Total Photoionization Cross Sections Research Articles

Partial cross sections and interfering resonances in photoionization of molecular nitrogen

We present an in-depth theoretical study of ${\mathrm{N}}_{2}$ photoionization in the region between the second (${}^{2}{\mathrm{\ensuremath{\Pi}}}_{u}$) and third (${}^{2}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$) ionization thresholds. In this region, the electronic continuum includes the Hopfield series of autoionizing states, corresponding to excitations to $ns{\ensuremath{\sigma}}_{d}$, $nd{\ensuremath{\sigma}}_{d}$, and $nd{\ensuremath{\pi}}_{g}$ molecular orbitals. Calculations have been performed by using the xchem code, which makes use of a Gaussian and B-spline hybrid basis in the framework of a close-coupling approach. We provide total and partial photoionization cross sections for all open channels, energy positions, and widths for the five lowest resonances of each series and, when resonances are well isolated from each other, Fano and Starace parameters. We also discuss how the coupling between the two series of overlapping resonances, $ns{\ensuremath{\sigma}}_{d}$ and $nd{\ensuremath{\sigma}}_{d}$, affects their energies and autoionization widths. These results show the potential of the xchem method to describe resonant photoionization in molecules.

Total photoionization cross section of planar helium: scaling laws and collision orbits

The total photoionization cross section of planar helium has been calculated up to the single ionization threshold I22 of triple P states. The cross section shows chaotic fluctuations as the energy E approaches the double ionization threshold E = 0. By analyzing the fluctuating part of the cross section, we show that its amplitude decreases as for as predicted in Byun et al (2007 Phys. Rev. Lett. 98 113001). The Fourier transform of the fluctuating part reveals peaks at the classical actions of closed triple collision orbits. Furthermore, the relative height of the peaks is consistent with the semiclassical predictions. Our findings underline that the fluctuating part of the photoionization cross section can be described by classical triple collision orbits in the semiclassical limit. These orbits all lie in the collinear eZe subspace, demonstrating that the fluctuations are dominated by the dynamics of this low dimensional phase space.

Photoionization and electron impact excitation cross sections for Fe I

Context. Iron is a major contributor to the opacity in the atmospheres of late-type stars, as well as a major contributor to the observed lines in their visible spectrum. Iron lines are commonly used to derive basic stellar parameters from medium/high resolution spectroscopy, that is, spectroscopy which shows metal content, effective temperature, and surface gravity. Aims. Here we present large R-matrix calculations for photoionization cross sections and electron impact collision strengths.Methods. The photoionization calculations included 35 configurations and 134 LS close coupling terms of the target ion. The eigenfunction expansion accounts for the photoionization of the outer nl subshells, with n ≥ 4, as well as the open inner 3d subshell. Our results include total and partial (term-to-term) photoionization cross sections for 936 energy terms of iron with principal quantum number ≤10, and total angular momentum from zero to seven. Our electron impact collision strengths include the lowest 46 LS terms of the atom.Results. The present photoionization cross sections should be considerably more accurate than those currently available in the literature. On the other hand, the electron impact cross sections, which are being reported for the first time, are needed in non-local thermodynamic equilibrium (NLTE) modeling of the solar spectrum and late-type stars in general.

Photoionization using the xchem approach: Total and partial cross sections of Ne and resonance parameters above the 2s22p5 threshold

The XCHEM approach interfaces well established quantum chemistry packages with scattering numerical methods in order to describe single-ionization processes in atoms and molecules. This should allow one to describe electron correlation in the continuum at the same level of accuracy as quantum chemistry methods do for bound states. Here we have applied this method to study multichannel photoionization of Ne in the vicinity of the autoionizing states lying between the $2{s}^{2}2{p}^{5}$ and $2s2{p}^{6}$ ionization thresholds. The calculated total photoionization cross sections are in very good agreement with the absolute measurement of Samson et al. [J. Electron Spectrosc. Relat. Phenom. 123, 265 (2002)], and with independent benchmark calculations performed at the same level of theory. From these cross sections, we have extracted resonance positions, total autoionization widths, Fano profile parameters, and correlation parameters for the lowest three autoionizing states. The values of these parameters are in good agreement with those reported in earlier theoretical and experimental work. We have also evaluated $\ensuremath{\beta}$ asymmetry parameter and partial photoionization cross sections and, from the latter, partial autoionization widths and Starace parameters for the same resonances, not yet available in the literature. Resonant features in the calculated $\ensuremath{\beta}$ parameter are in good agreement with the experimental observations. We have found that the three lowest resonances preferentially decay into the $2{p}^{\ensuremath{-}1}\ensuremath{\epsilon}d$ continuum rather than into the $2{p}^{\ensuremath{-}1}\ensuremath{\epsilon}s$ one [Phys. Rev. A 89, 043415 (2014)], in agreement with previous expectations, and that in the vicinity of the resonances the partial $2{p}^{\ensuremath{-}1}\ensuremath{\epsilon}s$ cross section can be larger than the $2{p}^{\ensuremath{-}1}\ensuremath{\epsilon}d$ one, in contrast with the accepted idea that the latter should amply dominate in the whole energy range. These results show the potential of the XCHEM approach to describe highly correlated process in the ionization continuum of many-electron systems, in particular molecules, for which the XCHEM code has been specifically designed.

Photoionization of atomic fluorine

SynopsisWe use R-matrix method to study the near threshold (17.5eV-20eV) photoionization of neutral fluorine atom and obtain total photoionization cross sections in 3P to 1D range. The theoretical calculation results fit the experimental results better after we consider core-valence electron correlation.

Probing Electronic Wave Functions of Sodium-Doped Clusters: Dyson Orbitals, Anisotropy Parameters, and Ionization Cross-Sections.

We apply high-level ab initio methods to describe the electronic structure of small clusters of ammonia and dimethyl ether (DME) doped with sodium, which provide a model for solvated electrons. We investigate the effect of the solvent and cluster size on the electronic states. We consider both energies and properties, with a focus on the shape of the electronic wave function and the related experimental observables such as photoelectron angular distributions. The central quantity in modeling photoionization experiments is the Dyson orbital, which describes the difference between the initial N-electron and final (N-1)-electron states of a system. Dyson orbitals enter the expression of the photoelectron matrix element, which determines total and partial photoionization cross-sections. We compute Dyson orbitals for the Na(NH3)n and Na(DME)m clusters using correlated wave functions (obtained with equation-of-motion coupled-cluster model for electron attachment with single and double substitutions) and compare them with more approximate Hartree-Fock and Kohn-Sham orbitals. We also analyze the effect of correlation and basis sets on the shapes of Dyson orbitals and the experimental observables.

Rayleigh scattering of X-ray and γ-ray by 2p electrons in ions and neutral atoms

Analytical formulae for the nonrelativistic 2p subshell Rayleigh scattering amplitudes and cross section are obtained using the second order S-matrix element and the Coulombian Green function method, including multipoles and retardation. Relativistic kinematics effects are taking into account, allowing to remove the spurious poles that occur in a usual nonrelativistic calculation with retardation included. The nonrelativistic limit is obtained by removing the relativistic higher order terms in ω/m. A simple formula is also obtained for the total photoeffect cross section for a 2p electron. In the realistic case of ionized and neutral atoms, the screening effects were included by using an effective charge Z eff approach. A good agreement within 10% is found when comparing the predictions given by our analytical results for total photoionization cross section with the full relativistic numerical calculations in the case of 2p subshell for neutral atoms with 26 ≤ Z ≤ 92 and photon energies up to 100 keV.

Validation of Cross Sections for Monte Carlo Simulation of the Photoelectric Effect

Several total and partial photoionization cross section calculations, based on both theoretical and empirical approaches, are quantitatively evaluated with statistical analyses using a large collection of experimental data retrieved from the literature to identify the state of the art for modeling the photoelectric effect in Monte Carlo particle transport. Some of the examined cross section models are available in general purpose Monte Carlo systems, while others have been implemented and subjected to validation tests for the first time to estimate whether they could improve the accuracy of particle transport codes. The validation process identifies Scofield's 1973 non-relativistic calculations, tabulated in the Evaluated Photon Data Library(EPDL), as the one best reproducing experimental measurements of total cross sections. Specialized total cross section models, some of which derive from more recent calculations, do not provide significant improvements. Scofield's non-relativistic calculations are not surpassed regarding the compatibility with experiment of K and L shell photoionization cross sections either, although in a few test cases Ebel's parameterization produces more accurate results close to absorption edges. Modifications to Biggs and Lighthill's parameterization implemented in Geant4 significantly reduce the accuracy of total cross sections at low energies with respect to its original formulation. The scarcity of suitable experimental data hinders a similar extensive analysis for the simulation of the photoelectron angular distribution, which is limited to a qualitative appraisal.

DiracR-matrix calculations of photoionization cross-sections of Ni xiii

In this paper, we report total photoionization cross-sections of Ni xiii in the ground state (3P2) and four excited states (3P1,0, 1D2, 1S0) for the first time over the photon energy range 380–480 eV. The target wavefunctions are constructed with fully relativistic atomic structure GRASP code. Our calculated energy levels and oscillator strengths of core ion Ni xiv agree well with available experimental and theoretical results. The ionization threshold value of ground state of Ni xiii is found to be more closer to the experimental ionization energy and improved over the previous calculations. The photoionization cross-sections are calculated using the fully relativistic darc code with an appropriate energy step of 0.01 eV to delineate the resonance structures. The calculated ionization cross-sections are important for the modelling of features of photoionized plasmas and for stellar opacities.

Comment on “Test of the Stark-effect theory using photoionization microscopy”

An article by Zhao et al. [Phys. Rev. A 86, 053413 (2012)] tests the local frame transformation (LFT) theory by comparing it with benchmark coupled-channel calculations. The system under consideration is an alkali-metal atom that is two-photon ionized in the presence of a static external electric field. Zhao et al. state that the differential cross sections computed in the LFT theory disagree with their supposedly more accurate coupled-channel calculations. They went on to diagnose the discrepancy and claimed that it originates in an inaccurate correspondence between the irregular functions in spherical and parabolic-cylindrical coordinates, a correspondence that lies at the heart of LFT theory. We have repeated the same tests and find that our calculations rule out the discrepancies that were claimed in Zhao et al. [Phys. Rev. A 86, 053413 (2012)] to exist between the LFT approximation and the exact calculations. This Comment thus helps to clarify the accuracy of the Harmin-Fano theory and demonstrates that it is in fact remarkably accurate not only for the total photoionization cross section in the Stark effect, but also for the differential cross section in photoionization microscopy.

Calculation of Photo-Ionisation Cross Sections and Radiative Recombination Rate Coefficients for CO and CO+ Molecules

A method based upon the weighted total cross section (WTCS) theory is proposed to calculate the photo-ionisation cross sections and the radiative recombination rate coefficients between the fundamental level of CO and the main electronic states of its corresponding ion. Total photo-ionisation cross sections and radiative recombination rate coefficients are determined from the calculation of elementary vibrational photo-ionisation cross sections. Transitions between CO+(X, A and B) and CO(X) are considered. Total photo-ionisation cross sections and recombination coefficients are computed in the temperature interval 500–15000 K.

Total photoionization cross-sections of excited electronic states by the algebraic diagrammatic construction-Stieltjes-Lanczos method

Here, we extend the L2 ab initio method for molecular photoionization cross-sections introduced in Gokhberg et al. [J. Chem. Phys. 130, 064104 (2009)] and benchmarked in Ruberti et al. [J. Chem. Phys. 139, 144107 (2013)] to the calculation of total photoionization cross-sections of molecules in electronically excited states. The method is based on the ab initio description of molecular electronic states within the many-electron Green's function approach, known as algebraic diagrammatic construction (ADC), and on the application of Stieltjes-Chebyshev moment theory to Lanczos pseudospectra of the ADC electronic Hamiltonian. The intermediate state representation of the dipole operator in the ADC basis is used to compute the transition moments between the excited states of the molecule. We compare the results obtained using different levels of the many-body theory, i.e., ADC(1), ADC(2), and ADC(2)x for the first two excited states of CO, N2, and H2O both at the ground state and the excited state equilibrium or saddle point geometries. We find that the single excitation ADC(1) method is not adequate even at the qualitative level and that the inclusion of double electronic excitations for description of excited state photoionization is essential. Moreover, we show that the use of the extended ADC(2)x method leads to a substantial systematic difference from the strictly second-order ADC(2). Our calculations demonstrate that a theoretical modelling of photoionization of excited states requires an intrinsically double excitation theory with respect to the ground state and cannot be achieved by the standard single excitation methods with the ground state as a reference.

Comment on “Photoionization of endohedral atoms usingR-matrix methods: Application to Xe@C60”

We demonstrate that what is called a total photoionization cross section in the work by T. W. Gorczyca, M. F. Hasoglu, and S. T. Manson [Phys. Rev. A 86, 033204 (2012)] is in fact a partial photoionization cross section. These quantities differ impressively even in isolated atoms. This demonstrates the prominent role of inelastic collisions of a photoelectron from an intermediate or inner shell not mentioned in their paper. We discuss briefly the correspondence between the experimental data, theoretical predictions, and $R$-matrix results from Phys. Rev. A 86, 033204 (2012). We call attention to the danger in using parameters of C${}_{60}$ potential selected by fitting the same experimental data that one wants to describe. We show that our criticism is applicable to the theoretical part of the most recent publication on photoionization of $\mathrm{Xe}@{\mathrm{C}}_{60}^{+}$ [R. A. Phaneuf et al., Phys. Rev. A 88, 053402 (2013)].

Photoionization of Al X from ground state using the relativistic R-matrix close-coupling method

The relativistic R-matrix method is used to calculate the total photoionization cross sections from the ground state 1s22s2 1S0 of Al X for photon energies ranges from the first ionization threshold to just above the eighth threshold of the residual ion Al XI. In this work, the relativistic distorted-wave method is employed to calculate the fine-structure energy levels and radial functions. The lowest eight level target states of Al XI are used in the photoionization calculations of Al X and should provide a reasonably complete database for practical application for photoionization cross section for Al X. The resonance energy levels and widths of 18 Rydberg series have been investigated.

Theoretical photoionization spectra for the Mg-like S4+ Ion in the energy range between the S5+ 4s and 4f thresholds

The partial and the total photoionization cross sections of the Mg-like S4+ ion, leaving the residual S5+ 3l and 4l states from the ground 3s21Se and the excited 3s3p3,1Po initial states, have been calculated for photon energies ranging from the S5+ 4s to the S5+ 4f threshold. The complex features appearing in the cross sections represent the tangled autoionizing Rydberg resonances converging to the different S5+ 4l thresholds. The present results are compared with the available previous National Institute of Standards and Technology(NIST) and Opacity Project(OP) results.

Total molecular photoionization cross-sections by algebraic diagrammatic construction-Stieltjes-Lanczos method: Benchmark calculations

In [K. Gokhberg, V. Vysotskiy, L. S. Cederbaum, L. Storchi, F. Tarantelli, and V. Averbukh, J. Chem. Phys. 130, 064104 (2009)] we introduced a new L(2) ab initio method for the calculation of total molecular photoionization cross-sections. The method is based on the ab initio description of discretized photoionized molecular states within the many-electron Green's function approach, known as algebraic diagrammatic construction (ADC), and on the application of Stieltjes-Chebyshev moment theory to Lanczos pseudospectra of the ADC electronic Hamiltonian. Here we establish the accuracy of the new technique by comparing the ADC-Lanczos-Stieltjes cross-sections in the valence ionization region to the experimental ones for a series of eight molecules of first row elements: HF, NH3, H2O, CO2, H2CO, CH4, C2H2, and C2H4. We find that the use of the second-order ADC technique [ADC(2)] that includes double electronic excitations leads to a substantial systematic improvement over the first-order method [ADC(1)] and to a good agreement with experiment for photon energies below 80 eV. The use of extended second-order ADC theory [ADC(2)x] leads to a smaller further improvement. Above 80 eV photon energy all three methods lead to significant deviations from the experimental values which we attribute to the use of Gaussian single-electron bases. Our calculations show that the ADC(2)-Lanczos-Stieltjes technique is a reliable and efficient ab initio tool for theoretical prediction of total molecular photo-ionization cross-sections in the valence region.

Nearest-neighbor atom interference effect on bound-free opacity of hot dense gold plasma

Quantum interference, similar to Young double-slit interference, takes place between the photoionization processes of two same kind atoms when the nuclei separation is less than or comparable to the de Broglie wavelength of the ionized electrons. In dense plasma, the average nearest-neighbor atom distance maybe comparable to or even less than the wavelength of the outgoing electrons, the photoionization cross section of the atoms as well as the opacity of the plasma will be affected by this kind of interferences among atoms. In the present work, we first attain the nearest-neighbor distributions of the atoms in hot dense plasmas by performing an average-atom molecular dynamics (AAMD) simulation. Then, the effective total photoionization cross section is obtained by integrating the two atom interference effects over the nearest-neighbor distributions. At last, the bound-free and Rosseland mean opacities of Au plasmas at 100 eV and different densities show that the interference effects are considerable when the density is larger than 1 g/cm3.

Photoionization and photoabsorption cross sections for the aluminum iso-nuclear sequence

K-shell photoionization and photoabsorption cross sections are presented for Li-like to Na-like Al. The calculations are performed using the Breit–Pauli R-matrix method where the effects of radiation and Auger dampings are included. We provide electronic data files for the raw cross sections as well as those convolved with a Gaussian of width ΔE/E=10−4. In addition to total cross sections for photoabsorption and photoionization, partial cross sections are available for photoionization.

Photoionization of Ar XVI and Ar XVII

Photoionization of Li-like argon, (hν+ArXVI→ArXVII+e), and He-like argon, (hν+ArXVII→ArXVIII+e), are studied using the relativistic Breit–Pauli R-matrix (BPRM) method. Results include both the partial and total photoionization cross-sections of fine structure levels with 1/2≤J≤17/2, n≤10 and 0≤l≤9 of Ar XVI and with 0≤J≤10, n≤10 and 0≤l≤9 of Ar XVII. They correspond to 98 bound levels of Ar XVI and 191 of Ar XVII. The close coupling wave function expansion for Ar XVI included 17 core levels up to n=3 thresholds and that of Ar XVII 16 core levels up to n=4 thresholds. Because of high-lying core excitations of these ions, the photoionization cross-section, σPI(nSLJ), decreases monotonically without features until at high energies where narrow high-peak resonances of Rydberg series of autoionizing states belonging to excited n=2 thresholds begin to appear. The dominant photoexcitation-of-core (PEC) or Seaton resonances also appear in the excited level cross-sections. The background of the total cross-section shows enhancement at n=2 thresholds due to resonant 1s–2p core excitations. However, the resonances become much weaker beyond n=2 thresholds. Radiation damping of resonances, important for these highly charged He- and Li-like ions, is included. These cross-sections are much improved over the existing TOPbase cross-sections where resonances, and background enhancements for Ar XVII were not included. With consideration of these effects, the present results should be accurate up to 10%–30% for various applications in modeling, recombination rates, opacities and diagnostic spectral analysis in the ultraviolet and X-ray regions. Cross-sections for H-like Ar are also included for completeness.

Near-threshold photoionization from the excited mp5 (m+l)p J = 0 − 3 levels of Ar, Kr, and Xe (m = 3 − 5)

Using the configuration interaction Pauli-Fock including core polarization (CIPFCP) approach we have calculated absolute total and partial cross sections for photoionization of the excited mp5(m+1)p J = 0 − 3 levels in Ar, Kr and Xe (m = 3 − 5) near threshold, including the region of the odd nl' (l' = 0, 2, 4) autoionizing resonances. For several intermediate levels of Ar and Kr, the computed cross sections are compared with laser spec-troscopic measurements; the theoretical and experimental lineshapes and branching ratios for different resonances show good mutual agreement.