Relative intensities in X-ray photoelectron spectra.: Part VIII

The photoionization cross-sections for the 3s and 3p shells of atomic Si, P, S, and Cl and the S²⁺ ion, and for the 2s and 2p shells of atomic F have been calculated using the random-phase approximation with exchange (RPAE) for the average-configuration term. Using the theoretical atomic cross-section values, the partial cross-sections for photoionization of the SF₆ molecule have been calculated for hv ? 54 eV and the photoelectron spectra have been interpreted. The calculation of relative intensities in the photoelectron spectra of H₂S is presented. The influence of the effective charge of an atom on the photoionization cross-section value for a molecular level is shown.     

Relative intensities in x-ray photoelectron spectra

An experimental determination of the relative intensities of X-ray photoelectron lines corresponding to the inner levels of elements with Z ? 20, and calculations of the total photo-ionization cross-sections for all shells of these elements with the Hartree—Fock—Slater potential are reported. The experimental and theoretical values agree well for the 1s levels while marked discrepancies are revealed for the 2p levels. The theoretical values of the cross sections for the atomic valence levels are used to calculate the relative intensities of molecular levels in CF₄, BF₄^?, BeF₄^2?, LiF, NO₃^?, CO₃^2?, CO, N₂, CO₂, H₂O and C₄H₅N. The results of the calculations agree satisfactorily with experiment.     

Relative intensities in X-ray photoelectron spectra

An experimental determination of the relative intensities of X-ray photoelectron lines corresponding to the inner levels of elements with Z ? 20, and calculations of the total photo-ionization cross-sections for all shells of these elements with the Hartree—Fock—Slater potential are reported. The experimental and theoretical values agree well for the 1s levels while marked discrepancies are revealed for the 2p levels. The theoretical values of the cross sections for the atomic valence levels are used to calculate the relative intensities of molecular levels in CF₄, BF₄^?, BeF₄^2?, LiF, NO₃^?, CO₃^2?, CO, N₂, CO₂, H₂O and C₄H₅N. The results of the calculations agree satisfactorily with experiment.     

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.     

Molecular photoionization cross-sections and their dependence on excitation energy

A general formula for the photoionization cross-section of a linear molecule in terms of atomic subshell cross-sections and diffraction effects is given. Example calculations are carried out for line intensities of CO and N₂ as a function of incident photon energy from threshold up to the soft X-ray region. The importance of associating CNDO coefficients to orthogonal Slater AO's is pointed out. General rules for dependence of photoionization cross-sections on excitation energy are discussed.     

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.     

Relativistic R-matrix close-coupling calculations for photoionization of Ne-like Al IV

We present relativistic close-coupling photoionization calculations of Al IV using the Breit-Pauli R-matrix method to obtain photoionization cross-section of Al IV from the ground state and the lowest two J=0 (even) excited states. A multi-configuration eigenfunctions expansion of the core Al V is employed with spectroscopic configurations 2s²2p⁵, 2s2p⁶, 2s²2p⁴3s, 2s²2p⁴3p, 2s²2p⁴3d and 2s²2p⁴4s. We have included, for the first time, the lowest 68 level target states of Al V in the photoionization calculations of Al IV. Extensive configuration interaction wavefunctions are used to describe both the initial Al IV states and the final Al V states. Cross-sections are compared from three level calculations including only 2s² 2p^{5 2}P^o _3/2, _1/2 and 2s 2p^{6 2}S_1/2 levels of Al V. The present calculation using the lowest 68 target levels of Al V are presented for the first time and should provide reasonably complete database for practical application for photoionization cross-section for Al IV, where high-energy cross-sections along with near-threshold photoionization cross-section is required.     

Relative partial photoionization cross-section of methylacetylene to the X2E ion state over the photon energy range 11–26 eV

Relative partial cross-sections for photoionization to the X²E ground state of the methylacetylene ion over the photon energy range 11–26 e V have been determined using synchrotron radiation. The observed cross-sections show a broad resonance feature similar to the results for photoionization to the X²II_u ground state of the acetylene ion. An explanation involving autoionization from a π^* (e) excited state is proposed.     

Comparison of photoelectron intensities and Franck-Condon factors in the photoionization of H2, HD and D2

The relative intensities of vibrational bands corresponding to the photoionization reactionX¹Σ_g⁺(υ″ = 0) + hv → X²Σ_g⁺(υ′ = 0, 1, 2 …) + e^? have been measured for H₂, HD and D₂, using He I radiation and a cylindrical mirror analyzer. These relative intensities differ significantly from squared overlap integrals (Franck-Condon factors) based on accurate potential curves for X¹Σ_g⁺ and X²Σ_g⁺, but are in good agreement with calculations performed by Itikawa which include the variation of transition moment with internuclear distance and the kinetic energy of the departing electron.     

Measurement of the K shell X-ray production cross-sections and fluorescence yields for Nd,Eu, Gd,Dy and Ho using radioisotope X-ray fluorescence in the external magnetic field

The effect of external magnetic field on the K_α and K_β X-ray production cross-sections and K shell fluorescence yields for ferromagnetic elements Nd, Gd and Dy and paramagnetic elements Eu and Ho have been measured at the excitation energy of 59.5 keV γ -rays from ²⁴¹Am radioactive source of strength 100 mCi in the external magnetic field of intensities ±0.75 T. Furthermore, I_Kβ /I_Kα intensity ratios for these elements have been measured in the external magnetic field. The K X-rays from different targets were detected using a high resolution Si(Li) semiconductor detector. For B = 0, the measured K X-ray production cross-sections, K shell fluorescence yields and the I_Kβ /I_Kα intensity ratios were compared with the experimental and theoretical data in literature. The results have shown that the fluorescence parameters as photoionization cross section, fluorescence yield, radiation rates and spectral linewidth can change when the irradiation is conducted in a magnetic field.     

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.     

Electron spectroscopy using excited atoms and photons IV. Penning ionization of ethylene

Using helium metastable atoms (2¹S, 2³S), the Penning ionization of C₂H₄ has been studied using a high resolution electrostatic electron analyzer. The Franck—Condon envelope for the ground state of C₂H₄⁺ (X²B_3u) is found to be the same for He* (2³S) Penning ionization and 584 Å photoionization. The ΔE shift values and the relative electronic transition probabilities are reported for four ionic states. Unusually large differences have been found for the relative electronic transition probabilities for Penning ionization and photoionization.     

Symmetry dependence of rms Charge Radii

The nucleon number dependence of rms charge radii is often approximated by some simple formula containing the mass number only, R(A)=r(A)A^1/3, where r(A) is a slowly varying function of A. However, for nuclei off the stability line, the mass number A=N + Z is not enough to characterise the dependence of the R(Z, N) radius surface on the nucleon numbers Z and N. In the present work, an additional term has been included, depending on the symmetry parameter I=(N ? Z)/A. Several parametrisations were tried, using weighted least-squares procedures for the fit to a present-day data base. The best fit (with χ²/ń=17) was found for R(A, I)=r(A)A^1/3 + b_I/(I ? I_stab), where I_stab=(N_stab ? Z_stab)/A is the value of the symmetry parameter of the stable isobar with mass number A, and b_I=?0.83 fm. The formula R(A, I)=[r(A) + a_I(I ? I_stab)]A^1/3 is only slightly inferior to the previous one, moreover, it is supported by simple model calculations; here a_I=?0.20 fm (χ²/ń=20). The difficulty in determining the right parametrisation is caused by the fact that the surface R_exp(A, I) is not smooth: there are strong shell and deformation effects. To avoid the distorting effect of these deviations on the parameter values, more than half of the original data had to be omitted.     

On the stability of the transeinsteinium elements

We calculate ground-state properties of nuclei in the Z≧100 region. The most stable superheavy elements are predicted for lower neutron number than in previous investigations, namely ₁₁₀ ²⁸⁸ X and ₁₁₀ ²⁹⁰ X, both with a calculated half-life of around 200 days. A new feature is a local minimum in the ground-state shell correction at Z=110 andN=162. Elements in this region are therefore expected to show increased stability relative to some earlier expectations.     

Second order logarithmic corrections to the Drell-Yan cross-section

We present a complete order α _s ² calculation of the large logarithmic terms of the type ln ⁱ (1?x)/(1?x) (x=Q ²/s), which appear in the Wilson coefficient of the total and differential DY cross-sections. These terms are computed using renormalizationgroup methods. It is shown that besides the well known constant part, they constitute the bulk of the radiative correction. This in particular holds for the higher τ-region which is still accessible to experiment. The large logarithmic corrections determine the shape of theK-factor and give a partial explanation of the phenomenon of anomalous scaling.     

Photoionization of molecular oxygen in the X3Σg− and a1Δg states

Calculations are carried out, at similar levels of approximation, of the photoionization cross-sections for the ground X³Σ_g^? and metastable a¹Δ_g states of O₂ leading to the X²Π_g state of O₂⁺. Estimates, based upon measurements for the X³Σ_g^? state, are made of the photoionization cross-section of the a¹Δ_g state for transitions populating excited states of O₂⁺.     

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.     

An expansion of Hartree-Fock and correlation energies,relativistic corrections and the dipole matrix element in the powers of of 1/Z

Feynman diagrammatic technique was used for the calculation of Hartree-Fock and correlation energies, relativistic corrections, dipole matrix element. The whole energy of atomic system was defined as a polen-electron Green function. Breit operator was used for the calculation of relativistic corrections. The Feynman diagrammatic technique was developed for 〈H_B>. Analytical expressions for the contributions from diagrams were received. The calculations were carried out for the terms of such configurations as 1s² 2sⁿ¹ 2pⁿ² (2 ≧n₁≧ 0, 6≧ n₂ ≧ 0). Numerical results are presented for the energies of the terms in the form $$E = E_0 Z^2 + \Delta {\rm E}_2 + \frac{1}{Z}\Delta {\rm E}_3 + \frac{{\alpha ^2 }}{4}(E_0^r + \Delta {\rm E}_1^r Z^3 )$$ and for fine structure of the terms in the form $$\begin{gathered} \left\langle {1s^2 2s^{n_1 } 2p^{n_2 } LSJ|H_B |1s^2 2s^{n_1 \prime } 2p^{n_2 \prime } L\prime S\prime J} \right\rangle = \hfill \\ = ( - 1)^{\alpha + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 1} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 [E^{(0)} (Z - B) + \varepsilon _{co} ] + \hfill \\ + ( - 1)^{L + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 2} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 \varepsilon _{cc} . \hfill \\ \end{gathered} $$ Dipole matrix elements are necessary for calculations of oscillator strengths and transition probabilities. For dipole matrix elements two members of expansion by 1/Z have been obtained. Numerical results were presented in the form P(a,a′) = a/Z(1+τ/Z).     

40.81 eV photoelectron spectroscopy of the thallous halides

Photoelectron spectra (using 40.81 eV photons) of TlF, TlCl, TlBr and TlI are presented. Absolute binding energies of the outermost halogen np levels with respect to the vacuum level and the energy separations between the thallium 5d_5/2 level and the halogen np level are compared with the corresponding energies predicted using the Born model for ionic solids. The thallium ion ²D_5/2 and ²D_3/2 final states display a non-statistical branching ratio and this is explained in terms of the relative photoionization cross-sections of d_5/2 and d_3/2 electrons. Structure in the spectrum of TIF is interpreted in terms of molecular orbital-like states.     

Formulae which relate pressure,activity and potentials of mean force to sums of integrals over Ursell-Mayer correlation functions of the distribution functions

The pure rotational spectrum in the far-infrared between 30 and 170 cm^-1 and its absolute intensity has been measured for CH₂D₂ in the vibrational ground state by high-resolution interferometric Fourier transform techniques. The analysis of the integrated cross-sections in the essentially water-free spectrum results in an accurate value for the permanent, vibrationally induced ground state electric dipole moment of CH₂D₂|μ₀| = (6·40±0·33) x 10^-3D.The influence of centrifugal effects on intensities and on the determination of the permanent dipole moment was investigated. Although centrifugal effects are important for the explanation of single band profiles, they appear to be of little relevance for the resulting permanent dipole moment. A new, more general 9- dimensional dipole moment function for methane is derived from ab initio calculations and experimental band strength information of CHD₃. Quantum Monte Carlo calculations using this function and a new, more general 9- dimensional analytical, anharmonic potential function for methane yield a semi-theoretical estimate μ₀ ^z = – (7·8±0·5)x10^-3D for CH₂D₂.