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.     

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.     

UV Subshell photoionisation cross-section of atomic Zn,Cd, and Hg: Experiment and theory

Partial photoionisation cross-sections have been measured at photon wavelengths of 584, 304, 256 and 243 Å for the valence d and s shells of zinc, cadmium and mercury atoms. These cross-sections have also been calculated using the GIPM, a simple one-electron method which obtains the final-state potential by an inversion of the Schrödinger equation for the initial orbital of the photoelectron in the Hartree-Fock wave function. Comparison shows good qualitative agreement between theory and experiment. The quantitative agreement is typically within a factor of 2. Angular asymmetry parameters have also been calculated and the branching ratio for the splitting of the d-subshell cross-section into ²D_{$\text{5}\text{2}$} and ²D_{$\text{3}\text{2}$} contributions has been measured.     

Photoionization cross-section measurements from the 2p, 3d and 3s excited states of lithium

The photoionization cross-sections from the 2p²P_{1/2, 3/2}, 3d²D_{3/2, 5/2} and 3s²S_1/2 excited states of lithium have been measured at different ionizing laser wavelengths, above the first ionization threshold. The experiments are performed by using a thermionic diode working in the space charge limited mode and the cross-sections are measured by employing the saturation technique. By changing the ionization photon energy, a smooth frequency dependence of the cross-sections has been observed for the 2p and 3d states. The cross-section from the 3s excited state has been measured at a single photon energy. The measured values of the photoionization cross are compared with the available data.     

Branching ratios and the partial photoionization cross-section for the 3s electron of argon

Binding-energy spectra obtained using the dipole (e, 2e) electron impact coincidence method have been used to derive the 3s/3p cross-section ratios for the photoionization of argon up to 75 eV. The 3s and 3p photoionization branching ratios have been obtained by making use of recently determined double photoionization yields. The partial photoionization cross-section (oscillator strength) for 3s ionization, obtained using the branching ratio and the known total photoionization cross-section, shows the deep minimum ca. 10 eV above threshold which has been predicted by those theoretical calculations which include electron correlation effects. Below 50 eV the cross-section is in excellent agreement with the SRPAE calculation. The results are in close agreement with recent measurements made using synchrotron radiation but are consistently smaller below the minimum and larger at the higher energies.     

Gas phase high temperature photoelectron spectroscopy: an investigation of the transition metals scandium and vanadium

The He(I) photoelectron spectra of atomic scandium and vanadium have been recorded in the gas-phase. For scandium two bands associated with a (4s)^?1 ionization and one band associated with a (3d)^?1 ionization of the neutral atom have been observed. Measurement of their relative intensities allows the σ_3d:σ_4s photoionization cross-section ratio in atomic scandium to be estimated as 57.1 ± 9.0. In the atomic vanadium spectrum, six bands were seen. Four of these correspond to (3d)^?1 and (4s)^?1 ionizations of the ground state of the neutral atom, the V a⁴F state, whereas two bands correspond to (3d)^?1 ionizations of an excited state, the V a₆D state, which is approximately 2100 cm^?1 above the ground state. Measurement of the intensities of bands arising from the V a₄F state allows σ_3d:σ_4s to be estimated as 29.8 ± 2.5 for vanadium. Spectra of vanadium have been recorded with both single- and multi-detector photoelectron spectrometers. Comparison of the data acquisition rates obtained with both spectrometers demonstrates the advantage of using a multidetector instrument in high temperature photoelectron spectroscopy.     

Relative intensities in x-ray photoelectron spectra. Part II

Experimental data on the relative intensities of X-ray photoelectron lines of some elements with 22 ? Z ? 56, and the calculations for the photoionization cross-sections for inner levels of some elements with 21 ? Z ? 63 are reported. The relationship between photoionization relative cross-sections and line relative intensities is examined. Theoretical values of the photoionization cross-sections were used in the calculations of relative intensities of molecular valence levels for AO₄^x? (A = Cl, S, P, Se, As), AF₆^x? (A = S, Si, Al), COS, CS₂ and H₂S.     

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.     

Ground-state inversion method applied to calculation of molecular photoionization cross-sections by atomic extrapolation: Interference effects at low energies

The ground-state inversion method, which we have previously developed for the calculation of atomic cross-sections [ 29 ], is applied to the calculation of molecular photoionization cross-sections. These are obtained as a weighted sum of atomic subshell cross-sections plus multi-centre interference terms. The atomic cross-sections are calculated directly for the atomic functions which when summed over centre and symmetry yield the molecular orbital wave function. The use of the ground-state inversion method for this allows the effect of the molecular environment on the atomic cross-sections to be calculated. Multi-centre terms are estimated on the basis of an effective plane-wave expression for this contribution to the total cross-section. Finally the method is applied to the range of photon energies from 0 to 44 eV where atomic extrapolation procedures have not previously been tested. Results obtained for H₂, N₂ and CO show good agreement with experiment, particularly when interference effects and effects of the molecular environment on the atomic cross-sections are included. The accuracy is very much better than that of previous plane-wave and orthogonalized plane-wave methods, and can stand comparison with that of recent more sophisticated approaches. It is a feature of the method that calculation of cross-sections either of atoms or of large molecules requires very little computer time, provided that good quality wave functions are available, and it is then of considerable potential practical interest for photoelectron spectroscopy.     

Calculation of X-ray and Auger transition rates, lifetimes, X-ray wavelengths, and fluorescence yields of variously ionized silicon atoms

X-ray and Auger transition rates, X-ray wavelengths, and fluorescence yields are calculated for variously ionized silicon atoms with configurations 1s2s^m2pⁿ, m=0-2, n=1-6. The calculation has been performed using the Hartree-Fock atomic model. Intermediate coupling and configuration interaction have been taken into account. The energies and widths are found to be strongly affected by configuration mixing. The results from the present calculation have been compared with those available in the literature. The theoretical K_α hypersatellite and satellite spectra fall into several well-separated regions, corresponding to each of the possible number of spectator electrons in the 2s and 2p shells. The dependence of radiative rates and fluorescence yields on the number of spectator electrons is also investigated.     

Photoionization branching ratios and asymmetry parameters for inner- and outer-valence shells of H2S in the 18–70 eV energy range

Branching ratios, asymmetry parameters and relative partial cross sections have been obtained for photoionization of the outer and the inner valence shells of H₂S. These measurements were made in the photon energy range 18–70 eV using synchrotron radiation. Our results are compared to a set of calculations using a developed extension of the self-consistent field-Xα scattered-wave method to the continuum states. This comparison shows a qualitative agreement between the experimental and calculated β curves of the outer valence shells. The largely predominant sulfur 3p contribution to the outer valence orbitais 2b₁, 5a₁, 2b₂ is revealed in the corresponding β curves by a Cooper minimum also predicted in the same energy range for the β(3p) of the atomic sulfur. This comparison also shows discrepancies in the branching ratios curves and we suggest that this theoretical framework is better adapted to predict photoionization processes in the outer valence shells than in the inner ones.     

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.     

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.     

Alternate technique for simultaneous measurement of photoionization cross-section of isotopes by TOF mass spectrometer

New measurements of photoionization cross-sections of the lithium isotopes are reported employing a Time of Flight (TOF) mass spectrometer in conjunction with an atomic beam apparatus. Using a two-step selective photoionization and saturation technique, we have simultaneously measured the photoionization cross-section of the 2p excited state of both the isotopes Li⁶ and Li⁷ as 15±2.5 Mb and 18 ±2.5 Mb where as the corresponding number densities have been determined as N₀≈5.3×10¹⁰ atoms/cm³ and N₀≈6.2×10¹¹ atoms/cm³ respectively.     

Photothermal ionization via excited states of sulfur donor in silicon

Structures in the photoionization cross-section spectra below the extrinsic edge of the doubly charged sulfur donor (613 meV) are attributed to the two-step photothermal excitation process in which the bound electron at the ground state first makes an optical transition to an excited state and it is then thermally released from the excited state to the conduction band. A weak peak (cross-section 7 × 10⁻¹⁹ cm²)at 425 meV is attributed to the intervalley optical transition 1s(A₁)→1s(T₂). Peak observed at 570 meV (10⁻¹⁷ cm²) is attributed to the 1s(A₁→2p₀ intervalley optical transition and the peak at 591 meV (3 × 10⁻¹⁷ cm²) to the 1s(A₁)→2p± intravalley optical transition. Data for electron bound at the neutral gold center has no structures which is consistent with the lack of excited states of a neutral impurity potential.     

Near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na, K, Rb, Cs; n = 3-6)

The effect of the polarization of the atomic core by the outer electron on near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na-Cs; n=3-6) is investigated. Partial and total cross-sections for photo-ionization of the np-electron were computed utilizing the configuration interaction technique with Pauli-Fock atomic orbitals (CIPF) and including the long range core polarization potential (CP). To calculate the core polarization potential the variational principle is applied. Comparison with previous theoretical results and with available experimental data is made for the total cross-section , for the electron angular distribution parameter , for the ratio of the reduced electric dipole matrix elements and for the phase shift difference , associated with the d-wave and s-wave continua, respectively. In the comparison, new experimental results for , , and , measured for laser-excited, polarized ³⁹K(4p _3/2) atoms, have been included. Received 21 July 1999 and Received in final form 14 October 1999     

Electronic structure of the valence band for perovskite-type titanium double oxides studied by XPS and DV-Xα cluster calculations

XPS spectra of the valence bands for the perovskite-type titanium double oxides BaTiO₃, SrTiO₃ and CaTiO₃ have been measured and analyzed by means of DV-Xα calculations for the TiO₆ embedded cluster model. The theoretical photoelectron spectra modulated by the photoionization cross-sections are in good agreement with experiment. The XPS results show that the O 2p valence band is constructed of two peaks whose spacing becomes larger in the order BaTiO₃ < SrTiO₃ < CaTiO₃. The DV-Xα results indicate that the greater part of the lower-energy peak is attributed to the levels which have O 2p orbitals pointing to Ti cations and are thus stabilized by the electrostatic potential concomitant with a decreased TiO bond distance. The electrostatic potential also reduces the O 2p-Ti 3d mixing and, together with the repulsion of the electron cloud between the Ti and O ions, makes the TiO bond more ionic.     

Electron spectroscopy using excited atoms and photons IX. Penning ionization of CO2, CS2, COS,N2O,H2S,SO2, and NO2

The electron spectra resulting from thermal collisions of He* (predominantly 2³S) metastable atoms with the seven triatomic molecules, CO₂, COS, CS², N₂O H₂S, SO₂ and NO₂, are compared with their respective 584-Å photoelectron spectra using a transmission-corrected electron spectrometer. The normalised relative electronic-state transition probabilities for production of ionic states in Penning ionization and photoionization are reported together with energy shifts (ΔE values) for He*(2³S) Penning ionization. The cross-section for Penning ionization to lower states of NO₂⁺ is extremely low as has been observed in other open shell molecules such as NO and O₂.     

Comparison of calculated photoionization cross-sections of diamond and silicon in the approximations of plane wave and orthogonalized plane wave

In the approximation of the orthogonalized plane wave the shape of X-ray photoelectron spectra of the valence band in diamond and silicon has been calculated. It is shown that consideration of orthogonality terms influences greatly the value of the ratio between photoionization cross-sections of s- and p-electrons. X-ray emission and photoelectron spectroscopy allow us to define the density of states for silicon valence electrons.X-ray photoelectron spectroscopy is at present widely used for the study of the electronic structure of solids. The photoelectron spectra of crystals clearly reveal all the variations in the density of states. However the curves for the photoelectron energy distribution may be different from the calculated density of states for valence electrons. This indicates the importance of the transition probability for the formation of a photoelectron spectrum. In refs. 1 and 2 the X-ray photoelectron spectra obtained with high resolution for diamond and silicon crystals are compared with the density of states and the conclusion made that the s-states lie higher than the p-states. Densities of states and X-ray photoelectron spectra for diamond and silicon have been calculated³. The wave functions of the valence electrons were found by the tight-binding method⁴ while plane waves were used as wave functions for the excited electrons. From a theoretical point of view it is more reasonable to use orthogonalized plane waves to describe the electron states in the conduction band. Both the core and valence states are to be orthogonalized.The present work reports calculation of the shape expected for X-ray photo-electron spectra of diamond and silicon valence electrons in the approximation of orthogonalized plane wave. Investigation was also made of the influence caused by the orthogonality terms on the ratio of photoionization cross-sections of s- and p-electrons. The electronic structure of diamond and silicon was calculated also by the tight-binding method with the use of the parameters from ref. 3. X-ray photo-electron spectra of valence electrons were calculated over 5230 points in 1/48 part of the Brillouin zone. For simplicity it was assumed that the polarization vector of the electromagnetic wave A is directed along the crystal Z-axis. As was done in ref. 3, the X-ray photoemission intensity was averaged over angular variables. As an example we shall give the formula used for calculation of the X-ray photoelectron spectrum for diamond I(ω, E) ～ ∝E σ_n,k [($\text{1}\text{3}$ET_2s² + $\text{1}\text{3}$T_2p²U_2p?2s² - $\text{2}\text{3}$ ∝ET_2sT_2pU_2p?2s)|C_sⁿ(K|² + $\text{1}\text{5}$ET_2p² (|C_xⁿ(K|² + $\text{3}\text{5}$ET_2p² + $\text{1}\text{3}$T_1sU_1s-2p + T_2sU_2s-2p)² + $\text{2}\text{3}$ √ET_2p(T_1sU_1s-2p + T_2sU_2s-2p) √C_zⁿ(k)|²] where T_nl(E) = fx_O^∞ r²R_nl(tr)_jl(∝Erdr and U_ij = (E_i-E_j fx8r³R_iR_j(r)R_j(r)dr R_i(r) is the radial part of the atomic wave function, C_iⁿ(k), is found from the Schrödinger equation by the tight-binding method. A similar formula is valid for silicon but the number of integrals T_nl and U_ij will be larger owing to the fact that there are more electron states in the silicon atomic core. In eqn. (1) the terms | C_xⁿ|²,|C_yⁿ|² and |C_zⁿ|² have different factors because the A vector is directed along the crystal Z-axis. These factors will be the same when the A vector is directed along (111). Therefore the contribution of p-electrons to the photoelectron spectrum will be proportional to the partial density of p-states.The formula (1) is simplified in the approximation of a plane wave I(ω, E ～ E^{$\text{3}\text{2}$} Σ_n,k[T_s²$\text{1}\text{3}$|C_sⁿ(k)|² + T_p² ($\text{1}\text{5}$|C_xⁿ(k)|² + C_yⁿ(k)|² + C_zⁿ(k)|²)] (2) Figures 1 and 2 show the results obtained from eqns. (1), (2). Here both the spectra calculated in the plane wave approximation and those found experimentally are given. The ratio between maximum III (p-states prevail) and maximum I (s-states dominate) is given in Table 1.As can be seen from Table 1 and Figs. 1 and 2, the spectra calculated in the

4. Relationship between maximum III and maximum I and between photoionization cross-sections of s- and p- electrons in diamond and silicon

     

20.

Theoretical study of photoionization of the isoelectronic sequence Rb<Superscript>+</Superscript>, Sr<Superscript>2+</Superscript>, and Y<Superscript>3+</Superscript>     

Ph. V. Demekhin  I. D. Petrov  B. M. Lagutin  V. L. Sukhorukov  A. Neogi  P. Yeates  E. T. Kennedy  M. W. D. Mansfield  J. T. Costello 《Optics and Spectroscopy》2007,102(2):149-158

The photoionization cross sections for the 4p shell of ions of the Kr isoelectronic sequence Rb⁺, Sr²⁺, and Y³⁺ are calculated. The configuration interaction theory and the perturbation theory are used to describe the many-electron effects. The relativistic effects are taken into account in the Pauli-Fock approximation. The calculated resonance structure of photoionization cross sections for the 4p shell in the region below the 4s threshold associated with the autoionization of the 4s-np singly excited states and the 4p4p-nln′l′ doubly excited states reproduces the results of recent measurements of total photoabsorption cross sections for the Rb⁺, Sr²⁺, and Y³⁺ ions. It is found that, as the nuclear charge in the isoelectronic sequence increases, the ratio between the direct and correlation parts of amplitudes of the 4s-(n/?)p transition changes and, as the consequence, the minimum of the photoionization cross section of the 4s shell shifts from the continuous spectrum to the region of states of discrete spectrum. This accounts for the strong changes in the shape of the 4s-np resonances in the photoionization cross sections for the 4p shell of Rb⁺, Sr²⁺, and Y³⁺, as well as the distinction between the shapes of the 4s-6p _1/2 mirror resonance in the partial 4p _1/2 and 4p _3/2 photoionization cross sections for the Y³⁺ ion which do not suppress each other in the total photoionization cross section, as is the case for similar resonances in Rb⁺ and Sr²⁺.     

	Diamond	Silicon
IIII/II
Density of states of valence electrons	2.64	2.29
XPS (in PW-approximation)	0.27	1.65
XPS (in OPW-approximation)	0.41	1.12
XPS (experimental)	0.44	1.40
σs/σp
PW-approximation	25.0	1.7
OPW-approximation	13.6	2.4
Free atom	12.0	3.4

Theoretical study of photoionization of the isoelectronic sequence Rb<Superscript>+</Superscript>, Sr<Superscript>2+</Superscript>, and Y<Superscript>3+</Superscript>

The photoionization cross sections for the 4p shell of ions of the Kr isoelectronic sequence Rb⁺, Sr²⁺, and Y³⁺ are calculated. The configuration interaction theory and the perturbation theory are used to describe the many-electron effects. The relativistic effects are taken into account in the Pauli-Fock approximation. The calculated resonance structure of photoionization cross sections for the 4p shell in the region below the 4s threshold associated with the autoionization of the 4s-np singly excited states and the 4p4p-nln′l′ doubly excited states reproduces the results of recent measurements of total photoabsorption cross sections for the Rb⁺, Sr²⁺, and Y³⁺ ions. It is found that, as the nuclear charge in the isoelectronic sequence increases, the ratio between the direct and correlation parts of amplitudes of the 4s-(n/?)p transition changes and, as the consequence, the minimum of the photoionization cross section of the 4s shell shifts from the continuous spectrum to the region of states of discrete spectrum. This accounts for the strong changes in the shape of the 4s-np resonances in the photoionization cross sections for the 4p shell of Rb⁺, Sr²⁺, and Y³⁺, as well as the distinction between the shapes of the 4s-6p _1/2 mirror resonance in the partial 4p _1/2 and 4p _3/2 photoionization cross sections for the Y³⁺ ion which do not suppress each other in the total photoionization cross section, as is the case for similar resonances in Rb⁺ and Sr²⁺.