Photoionization cross-sections for atomic orbitals with random and fixed spatial orientation

Atomic photoionization subshell cross-sections and asymmetry parameters necessary for determining the differential cross-sections of randomly-oriented atoms have been calculated within the one-electron, central-potential model and the dipole approximation for all subshells of C, O, Al, Si, S, Ni, Cu, Ga, Ge, As, Se, In, Sb, Cs, Ba, Ce, Ta, W, Pt, Au, and Pb for a photon energy range from 20 to 1500 eV, and the relevant Cooper minima located to within 10 eV. These values are tabulated for general use, together with the associated radial matrix elements and phase shifts. Differential photoionization cross-sections for fixed-orientation s-, p- and d-orbitals have also been derived within the same model for a completely general experimental geometry, and closed-form expressions depending on radial matrix elements and phase shifts are given. For the special geometry of a polarized excitation source with polarization parallel to the electron emission direction, it is further shown that such oriented-atom cross-sections are exactly proportional to the probability distribution of the initial orbital, a result equivalent to that derived by using a plane-wave final-state approximation. However, detailed numerical calculations of cross-sections for oriented Cu 3d and O 2p orbitals in various general geometries and at various energies exhibit significant differences in comparison to plane-wave cross-sections. By contrast, certain prior angular-resolved X-ray photoemission studies of single-crystal valence bands are found to have been carried out in an experimental geometry that fortuitously gave cross-sections close to the plane-wave predictions.     

Photoelectron asymmetries and two-electron satellites near the 3p → 3d giant-resonance region in atomic Mn

The partial cross-sections and photoelectron angular distributions for several lines in atomic Mn have been measured at photon energies between 50 and 72eV. The intensities of the 3d correlation satellites at 24–26 eV binding energy behave similarly to the mainline intensity near the 3p → 3d giant resonance, but show an enhancement near the 3p threshold which is not present for the main line. A configuration-interaction analysis is applied to help identify the origins of the satellites. The 3p/3d branching ratio from 55–72eV and the shape of the 3d cross section in the resonance region are in good agreement with many-body perturbation-theory calculations.     

Relative intensities in x-ray photoelectron spectra. Part VI. The spectra of He(I), He(II), Y Mζ and Zr Mζ

The 2s- and 2p-electron photoionization cross-sections at photon energies up to 190 eV have been calculated, using the RPAE method for averaged configurations of the C, N, O and Ne atoms. The RPAE method ensures a more accurate relation between the cross-sections, 2s/2p, than that obtained using the Hartree—Fock method. Within the framework of the Gelius—Siegbahn model, but with the use of theoretical atomic cross-sections, we have calculated the photoionization cross-sections for He(I), He(II), Y Mζ, Zr Mζ for CH₄, C₂H₆, C₃H₈, C₂H₄, C₂H₂, NH₃, H₂O, CN^?, N₂, CO, CO₂, N₂O and NO₂^? molecules. For CO, N₂, CO₂, N₂O and H₂O molecules, a comparison is made between the theoretical and experimental cross-sections for hν < 60 eV. The calculated absolute and relative values of the molecular-orbital cross-sections are in reasonable agreement with experiment, especially at hν ? 40 eV. The calculations correctly reproduce the change in intensities under the transition He(I) → He(II). We have shown that our calculations have a significant advantage over those performed using the PW and OPW approximations. It is shown for NO, N₂, CO, H₂O, CH₄, NH₃ and N₂O molecules that the total photoionization cross-section calculated taking into account the real structure of the molecular orbitals is in better agreement with the experimental photoabsorption cross-section than is the sum of the cross-sections for the atoms in a molecule.     

Scattered-wave calculations of photoionization cross-sections and asymmetry parameters for CO,H2O and H2S

Partial photoionization cross-sections and asymmetry parameters are calculated for the valence orbitals of the molecules CO, H₂O, and H₂S and of the atoms O and S using a recently developed extension of the self-cosistent field— Xα—scattered-wave method to continuum states. The convergence of the partial-wave expansions for both initial and final states is studied for electron kinetic energies in the range 2–1000 eV. Since convergence is very slow at high kinetic energies, the interesting region between 2 and 50 eV is emphasized, and comparisons are made with experimental UV photoemission results where such data are available. Overall the method appears to be far more reliable than previous calculations for polyatomic molecules which have used plane-wave or orthogonalized plane-wave final states.     

Total cross-section calculations for electrons colliding with molecular nitrogen over an extensive energy range from meV to keV

We report a comprehensive study of the electron impact total cross-sections for molecular nitrogen for impact energies from 0.01?eV to 2000?eV. Ab initio calculations are performed using the R-matrix formalism at low impact energies (up to ～15?eV), while the Spherical Complex Optical Potential formalism is utilised beyond this range. The two methods are consistent at the transition energy, which enables us to provide data for such an extensive range. The results obtained show overall good agreement with the available data.     

Absolute total cross-section measurements for electron scattering from silicon tetrachloride, SiCl, molecules

The absolute total cross-sections for electron scattering on SiCl₄ molecules have been measured in two distinct electron-transmission experiments, in Gdansk and in Trento laboratory, for impact energy ranging from 0.3 to 250 eV and from 75 to 4000 eV, respectively. The e^--SiCl₄ total cross-section function shows two very distinct resonant-like features: the strong peak at 1.9 eV and much broader main maximum centered near 10 eV with some additional substructure close to 5 eV. The present results are compared with low-energy total experimental data and elastic theoretical calculations for electron collisions with silicon tetrachloride molecules.     

Absolute dipole oscillator strengths for photoabsorption and photoionization of carbon disulphide

The absolute dipole oscillator strengths (cross-sections) for photoabsorption and photoionization (total and partial) of CS₂ have been obtained in the 5–40 eV energy range by magic-angle dipole (e, 2e) spectroscopy. Very strong absorption is detected below 20 eV, much of which is attributable to the excitation of molecules decaying by autoionization processes. Analysis of binding energy spectra taken at energy losses above 20 eV reveals extensive satellite structure in the range up to 35 eV. This structure is attributed to many-electron effects consistent with theoretical calculations found in the literature. Photoelectron branching ratios for CS₂ are also reported.     

Relative partial photoionization cross-sections and photoelectron branching ratios of ethylene

Relative partial photoionization cross-sections and photoelectron branching ratios of the valence bands (~10–25 eV binding energy) of ethylene are reported over the photon energy ranges 18–100 eV and 21–100 eV, respectively. The four lowest ionization energy bands (1b⁻¹_1u, 1b⁻¹_1g, 3a⁻¹_g, and 1b⁻¹_2u) show monotonic cross-section decreases with photon energy from 33 eV, the 1b⁻¹_1u CC π band showing the least rapid decline. In contrast, the 2b⁻¹_3u and 2a⁻¹_g bands show almost constant cross-sections up to ~50 eV photon energy, followed by similar, although slower, monotonic decreases. This is attributed to the substantial carbon 2s character of the 2b_3u and 2a_g orbitais. The cross-section behaviour of all bands is interpreted with the aid of SCF-LCAO-MO calculations on the neutral molecule using the Gaussian-80 series of programs.     

Photoemission studies of single crystals of titanium carbide

The electron distribution in the valence band from single crystals of titanium carbide has been studied by photoelectron spectroscopy with photon energies h?ω = 16.8, 21.2, 40.8 and 1486.6 eV. The most conspicious feature of the electron distribution curves for TiC is a hybridization between the titanium 3d and carbon 2p states at ca. 3–4-eV binding energy, and a single carbon 2s band at ca. 10 eV. By taking into account the strong symmetry and energy dependence of the photoionization crosssections, as well as the surface sensitivity, we have identified strong emission from a carbon 2p band at ? 2.9-eV energy. Our results are compared with several recent energy band structure calculations and other experimental data. Results from pure titanium, which have been used for reference purposes, are also presented.The valence band from single crystals of titanium carbide have been studied by means of photoelectron spectroscopy, with photon energies ranging from 16.8 to 1486.6 eV.By taking into account effects such as the symmetry and energy dependence of the photoionization cross-sections and surface sensitivity, we have found the valence band of titanium carbide to consist of two peaks. The upper part of the valence band at 3–4 eV below the Fermi level consists of a hybridization between Ti 3d and C 2p states. The C 2p states observed in our spectra were mainly excited from a band about 2.9 eV below the Fermi level. The APW^5–9, MAPW¹⁰ and EPM¹¹ band structure calculations predict a flat band of p-character between the symmetry points X′₄ and K₃, most likely responsible for the majority of C 2p excitations observed. The C 2s states, on the other hand, form a single band centered around ?10.4 eV.The results obtained are consistent with several recent energy band structure calculations^{5–11, 13} that predict a combined bonding of covalent, ionic and metallic nature.     

Scattering of muonic hydrogen atoms

Our measurement compares the energy dependence of the scattering cross-sections of muonic deuterium and tritium on hydrogen molecules for collisions in the energy range 0.1–45 eV. A time-of-flight method was used to measure the scattering cross-section as a function of the muonic atom beam energy and shows clearly the Ramsauer–Townsend effect. The results are compared with theoretical calculations by using Monte Carlo simulations. The molecular pdμ and ptμ formation creates background processes. We measure the formation rates in solid hydrogen by detecting the 5.5 MeV (pdμ) and 19.8 MeV (ptμ) γ-rays emitted during the subsequent nuclear fusion processes. This revised version was published online in August 2006 with corrections to the Cover Date.     

Subshell photoionization cross-sections,electron mean free paths and quantitative X-ray photoelectron spectroscopy

Subshell photoionization cross-sections (SPC) for elements of atomic number in the range 3?, z ? 82 have been determined from measurement of relative photoelectron intensities at a photon energy of 1486.6 eV (Al Kα). A correction procedure has been developed which permits such determinations even when sample surfaces are not atomically clean. The results obtained suggest that Scofield's SPC calculations [2] are reasonably reliable for 1s, 2p and 3d subshells but that the present, experimentally derived data are to be preferred for quantitative use. As a result of this work, a rapid method of quantitative surface-constituent analysis, accurate to ± 20%, has also been developed, which is expected to be of value particularly in industrial situations. A semi-empirical method of extracting electron mean free paths from measurements of relative photoelectron intensities is also illustrated.     

UV angle resolved photoelectron spectra of fluoro and chloromethane using synchrotron radiation

Photoelectron asymmetry parameters (β) and partial photoionization cross-sections have been measured for ionization from the molecular orbitals of CH₃F and CH₃Cl using synchrotron radiation in the photon energy range 19 to 115 eV. Cooper minima are observed in the β spectra of CH₃C1 for ionization from orbitals with Cl 3p character. Several shake-up bands observed in the F 2s and Cl 38 ionization energy region indicate a breakdown of the one-electron picture of ionization. The position and relative intensities of the satellite bands are compared with the results of Green's function calculations.     

Scattering of electrons from gas-phase N2O(1Σ): Computed cross-sections and angular distributions in comparison with experiments

Ab initio calculations are reported for the quantum scattering of electrons from N₂O molecules in the gas phase and for energies which range from near threshold up to about 100 eV. Elastic integral cross-sections and angular distributions are examined in detail and an extensive comparison is made with existing experiments. The agreement found with the latter data is fairly good and results are further discussed to explain the physical mechanisms at work for this polar target.     

Spin polarization of electrons elastically scattered from europium and bismuth atoms

We present calculations of differential, integrated elastic, total, momentum transfer cross-sections and spin-polarization parameters S, T and U for scattering of electrons from Eu and Bi atoms in the energy range 2.0 to 500.0 eV using semi-relativistic approach. The target-projectile interaction is represented both by real and complex parameter-free optical potentials in the solution of Dirac equation for the scattered electrons. The results for the differential cross-sections and spin-polarization parameters have been compared with the available calculations and experimental results. Received 17 February 2000 and Received in final form 15 June 2000     

Photoelectron spectroscopy of atomic oxygen using the Elettra synchrotron source

Atomic oxygen has been studied using angle resolved photoelectron spectroscopy (PES) and constant-ionic-state (CIS) measurements using radiation from the Elettra synchrotron as the photon source. Relative partial photoionization cross-sections and angular distributions for the O⁺(⁴S) ← O(³P) and O⁺(²D) ← O(³P) ionizations have been measured as a function of photon energy from threshold (13.6 eV) to 19.0 eV. Comparison of the results obtained with recent experimental work performed at lower resolution reveals a number of differences and comparison with results of recent calculations shows the need for the inclusion of coupling intermediate between the j-j and L-S limits in future calculations of photoionization cross-sections and angular distributions. This work has demonstrated the feasibility of and results to be expected from angle resolved PES and CIS measurements on reactive intermediates at Elettra, a third-generation synchrotron source, and further studies on small molecular radicals are proposed.     

Dissociative Excitation of the Even Quartet and Sextet Levels of the Manganese Atom by Collisions of Electrons with Manganese Diiodide Molecules

Dissociative excitation of even quartet and sextet levels of the manganese atom by electron collisions with manganese diiodide molecules was studied experimentally. Twelve excitation cross-sections for transitions from quartet levels and 23 cross-sections for transitions from sextet levels were measured at an incident electron energy of 100 eV. The optical excitation function (OEF) was recorded in the range of electron energies 0?100 eV for transitions originating at the 3d⁵4s4de⁶D_J levels. The potential channels of dissociative excitation in the range of low electron energies (E < 22 eV) were discussed.     

Elastic-scattering cross-section for electrons and positrons from atomic hydrogen

The differential cross-sections of atomic hydrogen for elastic scattering of electrons and positrons have been rederived with the help of a method using a single parameter-dependent unitary shift operator for the calculation of the direct contribution. When the parameter approaches zerc the new method leads to the well-known conventional Glauber results. The numerical calculations include polarization effects and the exchange corrections obtained according to alternative approximation methods. Results calculated with Franco’s exchange show a definite improvement over the earlier results for medium energy electrons at large angles of scattering. Total elastic cross-sections have been calculated for 50 and 100eV electrons and positrons.     

Exchange corrected Eikonal-Born approximation for elastic scattering of electrons by Helium

Differential cross-sections for elastic scattering of electron from Helium atom have been calculated using the Eikonal-Born Series method with the inclusion of exchange effect evaluated by Glauber Model. The results obtained for 300 eV incident electrons are compared with other theoretical calculations and with recent experimental data.     

Momentum distributions and ionization potentials for the valence orbitals of hydrogen fluoride and hydrogen chloride

The binding-energy spectra and momentum distributions for the valence orbitais of HF and HCI have been obtained at 1200 and 400 eV using (e, 2e) spectroscopy with symmetric kinematics For HC1, the strength of the innermost valence-orbital (4cr) is found to be significantly split among several ion~states in the range 20ú41 eV The corresponding orbital (2G) in HF is, however, not significantly split among ion states The measured momentum-distributions are compared with the results of several calculations of at least double-zeta quality, as well as with a one-particle Greenæs function calculation of the generalized overlap amplitude (GOA) Agreement in shape is quite good for the innermost orbitais, but for the ii and outer a orbitais of HF, the momentum distributions calculated directly from the molecular orbitais are significantly more extended in momen- tum space than are the measured distributions The Greenæs function calculations give momentum distributions in reasonable agreement with the data, and pole-strengths for transitions which are in qualitative agreement with the observed cross-sections     

Calculations of electron collision and ionisation of rare gas dimers

Thresholds to 2000 eV electron impact total inelastic cross-sections for rare gas dimers were calculated employing a spherical complex optical potential formalism. From these inelastic cross-sections, total ionisation cross-sections are derived by applying a complex scattering potential-ionisation contribution method. This is a maiden attempt to study the total ionisation cross-section for most of these targets. To the best of our knowledge, no measurements or calculations are available for all the targets in the literature with which we can compare our results. The results show a linear relationship between maximum ionisation cross-section and target radius, depending on its size. Such dependence can confirm the consistency of the data presented here.