Photoionization, cross sections processes

The lines of primary interest ia an xps spectmm ate those reflecting photoelectrons from cote electron energy levels of the surface atoms. These ate labeled ia Figure 8 for the Ag 3, 3p, and 3t7 electrons. The sensitivity of xps toward certain elements, and hence the surface sensitivity attainable for these elements, is dependent upon intrinsic properties of the photoelectron lines observed. The parameter governing the relative iatensities of these cote level peaks is the photoionization cross-section, (. This parameter describes the relative efficiency of the photoionization process for each cote electron as a function of element atomic number. Obviously, the photoionization efficiency is not the same for electrons from the same cote level of all elements. This difference results ia variable surface sensitivity for elements even though the same cote level electrons may be monitored. 

The adiabatic ionization potential (1A) of a molecule, as shown in Figure 4.1, equals the energy difference between the lowest vibrational level of the ground electronic state of the positive ion and that of the molecule. In practice, few cases would correspond to adiabatic ionization except those determined spectroscopically or obtained in a threshold process. Near threshold, there is a real difference between the photoabsorption and photoionization cross sections, meaning that much of the photoabsorption does not lead to ionization, but instead results in dissociation into neutral fragments. 

The H2 molecule is a system for which quite recently it has been possible to measure in unprecedented detail state-selected vibrationally and rotation-ally resolved photoionization cross sections in the presence of autoionization [27-29]. The technique employed has been resonantly enhanced multiphoton ionization. The theoretical approach sketched above has been used to calculate these experiments from first principles [30], and it has thus been possible to give a purely theoretical account of a process involving a chemical transformation in a situation where a considerable number of bound levels is embedded in an ensemble of continua that are also coupled to one another. The agreement between experiment and theory is quite good, with regard to both the relative magnitudes of the partial cross sections and the spectral profiles, which are quite different depending on the final vibrational rotational state of the ion. 

As asserted in the previous section, the height of the photolines shown in Fig. 2.4 does not provide the correct measure of the intensity of a photoline. It will now be demonstrated that the appropriate measure for intensities is the area A under the line, recorded within a certain time interval, at a given intensity of the incident light, and corrected for the energy dispersion of the electron spectrometer. This quantity, called the dispersion corrected area AD, then depends in a transparent way on the photoionization cross section er and on other experimental parameters. In order to derive this relation, the photoionization process which occurs in a finite source volume has to be considered, and the convolution procedures described above have to be included. In order to facilitate the formulation, it has to be assumed that certain requirements are met. These concern ... 

Some partial photoionization cross sections, derived in this way for neon, are shown in Fig. 2.11 as a function of photon energy. The uppermost curve is the total absorption cross section. At the onset of the ionization thresholds for the ejection of Is, 2s and 2p electrons this quantity shows the corresponding absorption edges (see the discussion related to equ. (2.11)). The partition of the total cross section into partial contributions cr(i) clearly demonstrates that the dominant features are due to main photoionization processes described by the partial cross sections satellite transitions from multiple photoionization processes are also present. If these are related to a K-shell ionization process, they are called in Fig. 2.11 multiple KL where the symbol KLX indicates that one electron from the K-shell and X electrons from the L-shell have been released by the photon interaction. Similarly, multiple I/ stands for processes where X electrons from the L-shell are ejected. Furthermore, these two groups of multiple processes are classified with respect to ionization accompanied by excitation, (e, n), or double ionization, ( ,e). If one compares in Fig. 2.11 the magnitude of the partial cross sections for 2p, 2s and Is photoionization at 1253.6 eV photon energy (Mg Ka radiation) and takes into account the different... 

This is a very important result. It states that both dipole amplitudes from the RRPA calculation are modified by a common factor that reflects the influences of electron correlations in the initial and final ionic states which are beyond mean-field electron-electron interactions. The A0a0 2-value is called the spectroscopic factor (or the quasi-particle strength or the pole strength or the renormalization factor) and describes the weight given to the improved 2p photoionization cross section as compared to a calculation which does not include these specific electron correlations. The remaining intensity is transferred to satellite processes... 

Values of P determined from angular distributions provide important information about the photoionization process and may help in the orbital assignment of bands in a PE spectrum. The problem of photoionization cross sections and photoelectron angular distributions is thoroughly discussed by Samson . 

A simple measurement of the total photoionization cross section (isotropic sample, cross section measured at a specified photon energy, integrated over all photoejection angles, without specification of the internal state of the photoion, without determination of ms of the ejected electron) contains no information about the distribution of Z, m -values of the ejected electron. However, measurable properties of the photoionization event can provide information about the mechanism of the photoionization process. The frequently measured quantities included f3, Aq, and A. The ft quantity describes the angular distribution of the photoelectrons and is defined analogously to the (3 for photodissociation (see Section 7.2.4), Ajp is the alignment ( Mm distribution) of the photoion. A (not to be confused with the spin-orbit constant) or alternatively P, is the spin-polarization of the ejected electron, which is relevant when the photoion has nonzero spin. 

These many-body theories utilize an altogether different operator basis, the many-body basis. These basis operators account for correlation in an approximate way, since they act on the correlation part of the ground state as well as the SCF term. Hence, the many-body basis operators have interesting physical interpretations as primitive ionization or excitation operators. In addition to the excitation operators, the complete many-body basis set for excitation energies includes primitive de-excitation operators, which have no analogs in traditional configuration interaction theory. The many-body basis for ionization processes includes operators that remove electrons from particle orbitals. These operators are also without simple counterparts in Cl theory. The various terms in the expression for photoionization cross sections have been analyzed in light of the physical content of the many-body basis set. 

The photoionization process involves an absorption of a photon as discussed in Section 6.3 on absorption spectroscopy. Rather than to use the result from that section, the photoionization cross section is discussed in terms of first-quantization. This will introduce some appreciation for how the electron propagator amplitudes are related to the wavefunctions of the N-, N - 1), and N + l)-electron systems. The differential cross section for photoionization, i.e., the probability that the system absorbs a photon and makes a transition from the ground state N) to the excited state N, s) in the continuum with one electron escaping into solid angle dflf with wave vector kf (and the rest of the system in a bound state) is ... 

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