Calculation Of Photoionization Cross Sections Research Articles

Mixed L2 basis set: STOs plus B-Splines. Calculation of the differential photoionization cross-section of Li 2

The convenience afforded by the use of L 2 functions in the calculation of the photoionization cross-section and of others properties depending upon the electronic continuum has prompted the examination of particular basis sets that, among those derived, could be able to mimic the continuum states in an extended region of space. Here results are reported for the differential photoionization cross-section of the Li 2 molecule, where a mixed L 2 basis set comprising multi-center STOs plus single-center radial B-Splines times spherical harmonics was employed.

Theoretical determination of the ionization cross-section of water

For H 2O taken as a model, a comparison is made between three approaches generally used for the determination of photoionization cross-section profile. The wave function results from an ab initio multiconfigurational calculation. The plane wave (PW) model including ionic core correlation leads to a good interpretation of the photoionization spectra and energy photon dependence is analyzed. In a L 2 approach associated with the Stieltjes moment method, a comparative study of two basis sets leads us to appreciate the respective importance of Rydberg and polarization functions. The last point of our work is devoted to the calculation of photoionization cross-section from the inversion of the Kramers–Krönig dispersion integral in a gauge invariant model. This approach allows to underline the importance of the pseudo states in the continuum discretization.

Absolute measurements and theoretical calculations of photoionization cross sections along the isonuclear sequence of multiply charged barium ions.

Photoionization of multiply charged ions of the Ba isonuclear sequence up to Ba6+ has been studied in a beam-beam experiment. A very strong increase in the resonance structures was observed when moving from Ba2+ to Ba6+. Absolute values of the photoionization cross sections were measured for Ba2+ and Ba3+ ions. The interpretation of the results is provided using theoretical multiconfiguration Dirac-Fock and relativistic random phase approximation calculations, showing that the collapse of the nf orbitals occurs for Ba4+.

Multipole effects in the angular distribution of photoelectrons

The influence of contributions corresponding to different multipoles L of a radiation field on the angular distribution of photoelectrons upon photoionization of an atom is considered for linearly polarized photons. Relativistic calculations of the differential photoionization cross section are carried out taking into account all multipoles, whose contributions are appreciable, for all shells of atoms with Z=10, 30, 54, 80, and 94 in the region of photoelectron kinetic energies 0.5 keV≤E k ≤500 keV. The self-consistent Dirac-Fock-Slater potential is used. The calculated results showed that for photoelectron energies E k ≲5 keV, the angular distribution is, on the average, well described in the quadrupole approximation ((L≤2). However, the quadrupole approximation is insufficient for the adequate description of the experimentally measured nondipole parameter ζ. In this case, the next, octupole approximation (L=3) contributes significantly. For energies E k ≳5 keV, it is necessary to consider higher multipoles (up to L≈50 at E k =500 keV). As the energy increases, the angular distribution of photoelectrons becomes increasingly asymmetric and is shifted toward smaller angles.

Manifestation of doubly excited atomic states in the photoionization cross-sections of Ar, Kr and Xe in the vicinity of the subvalence ns-shell threshold

Abstract Energy dependences of the total and partial ns-photoionization cross-sections in the vicinity of the ns-subvalence shell threshold were measured for the rare-gas atoms using photon-induced fluorescence spectroscopy. A resolution of 4.5, 3, and 1 meV was attained for Ar, Kr and Xe, respectively. The experimental cross-sections exhibit many well-resolved resonances of different shapes which are connected with the photoionization through the doubly excited atomic states. Calculated photoionization cross-sections of Ar and Kr show that some resonances are determined by doubly excited states including strongly delocalized n′f-excited electrons.

Photoionisation of Ground State of Ni XIX Using a Relativistic Breit–Pauli Approximation

The relativistic Breit–Pauli approximation is used within the R-matrix method to calculate photoionization cross-sections from the ground state of Ni XIX. Relativistic effects are clearly revealed by comparing the results with those obtained in the non-relativistic LS coupling approximation.

Time-dependent density functional calculations of molecular photoionization cross sections: N2 and PH3

A method based on the time-dependent density functional theory (TD-DFT) is proposed to calculate the photoionization cross section employing the explicit continuum wave-function, within a One Center Expansion and B-Splines radial basis set. The LB94 exchange-correlation potential with correct asymptotic behavior is employed. The results obtained for N2 and PH3 are in excellent agreement with the experimental data and are of comparable accuracy of ab initio methods. A deterioration is still present in the inner valence. For PH3 the effect of TD-DFT is dramatic and recovers completely the Kohn–Sham deficiency. The method has proven efficient for both valence and core ionization.

Mechanisms of giant resonance in 4d photoionization of Eu

We have studied the mechanisms of giant resonance in 4d photoionization of Eu atoms by density functional theory with the optimized effective potential and self-interaction correction method. The dynamic electron correlation is taken into account by the linear density response method. Our calculated photoionization cross sections in the giant resonance region are in good agreement with experimental measurements. Since Eu is a highly spin polarized system, by decomposing the contribution of 4d electrons in spin-up and spin-down states, we clearly identified that the strong asymmetry line profile of the giant resonance is due to a broad resonance of 4d spin-down electrons interaction with a sharp resonance of 4d spin-up electrons.

Iterative calculations of photoionization cross sections by using the Lanczos algorithm and the complex coordinate method in the discrete variable representation

The combination of the Lanczos algorithm and the complex coordinate method, implemented in the discrete variable representation is used to obtain directly the complete photoabsorption spectrum in a single calculation. The method is iterative, based on the continued fraction representation of the Green function. Test calculations of the cross sections for photoionization of hydrogen, lithium and sodium atoms are presented. The convergence properties of the method are discussed.

Measurement of the Absolute Photoionization Cross Section of C[TSUP]+[/TSUP] near Threshold

The absolute photoionization cross section of the ground-state C+ ion has been measured from the ionization threshold at 24 eV to 31 eV using a merged ion-photon beam setup with synchrotron radiation from an undulator. The experimental results have been compared with nonrelativistic theoretical data from the Iron Project and the agreement is generally good in the near-threshold region, but differences in the magnitude of the continuum cross section of 15%-35% at higher energies and several deviations in the resonance structure are observed. The present measurements are a part of an experimental program to test the extensive theoretical photoionization cross section calculations performed within the framework of the Opacity Project and the Iron Project.

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.

Resonances in the photoionization cross section of M@C 60 endohedrals

A model for the calculation of photoionization cross sections of an atom introduced inside the fullerene cage has been proposed. A comparative investigation of the photoionization cross sections of an isolated M atom and the same one in the M@C 60 endohedral has been carried out. It has been shown that the resonance peaks in the photoionization cross sections of the endohedral appear near the thresholds of ionization of atomic subshells. The positions of these peaks on the scale of the photoelectron energy are defined by the fullerene shell radius and the affinity energy of the electron to C 60.

Resonances in photoionization cross sections of inner subshells of atoms inside the fullerene cage

A model for the calculation of photoionization cross sections of an atom inside the fullerene cage is proposed. In the frame of this model the M@C60 endohedral is considered as an isolated M atom located in the centre of the spherically symmetrical fullerene shell. The potential of this shell is written as the Dirac delta function in the radial coordinate. On the basis of this model a comparative study of the photoionization cross sections of an isolated M atom and the same atom in M@C60 is carried out. It is shown that near the thresholds of ionization of atomic subshells the resonance peaks appear in the photoeffect cross sections. The positions of these resonances on the scale of photoelectron energy are defined by the fullerene radius and the affinity energy of an electron to C60. The general formulae derived are used to calculate the photoionization cross sections of the inner subshells of the He, Ne and Ca atoms inside the fullerene cage.

XPS of lanthanoide orthoniobates

Abstract Using the XPS method, orthoniobate lanthanoids LnNbO 4 , where Ln=lanthanoids except Pm and Tm, representing a new number of ferroelectrics were studied in the range of electron binding energies from 0 up to 1350 eV. It is noted that the fine structure in the range of electron binding energies from 15 to 50 eV is generally caused by the electrons of inner valence molecular orbitals. The experimental values of relative intensities for Ln4f-electron spectra lines in orthoniobate lanthanoids LnNbO 4 were found and compared with the analogous values for oxides Ln 2 O 3 , and obtained on the basis of calculated photoionization cross-sections. The spectral characteristics of Ln4f-electrons in orthoniobates and oxides are very similar; and the data obtained do not contradict the assumption concerning the possible participation of Ln4f atomic orbitals in molecular orbital formation in lanthanoid compounds. The decreasing of the relative shake-up of satellite intensity with the decreasing of the electron binding energy of various subshells of the lanthanum ion was confirmed. The parameters of splitting of Ln5s-, Ln4s-electron lines connected with multiplet splitting, and the parameters of the fine structure of the Ln4p-electron spectra line occurring as a result of dynamic effect were obtained.

Electron correlations inL-subshell photoionization of intermediate-Zelements(47<~Z<~51)

The x-ray mass attenuation of ${}_{48}\mathrm{Cd},$ ${}_{49}\mathrm{In},$ ${}_{50}\mathrm{Sn},$ and ${}_{51}\mathrm{Sb}$ in the energy regime of the $L$-subshell edges has been measured. For a comparison of the data of neighboring elements, these were scaled to ${}_{47}\mathrm{Ag}.$ The scaled data were compared with theoretical calculations of photoionization cross sections by Scofield, which use the common single electron approach. The comparison reveals minor but significant deviations between measurement and calculation: The measured cross sections are smaller than the prediction in the regime between the ${L}_{3}$ and ${L}_{2}$ edges, they have a flatter slope in the regime between the ${L}_{2}$ and ${L}_{1}$ edges, and they exhibit a decrease just above the ${L}_{3}$ and ${L}_{2}$ edges. All observed deviations can be explained as electron correlation effects originating from a polarization of the whole electron cloud by the ionizing radiation, since they are qualitatively reproduced by comparative calculations of the ionization process either omitting (independent particle approach) or including (in the linear response approximation) the electron correlations. However, the comparative calculations quantitatively overestimate the electron correlation effects.

Recombination of helium-like ions - I. Photoionization cross-sections and total recombination and cooling coefficients for atomic helium

A B STR A CT A new calculation of photoionization cross-sections is described for the ground and excited states of atomic helium up to principal quantum number n\25 and angular momentum quantum number l\5. These cross-sections are used to calculate total recombination and cooling coefficients for atomic helium for electron temperatures given by log(T )\1(0.2)4.4. A comparison of the threshold photoionization crosssections obtained here with extrapolations of the highly accurate bound‐bound oscillator strength calculations by Drake shows that the new calculations are in error by no more than 1 per cent. The accuracy of the photoionization cross-sections used by previous workers to derive recombination coefficients is also discussed.

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.

Relativistic calculations of photoionization cross sections

Relativistic calculations of photoionization cross sections

The calculation of high-energy photoionization cross sections for the Be isoelectronic sequence

R-matrix and distorted-wave calculations are carried out for photoionization for the Be-like ions Be I - Fe XXIII at high energies. Both methods include the inner-shell excitation process; in the R-matrix calculations these give rise to autoionizing resonances just below threshold for the onset of excitation from inner shells. Differences in the background cross section apparent for neutral Be become much less significant for the ionized species. The new calculations form a benchmarking exercise prior to upgrading the Opacity Project `TOPBASE' database for high energies.

Theoretical study of ultraviolet photoelectron spectra of carbonyl systems: CO,Cr(CO)6, and CO/Cu(100)

We present calculations of partial-channel photoionization cross sections and photoelectron spectra in the ultraviolet energy region of the carbonyl systems CO, Cr(CO)${}_{6}$, and CO/Cu${}_{14},$ the latter system modeling CO/Cu(100). The dependence on photon energy, including He I and He II spectra, and on the particular ionization channel has been investigated for the three systems by means of the independent-channel static exchange method. It is found that the method is able to reproduce all essential trends and features of the spectra as well as the energy dependence of the cross sections. The COCu${}_{14}$ model can be used to reproduce the organization of states in the spectra of CO/Cu(100) and for the photon energy dependence of the individual channel cross sections, while the relative cross sections between the different parts of the spectra can only be qualitatively assessed due to the limited representation of the metal density of states in the cluster model.