Matrix element effects

In extreme cases a multiple-scattering, sharp resonant structure can result in which the electron is in a quasi-bound state (155). One example is the white line, which is among the most spectacular features in X-ray absorption and is seen in spectra of covalently bonded materials as sharp ( 2eV wide) peaks in absorption immediately above threshold (i.e., the near continuum). The cause of white lines has qualitatively been understood as being due to a high density of final states or due to exciton effects (56, 203). Their description depends upon the physical approach to the problem for example, the LiUii white lines of the transition metals are interpreted as a density-of-states effect in band-structure calculations but as a matrix-element effect in scattering language. 

Synchrotron-radiation and x-ray photoemission studies of the valence states of condensed phase-pure Cm showed seventeen distinct molecular features extending 23 cV below the highest occupied molecular states with intensity variations due to matrix-element effects involving both cluster and free-electron-like final states. Pseudopotential calculations established the origin of these features, and comparison with experiment was excellent. The sharp C Is main line indicated a single species, and the nine satellite structures were due to shakeup and plasmon features. The 1.9-eV feature reflected transitions to the lowest unoccupied molecular level of the excited state. 

Our results also show interesting matrix-element effects for features 4 and 5. In particular, the shallowest component of peak 4 at 6 eV is almost resolution limited at /iv 50 eV (Fig. 2) but is only a weak shoulder at Av—65 eV (Fig. 1). Feature 5 is clear from Av—50 to 80 eV but was not discernible at other energies, despite the fact that the experimental resolution was not varied. Again, these effects demonstrate the importance of dipole selection rules for these highly symmetric molecules. In contrast, solids rarely exhibit modulation in structure at such high photon energies except for transitions related to critical points, i.e., primary Mahan cone emis-... 

The various forms of photoelectron spectroscopy presently available permit a straightforward determination of occupied and unoccupied surface states. The most comprehensive and authoritative collection of reviews is in the book edited by Feuerbacher et al. [44], while Ertl and Kiippers [15] also provide useful information. Here, we will only attempt to summarize how the principal versions of the technique can be used in the determination of surface electronic structure. In this context the crucial factor is that photoemission spectra represent a direct manifestation of the initial and final density of states of the emitting system. Because selection rules (matrix element effects) can be involved in the transition, the state densities may not always correspond to those derived from the band structure, but in practice there is frequently a rather close correspondence. 

As in PPP, a quite flat n valence-band should dominate the photoelectrmi spectra of this material. The XPS spectrum posseses peaks at -5, -8, -12, -16, -18, -24 and -30 eV [60,61]. In principle, the XPS spectrum is the density of states, but modulated by matrix-element effects. Our results predict peaks roughly at -8, -10, -12, -16, -21, -23, and -24 eV, whereas the top of the valence band should hardly be resolved in the experiment. The agreement is reasonable, in particular when noticing that the experimental peaks are veiy broad ( l-2 eV). The most disturbing point, however, is the experimentally observed deepest peak for which we could not find any assessment. A detailed comparison between our density of states and with the experimental XPS and UPS spectra of PPV... 

Fig. 3. Construction of an electron energy distribution curve (EDC) from a density of states. The top panel depicts a parabolic density of states with structure centered around E-,. For simpUcity, we show photoexcitation of three initial state levels by a photon energy hv with no account taken of dipole matrix element effects. p is the Fermi energy, Vo is the inner potential,

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