Chapter 1

The spectral distribution of the absolute total photoionization cross section of an atom or molecule can be partitioned into absolute partial cross sections in a variety of ways. Here, the partition is made largely in terms of ionization from Hartree-Fock-like orbitals following Koopmans' theorem, primarily because of the availability of such experimental data over a broad energy range, made possible by the increased spectral output of modern synchrotrons, and the more sophisticated detection methods, including photoelectron, photoion (separately and in coincidence). Partial cross sections for atoms may involve multiple ionization, and for molecules, fragment ions. Deviations from independent particle behavior, especially by ionization from inner-valence orbitals, are recognized. Each of the foregoing methods is discussed in detail in the chapters that follow.

The spectral distribution of the absolute total photoionization cross section of an atom or molecule can be decomposed into absolute partial cross sections in a variety of ways.

An experiment is said to be“perfect” or “complete,” within a certain theoretical framework, if from different experimental observations complementary information can be obtained that enables one to determine all the matrix elements involved and therefore recover all possible observables.

See Bed 69, Kes 81, and Sch 97.

This approach is sometimes referred to as the amplitude–phase method of scattering theory. As an example, consider photoionization from the inner-valence shell of Mg, i.e., 1s2 2s2 2p6 3s2 (1S0) + hν → 1s2 2s2 2p5 3s2 (2P3/2,1/2) + e. Two experiments can be readily performed: the partial cross-section σ2p and the photoelectron angular distribution parameter, β2p. They can be described by

2p=(4π2/3)αEph(|Ds|2+|Dd|2)

2p=|Dd|2−8|Ds||Ds|cosΔ|Ds|2+|Dd|2

where Δ is a relative phase defined by Δ = (φεs − φεd) + (δεs − δεd), φ refers to the phase from the Coulomb field, δ from the short-range potential, |Ds| and |Dd| are the conventional dipole matrix elements: Ds|=2∫o∞Pεs(r)rP2p(r)dr,|Dd|=2∫o∞Pεd(r)rP2p(r)dr. In this instance, α is the fine structure constant and Eph is photon energy. Thus, we require three independent parameters (Δ,|Ds|,|Dd|), but only two observables are readily available (σ2p,β2p). If spin-orbit splitting can be resolved such that 2p3/2 and 2p1/2 can be measured separately, it nevertheless does not advance matters because the variables have the same dependence on |Ds| and |Dd|. The same situation prevails for 2p3/2 and 2p1/2.

Generally, an additional observation comes from measurement of the three electron-spin polarization parameters ξ, η, and ζ. However, for unresolved fine-structure components in the initial state, and neglecting spin-orbit effects in the continuum, no spin polarization is observable (Sch 92). In some special cases, like Auger decay from …2p3/2−13s2→…2p63so, a measurement of the Auger electron angular distribution can provide a third independent observable.

The more general (closed-shell atom) case involves three electric dipole matrix elements, e.g., np−1(2P3/2) εd5/2, εd3/2, εs1/2, and two relative phases, Δ2 and Δ2. Hence, five observables are required in order to provide five independent equations relating the observables to the defining parameters. From the 1980s to 2000, it was generally accepted that five such equations existed, and numerous experiments utilized measurements of σℓ, βℓ, ξ, η, and ζ to deduce the three Ds and two Δs. Schmidtke et al. (Sch 00a) showed that these equations were not independent, and derived an equation relating them. Approximations have been made since then. Cherepkov (Che 05) recommends Δ1 ≡ Δ5/2 − Δ3/2; that is, the spin-orbit phase shift difference is assumed to be zero.

Open-shell atoms are typically more difficult to generate, requiring, e.g., electric discharges, laser photodissociation, chemical reactions, or high temperature sublimation. Electric dipole selection rules remain the same; one still seeks three dipole amplitudes and two relative phase shifts to define the system. To compensate for the lower number density of such atoms, advantage may be taken of their potential for being oriented or aligned, ionizing them with linearly or circularly polarized radiation, and measuring photoelectron angular distributions. Examples include O(3P) studied by Plotzke et al. (Plo 96) and Prümper et al. (Prü 97), and Cr ... 3p6 3d5 4s (7S3) investigated by von dem Borne et al. (von 97).

In molecules, due to the nonspherical nature of the molecular potential, the orbital angular momentum ℓ is not a good quantum number, and any wave function can be represented only as an infinite expansion in spherical harmonics. Therefore, the photoionization process in molecules is in principle described by an infinite number of dipole matrix elements, and a complete experiment is not feasible (Che 05). As a good approximation, one can truncate a partial wave expansion in spherical harmonics to ℓ ∼ 4–5 at photoelectron energies hν ≲ 50 eV. This necessitates the determination of more parameters (for heteronuclear molecules with ℓmax = 4, one needs five σ, four π dipole matrix elements, and eight phase differences (Che 05). For randomly oriented species, we have noted that at most five parameters can be deduced. To get sufficient information for even the simplest molecules, one must attempt the angular distribution of photoelectrons from fixed-in-space molecules. To date, most experimental approaches have employed coincidence detection of photoelectrons and fragment photoions, where the photodissociative ionization occurs in less time than the rotation period of the molecular ion (axial recoil approximation). This proviso effectively restricts such studies to certain inner-valence ionizations and core photoejection for common molecules. One of the most extensive of these studies, by Motoki et al. (Mot 02), involves photoionization from the inner-valence 2σg shell of N2, the 2+ dissociating promptly to N(2D) + N+(3P). Photoelectron angular distributions were measured relative to the axis of dissociation at four photon energies between 40 and 65 eV. The homonuclear N2 confines outgoing waves to odd symmetry, which (for ℓ ≤ 3) reduces the dipole matrix elements to four (three relative), with three relative phases. However, since the equations relating the angular distribution coefficients to the desired parameters are quadratic in the dipole matrix elements, eight sets of solutions result, and the “correct” solution must incorporate other arguments. Motoki et al. succeeded in demonstrating that the dominant outgoing wave was fσ (ℓ = 3), and hence that this constituted an angular momentum barrier that characterized the broad shape resonance having its maximum at a photon energy of ∼50 eV, as previously surmised. Thus, successful implementation of the phase–amplitude method provides significantly more information than partial cross-sections of Koopmans-type orbitals. However, the effort expended in determining the parameters of a single energy point must be a tour de force even with third-generation synchrotrons. As described above, the method is limited to rapidly dissociating states of linear molecules. A quasidiatomic analysis of dissociative ionization of CF3I (both to 3++I and I+ + CF3) has been carried out by Downie and Powis (Dow 99a; Dow 99b). Means other than rapid dissociation have been tried for orienting molecules in the context of photoionization, including adsorption of a gas on a transition metal surface (typically CO on Ni) (Smith et al., Smi 76a; Allyn et al., All 77) and passing CH3I through an electrostatic hexapole field (Kaesdorf...