Atomic Photoionization Cross Sections Research Articles

Density-dependent expressions for photoionization cross-sections

Alternative expressions for photoionization cross-sections and dielectric influence functions are suggested to study the photoionization cross-sections of atoms in solid system. The basic picture is that the photoionization cross-section of atoms in a real system can be described as the coupling between quantum quantity (QQ) and classical quantity (CQ) parts. The QQ part represents the photoionization cross-sections of an isolated particle, while the CQ part may represent most of the important influence of the macroscopic effects (e.g., the interactions of all surrounding polarized particles, and the dielectric property, etc.) on the photoionization cross-sections. The applications to the barium system show that the number-density-dependent new photoionization formula not only obtains the same cross-sections as those from the first order approximation for ideal gas, but also can generate the cross-sections for solid barium by transforming those of ideal gas of the same species using the dielectric influence function.

Transferability of the Valence Ionization Intensities of Chemical Functional Groups between Molecules

The transferability of the valence ionization intensities of chemical functional groups is investigated with three common laboratory ionization sources (Ne Iα, 16.7 eV; He Iα, 21.2 eV; and He IIα, 40.8 eV) for a series of molecules. Each molecule contains two different functional groups that are well separated electronically and spatially by an alkane chain linker. The optimum length of the alkane chain between the functional groups is investigated. In this initial study, the functional groups are RCl, RBr, RSH, and RFc, where R is an alkane chain and Fc is ferrocene with an alkane chain bonded to one cyclopentadienyl ring. An additional feature of this study is that each functional group contains a molecular orbital with nearly pure atomic character, allowing comparison to theoretical atomic ionization cross-section ratios. In general, the observed photoelectron intensity changes are more gradual than those predicted by either theoretical atomic photoionization cross sections or by a complete Gelius analysis based on molecular orbital compositions obtained from electronic structure calculations. Experimentally, there is a high degree of transferability of the relative ionization intensities of the chemical functional groups between the molecules of this set. These results indicate that an empirical library of the relative ionization cross sections of chemical functional groups as a function of photon energy will be a useful aid to the study of more complex molecules and will provide an experimental foundation for further theoretical studies of molecular photoelectron cross sections.

The physical conditions within dense cold clouds in cooling flows - II

This is a progress report on our numerical simulations of conditions in the cold cores of cooling flow condensations. The physical conditions in any non-equilibrium plasma are the result of a host of microphysical processes, many involving reactions that are research areas in themselves. We review the dominant physical processes in our previously published simulations, to clarify those issues that have caused confusion in the literature. We show that conditions in the core of an X-ray-illuminated cloud are very different from those found in molecular clouds, largely because carbon remains substantially atomic and provides powerful cooling through its far infrared lines. We show how the results of the Opacity Project have had a major impact on our predictions, largely because photoionization cross-sections of atoms and first ions are now calculated to be far larger than estimated previously. Finally, we show that the predicted conditions are strongly affected by complexities such as microturbulence or the presence of small amounts of dust. Large masses of cold dense gas, in addition to the warmer molecular gas detected recently, could be present in cooling flows.

Strong impact of the electron-photon matrix element on angle-resolved photoelectron spectra of Sr 2 CuO 2 Cl 2

In recent years insight has been gained into the electronic structure of layered cuprates using angle-resolved photoelectron spectroscopy. In many of these studies it is assumed that the electron-photon matrix element follows the trends set by the atomic photoionization cross sections and does not influence lineshape, dispersion and the k-dependence of the spectral intensity. In this study using Sr2CuO2Cl2 as an example it will be shown that the electron-photon matrix element can have a strong impact on both strength and shape of a feature in an angle-resolved photoelectron spectrum of a layered cuprate which can strongly affect information on character and the momentum-dependence of the energy and spectral weight of a state deduced from the spectra. The results of this study put an emphasis on the need to employ the whole parameter range of the ARPES method to get reliable information on the spectral function of cuprates for which purpose synchrotron radiation is an uniquely suited tool.

The role of exchange and correlation in time-dependent density-functional theory for photoionization

Atomic photoionization cross sections are calculated by time-dependent density-functional (TDDF) methods using different exchange-correlation potentials including the exact one. The exchange-correlation kernel is treated in the adiabatic local density approximation (ALDA). Results for the exact full and the exact exchange-only Kohn–Sham (KS) potential are very similar, the calculated photo cross section agree very well with experimental data. Thus the exact correlation potential seems to have no influence on photoionization and the ALDA for the exchange-correlation kernel seems to be sufficient for most features of the cross sections. The TDDF method employing the exact exchange-only KS potential in combination with the ALDA exchange-correlation kernel therefore is a promising approach to describe photoionization. Deviations from experiment are observed for the widths and shape of the autoionization resonances and have to be attributed to deficiencies of the ALDA exchange-correlation kernel. The calculation of widths and shapes of autoionization resonances therefore may serve as a severe test for new approximate exchange-correlation density-functionals. The asymptotically exact exchange-correlation potential of van Leeuwen and Baerends also leads to quite good photo cross section, which, however, shows deficiencies close to the ionization threshold and in the energetic position of the autoionization resonances. Supplementation of the exact exchange potential with the LDA correlation potential leads to a worsening of the photo cross section because the LDA correlation potential is too attractive.

Polarization studies in the photoionization of atoms using agraphical technique

An alternative method to the density matrix formalism and based on thegraphical technique of angular momentum theory is applied to derive theexpression for the photoionization cross section of atoms. This expressionis suitable for calculating the polarization parameters of the remainingion and photoelectron in the case of the ionization of polarized atomsexposed to polarized radiation. The atom and ion are described by thequantum numbers LSJ and LSJIF (I is nuclear spin). The expressionsare verified by the calculation of the asymmetry parameter β of theangular distribution of photoelectrons in single and shake-upphotoionization of the 2p subshell of Na atoms.

Qualitative modification of the high energy atomic photoionization cross section

It is demonstrated that the nonrelativistic high energy omega-->infinity behavior of the photoionization cross section of an nl atomic subshell, sigma(nl)(omega), for l>0 is independent of l and is given by sigma(nl)(omega) approximately 1/omega(9/2), rather than the previously generally accepted sigma(nl)(omega) approximately 1/omega(l+7/2). Furthermore, for l = 1, although the exponent does not change, the coefficient is significantly altered. This modification of sigma(nl)(omega) is due to the interchannel interaction between ns photoionization channels and l not equal0 channels in the atom. As a result, for the photoionization of l not equal0 electrons, the single-particle approximation is never correct in the omega-->infinity limit. This has important consequences for sum rule calculations.

Photoionization of atomic scandium in the ground state: Total cross sections and3p→3dresonances

A methodology is developed combining many-body-perturbation theory and close coupling of final-state channels with multiconfiguration Hartree-Fock theory to calculate photoionization cross sections of open-shell atoms with accurate threshold and resonance energies. Photoionization calculations of the ground ${1s}^{2}{2s}^{2}{2p}^{6}{3s}^{2}{3p}^{6}{3d4s}^{2}D$ state of atomic Sc, the first of the transition metals, are performed from threshold to 60 eV using this method. All single-electron transitions from $4s,$ $3d,$ and $3d$ subshells are included. Over a broad region of energy, the cross section is dominated by the strength of the $3\stackrel{\ensuremath{\rightarrow}}{p}3d$ resonances which are split into nine distinct transitions through the angular momentum coupling with the open shells. The total cross section and the $3\stackrel{\ensuremath{\rightarrow}}{p}3d$ resonances are presented in detail and reasonably good agreement with available experiment, for both energies and cross section, is obtained. Classifications of a number of the $3\stackrel{\ensuremath{\rightarrow}}{p}3d$ resonances are proposed. In the low-energy region, good agreement with a previous R-matrix calculation is found.

Photoionization cross sections and oscillator strengths for oxygen ions: O I-O VII

Ab initio close-coupling calculations are reported using the R-matrix method for photoionization cross sections $({\ensuremath{\sigma}}_{\mathrm{PI}}),$ oscillator strengths (f values), and energy levels (E) for oxygen ions: O I, O II, O III, O IV, O V, O VI, and O VII. Total, partial, and state-specific photoionization cross sections are computed and investigated in detail. Important features are found that should affect overall photoionization and recombination, especially at high temperatures and energies. Although these ions have been previously studied individually, present work aims at studying them as an isonuclear sequence and obtaining more accurate and complete results for applications. More extended eigenfunction expansions than in previous works, including $n=3$ states, show correlation effects primarily manifested as additional groups of resonances in photoionization of oxygen ions such as O VI and O VII that are of importance in extreme ultraviolet and x-ray laboratory and astrophysical plasmas. Lifetimes of excited bound states are obtained from the present oscillator strengths and compared with experiments. The computed radiative atomic parameters, energy levels, oscillator strengths, and photoionization cross sections constitute a larger dataset than the Opacity Project data [M. J. Seaton, J. Phys. B 20, 6363 (1987)], with which comparisons are made.

Resonance‐averaged Photoionization Cross Sections for Astrophysical Models

We present ground-state photoionization cross sections of atoms and ions averaged over resonance structures for photoionization modeling of astrophysical sources. The detailed cross sections calculated in the close-coupling approximation using the R-matrix method, with resonances delineated at thousands of energies, are taken from the Opacity Project database TOPbase and the Iron Project, including new data for the low ionization stages of iron Fe I-Fe V. The resonance-averaged cross sections are obtained by convolving the detailed cross sections with a Gaussian distribution over the autoionizing resonances. This procedure is expected to minimize errors in the derived ionization rates that could result from small uncertainties in computed positions of resonances while preserving the overall resonant contribution to the cross sections in the important near-threshold regions. The detailed photoionization cross sections at low photon energies are complemented by new relativistic distorted-wave calculations for Z ≤ 12 and from central-field calculations for Z > 12 at high energies, including inner shell ionization. The effective cross sections are then represented by a small number of points that can be readily interpolated linearly for practical applications; a FORTRAN subroutine and data are available. The present numerically averaged cross sections are compared with analytic fits that do not accurately represent the effective cross sections in regions dominated by resonances.

Generalization of the atomic RPA method for diatomic molecules: H 2 photoionization cross-section calculation

The well-known procedure of atomic photoionization cross-section calculations in the random-phase approximation is generalized here for diatomic molecules. As an orthonormal zero-order basis set, the Hartree–Fock wavefunctions of the discrete and continuous spectrum are used; they are calculated in prolate spheroidal coordinates. The photoionization cross-section of the H 2 molecule obtained by this method in the photon energy range from the ionization threshold up to 160 eV is in good agreement with experimental data.

Evaluation of Molybdenum−Sulfur Interactions in Molybdoenzyme Model Complexes by Gas-Phase Photoelectron Spectroscopy. The “Electronic Buffer” Effect

The first ionization energy in the gas-phase photoelectron spectra (PES) of Tp*Mo(E)(tdt) complexes (where E = O, S, NO; Tp* = hydrotris(3,5-dimethyl-1-pyrazolyl)borate; tdt = 3,4-toluenedithiolate) is essentially independent of the nature of E, even though the formal oxidation state of the Mo center ranges from +2 to +5. The PES data for the tdt complexes contrast with the results for analogous complexes with alkoxide ligands, which show large variations in first ionization energy (Westcott, B. L.; Enemark, J. H. Inorg. Chem. 1997, 36, 5404−5405). For the tdt complexes the relative intensities of the two lowest energy ionizations do not substantially change as the excitation source is varied among Ne I, He I, and He II radiation, even though the atomic photoionization cross sections for Mo 4d and S 3p orbitals change dramatically over this energy region. These results all point to substantial covalency in the Mo−S bonds. It is proposed that the S atoms of the tdt ligand act as an “electronic buffer” to t...

Algebraic variational approach to atomic and molecular photoionization cross sections: Removing the energy dependence from the basis

We describe a variational method for calculating photoionization cross sections from a matrix element of the resolvent operator. Scattering boundary conditions are enforced by expanding the resolvent in a basis of square-integrable (${\mathrm{L}}^{2}$ ) and outgoing wave continuum basis functions. By employing several continuum basis functions, with overlaps defined by a suitable analytic continuation, we can, in a single calculation, express the cross section over a continuous range of energies without explicitly resolving the variational equations at each desired energy. The method is illustrated by calculation of the photoionization cross section of atomic Be in the autoionizing region between the ${1\mathrm{s}}^{2}$ 2s and ${1\mathrm{s}}^{2}$ 2p states of ${\mathrm{Be}}^{+}$ .

Atomic Data for Astrophysics. II. New Analytic FITS for Photoionization Cross Sections of Atoms and Ions

We present a complete set of analytic fits to the non-relativistic photoionization cross sections for the ground states of atoms and ions of elements from H through Si, and S, Ar, Ca, and Fe. Near the ionization thresholds, the fits are based on the Opacity Project theoretical cross sections interpolated and smoothed over resonances. At higher energies, the fits reproduce calculated Hartree-Dirac-Slater photoionization cross sections.

Quantum Zeno Effect, Nuclear Conversion and Photoionization in Solids

The quantum Zeno effect in continuous passive observation of radioactive decay is described starting from the “first principles”. It is argued, that in this case the quantum Zeno effect reduces to the influence of inelastic scattering of decay products in surrounded media to decay constant. A new class of quantum Zeno effects is introduced, which are named as “threshold quantum Zeno effects” (TQZE). It is shown, that TQZE could explain recently discovered deep suppression of the conversion decay of 1/2+-isomer of uranium-235 in the lattice of silver. TQZE predicts also some new phenomena, which may be observed in the near-threshold behavior of atomic photoionization cross-sections. Possible experimental manifestations of this new phenomena are discussed.

Exploiting the analyticity of Schrödinger operators: Theory and the computation of partial cross sections

The idea of dilation, or dilatation, analyticity with respect to complex scaling of the interparticle distances for nonrelativistic atomic or molecular electronic Hamiltonians is now over 20 years old and the first major reviews are just over 10. The method continues to be a fruitful source of new theoretical and computational results. Under the scale transformation r reiθ, the usual “spectrum” of bound states is exactly preserved, and scattering continua are “rotated” off the real axis by an angle of −2Re(θ) about their respective thresholds. Useful features of this transformation are (1) that resonances are exposed, and, thus, (complex) resonance eigenvalues are easily calculated as the wave functions are L2, and standard results of Kato-type perturbation theory can thus be applied to them; (2) that utilization of this technique to study atoms in ac and dc fields was an early, and still evolving extension of the original theory; and (3) the fact that the “continua” are rotated off the real energy axis allows scattering information to be extracted from computations carried out entirely L2 in bases as the usual resolvents of scattering theory are no longer singular on the real axis. After a brief survey of the technique and its applications, these ideas are illustrated by discussion of positive energy-bound states and resonances, the extension of the theory to include the dc Stark effect, and a review of the resolution of the initially perplexing problem of atomic and molecular bound states in continua. These theoretical results are followed by a discussion of some very recent computational results, allowing computation of atomic partial photoionization cross sections with no specific coordinate space enforcement of boundary conditions, a highly advantageous situation for calculation of the partial cross section for three-body breakup, as in the process ℏ ω + He He2+ + e− + e−. © 1996 John Wiley & Sons, Inc.

Wavelength dependence of the nonresonant photoionization cross section of a two-electron atom near the ionization threshold

We present the theoretical near-threshold photoionization cross sections of He atoms from bound excited states, using a B-spline-based configuration-interaction method. Our study has shown that in the absence of a strongly energy-dependent feature such as a doubly excited resonance, the photoionization cross sections in the immediate vicinity of the ionization threshold depend linearly on the wavelengths of the incident light. Qualitatively, following the quantum-defect theory, this linear dependence can be linked directly to the expected nearly energy-independent scattering phase shift corresponding to the wave function of the ionized electron at near-zero photoelectron energy.

Redetermination of absolute partial photoionization cross sections of He and Ne atoms between 20 and 300 eV photon energy

Using photoelectron spectroscopy, we have measured some relative partial photoionization cross sections in He and Ne atoms. By compiling these results, along with previously published data obtained from photoabsorption, photoion and photoelectron spectroscopies, we have determined accurate absolute partial photoionization cross sections, up to 300 eV photon energy. The absolute scale was obtained by normalization to the photoabsorption cross sections. The best recommended values, determined by this self-consistent experimental procedure, are compared with the results of various theoretical determinations of the photoionization cross sections.

Photoelectron Spectroscopic Studies of the Electronic Structure and Bonding in TiC and TiN

Titanium carbide (TiC) and titanium nitride (TiN) possess remarkable physical properties, such as extremely high hardness and melting point, that promote their use as antiwear materials under harsh tribological conditions. These physical properties must arise from chemical bonding phenomena that result from the inclusion of the non-metal atom within the metallic matrix, and these bonding phenomena should be apparent in measurements of the valence-band electronic structures of TiC and TiN. This paper explores the surface electronic structure and bonding in TiC(100) and TiN(110) with core and valence level photoelectron spectroscopies (PES's) using X-rays (1486.6 eV) and synchrotron radiation in the range 28-180 eV. Intensity changes in the valence-band features are followed as a function of incident photon energy; these changes are then compared to theoretical atomic photoionization cross sections to determine the atomic origins of these features. Resonant PES at the Ti 3p absorption edge is used to determine titanium 3d contributions to the valence band and to show differences in the electronic structures in TiC and TiN. A new resonance phenomenon near the Ti 3s edge in TiC was observed and its possible assignment is discussed. The electronic structure and bonding in these materials is well described by molecularmore » orbital theory, where the Ti and non-metal ions in their formal oxidation states (e.g., Ti[sup 4+] and C[sup 4[minus]] in TiC) undergo covalent bonding interactions. Overall, the PES results indicate greater covalent mixing for TiC as compared to TiN, consistent with the differences in the electronegativities of the atoms. Specifically, stronger covalent interactions between the C 2s, 2p and the Ti 3d, 4s, 4p levels must occur to explain the spectroscopic differences between TiC and TiN.« less

Subshell Photoionization Cross Sections and Ionization Energies of Atoms and Ions from He to Zn

Partial photoionization cross sections of atoms and ions from He to Zn for all subshells nl of ground-state species are calculated with the Hartree-Dirac-Slater method for photon energies E ⪝ 100 E th, where E th is the photoionization threshold. The cross sections are fitted by simple analytic expressions for E ⪝ 50 keV, and the ionization energies are fitted by simple polynomials of atomic number Z and number of atomic electrons N. The fit parameters are tabulated.