectroscopy (PES)] in order to determine partial photoionization cross sections rather than the sum of all emitted electrons in the form of the total photoionization cross section. Early PES studies concentrated solely on the line structure of the photoelectron spectra, determining line positions and deriving electron binding energies which reflect the orbital structure of the atomic or molecular system under study.(2,3) In fact, electron spectroscopy for chemical analysis (ESCA) became a major tool in chemical and materials sciences. However, beyond these purely spectroscopic objectives, quantitative analysis of the line intensities attracted increasing interest over time. These studies were limited at the beginning to a very select number of photon energies, corresponding to the atomic transitions excited in VUV discharge lamps and x-ray sources. Nevertheless, the pioneering measurements of partial photoionization cross sections were made using these discrete photon sources; this is particularly true for most of the early high-resolution data. On the other hand, the restriction to this limited number of photon energies was a severe handicap in the exploration of the photon-energy-dependent partial cross section behavior. It was at this time when theory made several advances in the calculation of partial cross section behavior, predicting characteristic features such as delayed onsets, shape resonances, and Cooper minima.(4,5). In addition to these “one-electron” features, “many-electron” effects were predicted to show up in the partial cross section.(6,7)