Photoelectron energies

This method has already been used successfully for metallic iron. It presents several important advantages. It is a real space calculation for which no translational invariance is required. Calculation up to 500 eV above the edge can be performed because the basis set increases proportionally with the photoelectron energy. The separation between the three contributions (ai, Ojg and ajn) gives also new insight into the physics that is at the origin of XMCD. 

The Si(k) term takes into account amplitude reduction due to many-body effects and includes losses in the photoelectron energy due to electron shake-up (excitation of other electrons in the absorber) or shake-off (ionization of low-binding-energy electrons in the absorber) processes. 

Fig. 1. X-ray absorption spectrum (XAS) of Cu—Zn metallothionein at the Cu and Zn K-edges. The structure near the edge, referred to as XANES is dominated by multiple scattering events while the extended structure, referred to as EXAFS, at photoelectron energies greater than 30-50 eV is primarily due to single scattering events...

Full derivations of the theory were presented by Lee and Pendry and Ashley and Doniach in 1975. They showed that a complete quantitative description of th EXAFS process was possible and that accurate bond lengths and coordination numbers could be extracted from the analysis of EXAFS data. Lee and Pendry also showed that at high photoelectron energies, the curvature of the electron wave can be neglected and thus the theory can be greatly simplified into what has beeome known as the plane-wave approximation. This approximation results in an expression equivalent to that derived by Stem semi-empirically ... 

Fig. 15. Angle-integrated photoelectron energy distribution curves of uranium in the region of the giant 5 d -> 5 f resonance (90 eV < hv < 108 eV). The 5 f intensity at Ep is suppressed by more than a factor of 30 at the 5 ds/2 threshold (see the spectra for hv = 92 and 94 eV) and resonantly enhanced above threshold (see, e.g., the spectrum for hv = 99 e V). At an initial energy 2.3eV below Ep a new satellite structure is observed which is resonantly enhanced at the 5 d5/2 and 5 ds onsets. At threshold the satellite coincides with the Auger electron spectrum, which moves to apparently larger initial energies with increasing photon energy (from Ref. 67)...

Two rather different techniques that exploit the same underlying phenomenon of coherent interference of elastically scattered low energy electrons are photoelectron diffraction [5] and surface extended X-ray absorption fine structure (SEXAFS) [6,7]. Figure 1.1. shows schematically a comparison of the electron interference paths in LEED and in these two techniques. In both photoelectron diffraction and SEXAFS the source of electrons is not an electron beam from outside the surface, as in LEED, but photoelectrons emitted from a core level of an atom within the adsorbate. In photoelectron diffraction one detects the photoelectrons directly, outside the surface, as a function of direction or photoelectron energy (or both). The detected angle-resolved photoemission signal comprises a coherent sum of the directly emitted component of the outgoing photoelectron wavefield and other components of the same wavefield elastically scattered by atoms (especially in the substrate) close... 

Each photoelectron has an energy determined by the difference between the energy of the incident X-ray photon and that of the electronic level initially occupied by the ejected electron. The photoelectron energy spectrum is the basis of a method called ESCA (Electron spectroscopy for the chemical analysis). 

Fig. 2. Photoelectron energy distributions of trans-stilbene following the excitation with different photon energies, a) 316nm, b) 3 lOnm, c) 301nm and d) 266nm.

Fig. 19.6 A schematic view of an apparatus for measuring photoexcitation cross sections and photoelectron energy and angular distributions. The atom beam comes out of the page, and Di and D2 are the electron and ion detector, respectively (from ref. 25).

Here hco = In[j + e, where e refers to photoelectron energy and I ij is the binding energy of the nly-electron in the atom. Performing the summation in (33.9) over j and neglecting the dependence of e on j, we arrive at the following expression for total photoionization cross-section of the closed shell ... 

In Eq. (78), E and 2 denote the photoelectron energy and propagation direction, respectively the sum runs over the projection m of the angular momentum of the electron in the parent ion, its spin a, and the spin of the photoelectron a. The scattering states are computed with the procedure detailed in Section 5.1.1. 

N = 2 ionization threshold by roughly the energy of three and one IR photons, respectively. Since the absorption of an odd number of photons by a 1P° state results in an even parity state, the 2p multiphoton ionization amplitude, created by the IR pulse, should have odd parity right above the threshold and change to even parity for photoelectron energies around 1.4 eV (corresponding to absorption of four IR photons from the spj resonance and two from... 

Figure 6 Nondipole asymmetry parameter xis(e) as a function of the photoelectron energy s for the Ne Is photoionization from e Cgo calculated [36] in two different approximations 1, the 5-potential model. 2, 3 and 4, the A-potential model with the following values for Rgq, f/gQ and A (all in au) ...

Figure 22 RRPA calculated data [29] for the Mg 3s photoionization cross section of free Mg and Mg C60 Mg, marked Mg, as a function of photoelectron energy. The data were obtained at two levels of the RRPA calculations, namely accounting for, (a) only two RRPA interacting channels ( 2ch ) and (b) nine RRPA channels ( 9ch ).

Table 1 RRPA calculated [29] photoelectron energy positions of the Cooper minima (au) for the free and encaged Ca, Sr and Ba...

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