Photoelectron sudden approximation

In photoelectron. Auger and X-ray spectroscopies, the frozen core and sudden approximations have frequently been used for their simplicity. However, interesting chemical bond effects in Auger and X-ray spectra have not yet been explained by such over simplified approximations. The representatives are remarkable changes in satellite intensity distributions appeared in X-ray and Auger spectra emitted from a series of fluorides [14-20], Introduction of a new concept of... 

The main peaks in X-ray Photoelectron Spectroscopy (XPS) for molecules appear because of the photoionization of core electrons. In addition, satellite peaks on the high binding energy side of the main peak have often been observed. These peaks are generally referred to as shakeup satellite peaks. In the sudden approximation, the shakeup process which accompanies photoionization can be considered as a two-step process. First, a core electron is emitted as a photoelectron, creating an inner shell vacancy. In the next step, electron(s) in the same molecule transfer from valence orbital(s) to unoccupied orbital(s) with relaxation of orbital energies. It is important to study these satellites in order to understand the valence and excited states of molecules (1). 

The observed shakedown is analogous to the satellites observed in photoelectron spectroscopy and can be treated in a similar manner [25]. This analysis enables us to quantify the intensity of the Is —> 4p + LMCT shakedown feature as a percentage of the total Is > 4p transition intensity. Comparison of the shakedown intensity to that of the Is > 3d(+4p) pre-edge transition (at 8,979 eV) then allows for quantitation of the amount of 4pz mixing into the 3d orbital. Within the sudden approximation [28-30], the creation of the core hole occurs rapidly, before the electron adjusts to the new potential. Here, the intensity /j of a given transition corresponding to either the main (Is —> 4p ) or shake down (Is —> 4p + LMCT) final state can then be given by the Sudden approximation... 

The physics of the photoelectron emission for XPS is depicted schematically in Fig. 8. The figure assvunes the most simple approximation to the excitation process known as the sudden approximation of an atom, which is in detail a quantum mechanical process described by the overlap integral between a bound atomic state and a series of final orbital states through which the electron is... 

The evaluation of P requires knowledge about the photoelectron amplitude. It should, of course, be calculated as a continuum amplitude from the Dyson equation, but for a general molecule that is still a tough problem, and one proceeds by making more or less ad hoc choices. The perhaps simplest description of the photoelectron is v kf,r) — (27t) 5 ex.p ikf r). This choice of a plane wave is often referred to as the sudden approximation, or the zeroth-order Born approximation. If a primitive atomic orbital basis aj(r — Pa) is used. 

The difference between the adiabatic and sudden approximations is generally not important for valence band photoelectron spectroscopy of metals because a large... 

Fig. 2. Plot of the relative proportionality constant a as a function of the saturation (65,536 counts). Each data point represents at least 10 photoelectrons thus the uncertainty due to Poisson statistics is 10 . The data rvere accumulated using a very stable incandescent lamp and various accurately gated integration times. Plot (a) is the result of 42 tests of 5 different diodes across the array. In each test, the number of counts for a given exposure was compared with the number of counts recorded for a reference exposure corresponding to approximately 50% of saturation. The a value drops suddenly beyond 96% saturation. Plot (6) depicts the same data as (a) on an expanded scale in order to show the rapid dropoff of a as the percent of satination exceeds 96%. (Reprinted with permission from Menningen etal., 1995a, Contrib. Plasma Phys. 35, 359, 1995 Wiley-VCH, Inc.)...

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