The Photoionization Process

The problem of the static and dynamic behavior of a core hole is intimately connected with the question of how the core hole was created. The energy level spectrum of the core hole is uniquely given by the energy level spectrum of the residual ion but the intensity distribution is determined by the excitation process. In order to interpret a photoelectron spectrum we therefore have to understand the photoionization process which gave rise to the photoelectrons. The purpose of this section is to discuss in simple terms the physics of. the photoionization process and to demonstrate how the various contributions to the photoelectron spectrum can arise. A more formal discussion is presented in Section 3. 

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The photoionization process with which we shall be concerned in both UPS and XPS is that in Equation (8.4) in which only the singly charged is produced. The selection mle for such a process is trivial - all ionizations are allowed. 

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. 

SNMS sensitivity depends on the efficiency of the ionization process. SNs are post-ionized (to SN" ) either hy electron impact (El) with electrons from a hroad electron (e-)heam or a high-frequency (HF-) plasma (i.e. an e-gas), or, most efficiently, hy photons from a laser. In particular, the photoionization process enables adjustment of the fragmentation rate of sputtered molecules by varying the laser intensity, pulse width, and/or wavelength. 

In Eq. (12), l,m are the photoelectron partial wave angular momentum and its projection in the molecular frame and v is the projection of the photon angular momentum on the molecular frame. The presence of an alternative primed set l, m, v signifies interference terms between the primed and unprimed partial waves. The parameter ct is the Coulomb phase shift (see Appendix A). The fi are dipole transition amplitudes to the final-state partial wave I, m and contain dynamical information on the photoionization process. In contrast, the Clebsch-Gordan coefficients (CGC) provide geometric constraints that are consequent upon angular momentum considerations. 

The cluster reactor is attached to the pulsed cluster source s condensation channel, as shown in Figure 6. (16) To it is attached a high-pressure nozzle from which a helium/hydrocarbon mixture is pulsed into the reactor at a time selected with respect to the production and arrival of the clusters. The effect of turbulent mixing with the reactant pulse perturbs the beam, but clusters and reaction products which survive the travel from the source to the photoionization regime ( 600y sec) and the photoionization process are easily detected. 

With increasing energy of the incident photons the photoionization process is accompanied by a rupture of valence bonds, leading to various ionized fragments, the identification of which requires complementary methods of analysis. During the last decade much progress has been achieved in the mass spectrometry of the photoionization products in various diatomic or polyatomic gases under vacuum u.v. irradiation. 

Fig. 6. Spectral efficiency of the photoionization processes in benzylamine vapor...

In ordinary spectroscopy one measures the frequency (or wavelength) and therefore the energy of photons absorbed or emitted (or scattered, as in the Raman effect) by molecules. In photoelectron spectroscopy (PES) one measures the energy of electrons emitted by molecules when they are photoionized by the absorption of high-energy (UV or x-ray) photons. If M stands for a molecule, the photoionization process can be symbolized by... 

In this experiment, no use is made of femtosecond laser pulses, although the photoionization process itself is a femtosecond event. The next natural steps are experiments using femtosecond pulses and the traditional (not projection) electron optics. This materially extends the class of possible experiments. 

If the isotopic shift of a spectral line in an atom or in a molecule is more Hi... the Doppler width, it is in principle possible to selectively excite a parti, id... isotopic species from isotopic mixtures by monochromatic light of w.u. length in coincidence with the absorption of the particular isotopic spe> < In a typical example, 2°2Hg atoms in natural Hg vapor containing 204. o 201, 200, 199, and 198 isotopes are preferentially excited by the 2b i V resonance line of 202Hg atoms. It has recently been demonstrated tlm 235U atoms are enriched in the photoionization processes of Mi. t... 

Since ionization is only a special case of excitation it is also possible to simulate the photoionization process using fast electrons. We may compare the processes... 

Several reasons have been put forward to explain the change in the angular intensity pattern of the photoelectrons. One explanation is that intermediate neutral energy levels are ac-Stark shifted into resonance and contribute new selection rules to the photoionization process [53,54], Another possibility is that the electrons of the Kr or D2 are driven into the core Kr+ or D2 in a scattering-like process that creates interference fringes in the photoelectron angular distribution due to interference between multiple scattering channels [55],... 

The combined effect of the individual energy distribution functions which are of relevance for the photoionization process and for the detection of photoelectrons, can now be discussed. As a first step, the photoionization process alone, i.e., without any detection device, is discussed with the help of Fig. 2.9. The y-axis represents an energy scale with respect to the ground state, and different states of neon are plotted along the x-direction. For photons with sufficient energy hv and with a distribution function GB( ph, Eph), one reaches the continuum above the Is... 

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 ... 

Formally, alignment and orientation follow from the general symmetry properties of statistical tensors pkK introduced in Section 8.4. Spherical symmetry leads to k = k = 0, axial symmetry to k — 0, and alignment requires k = even, and orientation k = odd. Since the dipole approximation in the photoionization process restricts k to k < 2, a photoionized axially symmetric state can only have Poo, p10, and p20 Poo describes isotropy, and the alignment is given by [BKa77]... 

Closed-shell atoms are considered here, because in open-shell systems the photoionization process is generally determined by more than three matrix elements (five parameters). 

The spin-dependent terms of the photoionization process are those associated with the spin-dependent Stokes parameters of the detector. There it can be seen that... 

The previous formulation for the photoionization process provides the starting point for theoretical calculations. For simplicity, and because the conditions are well fulfilled, in many applications the dipole approximation is often used. (For extensions and derivations, relevant in the present context of photoionization studies with synchrotron radiation, see [KJG95] and references therein.) This approximation is based on a special property of the matrix element ... 

Hence, the photoionization process under consideration is determined... 

The summations over Mf and ms are needed because no observation is made with respect to these final-state quantum numbers. ka and Kph are the wavenumber vectors of the Auger electron and the photoelectron, the minus sign indicates the correct asymptotic boundary condition for the wavefunctions, Vc is the Coulomb interaction between the electrons causing the Auger transition, and is the dipole operator causing the photoionization process. 

The population numbers a(JMj) can be related directly to the photoionization process, because they are equal to the partial cross section which depends on the... 

The correct normalization from the photoionization process gives a factor (47i)2a ph/3 and that from the Auger decay a factor coJAn, which finally leads to... 

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