Berkowitz Atomic and Molecular Photoabsorption

Absolute Partial Cross Sections
1. Auflage 2015
ISBN: 978-0-12-801958-0
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 532 Seiten

Atomic and Molecular Photoabsorption: Partial Cross Sections is a companion work to Joseph Berkowitz's earlier work, Atomic and Molecular Photoabsorption: Absolute Total Cross Sections, published with Academic Press in 2002. In this work Joseph Berkowitz selected the 'best' absolute partial cross sections for the same species as included in the companion work. A contrast, however, is that photoabsorption measurements, being of order I/Io, do not require the most intense light sources, whereas acquiring data on the products of light interactions with gaseous matter (ions, electrons, various coincidence measurements) has benefited significantly with the arrival of second- and third-generation synchrotrons. The newer devices have also extended the energy range of the light sources to include the K-shells of the species discussed here. The newer light sources encouraged experimentalists to develop improved instrumentation. Thus, the determination of partial cross sections continues to be an active field, with more recent results in some cases superseding earlier ones. Where the accuracy of the absolute partial cross sections is deemed sufficient (less than five percent), numerical tables are included in this new work. In other cases, the available data are presented graphically. - Includes data on atoms, diatomic molecules, triatomic molecules, and polyatomic molecules - Written by world-leading pioneer in the field of photoionization mass spectrometry - Very clear presentation of the useful, quantitative information in both tables and graphs

Autoren/Hrsg.

Berkowitz, Joseph

Leseproben

Chapter 1 Alternative Designations of Absolute Partial Cross Sections
Abstract
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. 1.1. The So-Called Complete, or Perfect, Experiment
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) + h? ? 1s2 2s2 2p5 3s2 (2P3/2,1/2) + e. Two experiments can be readily performed: the partial cross-section s2p and the photoelectron angular distribution parameter, ß2p. They can be described by 2p=(4p2/3)aEph(|Ds|2+|Dd|2) 2p=|Dd|2-8|Ds||Ds|cos?|Ds|2+|Dd|2 where ? is a relative phase defined by ? = (fes - fed) + (des - ded), f refers to the phase from the Coulomb field, d from the short-range potential, |Ds| and |Dd| are the conventional dipole matrix elements: Ds|=2?o8Pes(r)rP2p(r)dr,|Dd|=2?o8Ped(r)rP2p(r)dr. In this instance, a is the fine structure constant and Eph is photon energy. Thus, we require three independent parameters (?,|Ds|,|Dd|), but only two observables are readily available (s2p,ß2p). 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 ?, ?, and ?. 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) ed5/2, ed3/2, es1/2, and two relative phases, ?2 and ?2. 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 sl, ßl, ?, ?, and ? to deduce the three Ds and two ?s. 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 ?1 = ?5/2 - ?3/2; 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 h? ? 50 eV. This necessitates the determination of more parameters (for heteronuclear molecules with lmax = 4, one needs five s, four p 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 2sg 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 fs (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...