Calculation Of Photoionization Cross Sections Research Articles

NLTE Analysis of Copper Lines in Different Stellar Populations∗

Abstract The copper abundances of 29 metal-poor stars are determined based on the high-resolution, high-signal-to-noise ratio spectra from the UVES spectrograph at the ESO VLT telescope. Our sample consists of the stars of the Galactic halo, thick- and thin-disk, with [Fe/H] ranging from ∼−3.2 to ∼0.0 dex. The non-local thermodynamic equilibrium (NLTE) effects of Cu i lines are investigated, and line formation calculations are presented for an atomic model of copper including 97 terms and 1089 line transitions. We adopted the recently calculated photoionization cross sections of Cu i, and investigated the hydrogen collision by comparing the theoretical and observed line profiles of our sample stars. The copper abundances are derived for both local thermodynamic equilibrium (LTE) and NLTE based on the spectrum synthesis methods. Our results show that the NLTE effects for Cu i lines are important for metal-poor stars, in particular for very metal-poor stars, and these effects depend on the metallicity. For very metal-poor stars, the NLTE abundance correction reaches as large as ∼+0.5 dex compared to standard LTE calculations. Our results indicate that [Cu/Fe] is under-abundant for metal-poor stars (∼−0.5 dex) when the NLTE effects are included.

Distorted wave photoionization cross sections for use in NLTE model atmospheres: Ni – Ni10+

SynopsisThe Opacity Project is a highly successful venture in which energy levels, oscillator strengths, and photoionization cross sections were calculated for astrophysically important elements up to iron. However, metals heavier than iron are being discovered in stellar atmospheres. The photoionization cross sections for elements and ions not covered by the Opacity Project are usually approximated with hydrogenic formulae. We present a series of valence and inner-shell distorted wave photoioniza-tion cross section calculations for use in model atmosphere calculations covering Ni - Ni10+. We discuss current progress, and future work.

Single photoionization of the Zn ii ion in the photon energy range 17.5–90.0 eV: experiment and theory

Measurements of the single photoionization cross section of Cu-like Zn$^+$ ions are reported in the energy (wavelength) range 17.5 eV (709 \AA) to 90 eV (138 \AA). The measurements on this {\it trans}-Fe element were performed at the Advanced Light Source synchrotron radiation facility in Berkeley, California at a photon energy resolution of 17 meV using the photon-ion merged-beams end-station. Below 30 eV the spectrum is dominated by excitation autoionizing resonance states. The experimental results are compared with large-scale photoionization cross-section calculations performed using a Dirac-Coulomb $R$-matrix approximation. Comparison are made with previous experimental studies, resonance states are identified and contributions from metastable states of Zn$^+$ determined.

Application of sampling theory in modelling of continuum processes: photoionization cross-sections of atoms

We describe a method for the calculation of photoionization cross-sections using square-integrable amplitudes obtained from the diagonalization of finite-basis set representations of the electronic Hamiltonian. Three examples are considered: a model example in which the final state is a free particle, the hydrogen atom and neutral atomic sodium. The method exploits the Whittaker–Shannon–Kotel’nikov sampling theorem, which is widely used in digital signal sampling and reconstruction. The approach reproduces known data with very good accuracy and converges to the exact solution with increase of the basis set size.

X-ray multiphoton ionization dynamics of a water molecule irradiated by an x-ray free-electron laser pulse

We present a theoretical investigation of x-ray multiphoton ionization dynamics of polyatomic molecules, based on the rate equation model and molecular electronic structure calculations. An efficient numerical procedure is developed to calculate photoionization cross sections, Auger rates, and fluorescence rates for all possible electronic multiple-hole configurations of molecules. We investigate the charge-state distribution of a water molecule after interaction with an intense x-ray pulse and discuss its dependence on the fluence and the pulse duration of the x-ray beam. Our results demonstrate that a water molecule exposed to an intense x-ray pulse is more ionized than what would be expected within the independent-atom picture.

Dirac R-matrix calculations of photoionization cross-sections of Ca iv

Dirac R-matrix calculations of photoionization cross-sections of Ca iv

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.

Excited state non-adiabatic dynamics of N-methylpyrrole: A time-resolved photoelectron spectroscopy and quantum dynamics study.

The dynamics of N-methylpyrrole following excitation at wavelengths in the range 241.5-217.0 nm were studied using a combination of time-resolved photoelectron spectroscopy (TRPES), ab initio quantum dynamics calculations using the multi-layer multi-configurational time-dependent Hartree method, as well as high-level photoionization cross section calculations. Excitation at 241.5 and 236.2 nm results in population of the A2(πσ(∗)) state, in agreement with previous studies. Excitation at 217.0 nm prepares the previously neglected B1(π3py) Rydberg state, followed by prompt internal conversion to the A2(πσ(∗)) state. In contrast with the photoinduced dynamics of pyrrole, the lifetime of the wavepacket in the A2(πσ(∗)) state was found to vary with excitation wavelength, decreasing by one order of magnitude upon tuning from 241.5 nm to 236.2 nm and by more than three orders of magnitude when excited at 217.0 nm. The order of magnitude difference in lifetimes measured at the longer excitation wavelengths is attributed to vibrational excitation in the A2(πσ(∗)) state, facilitating wavepacket motion around the potential barrier in the N-CH3 dissociation coordinate.

R-matrix calculations of photoionization cross section of Ne-like tungsten

The photoionization cross section calculation for the ground state 1s22s22p6 1S (J = 0) of Ne-like W64+has been performed in the close-coupling approximation using the Dirac–Coulomb R-matrix method. The resonance structures are analysed and described by finding the resonance energy positions of prominent Rydberg series 2s2p6(2S)np1P0for W LXV ion. To calculate fine structure energy levels, multi-configuration Dirac–Fock and relativistic distorted-wave methods have been employed. Wherever possible we have compared our work with the available data. The present results will be useful for diagnostics and modeling of plasma in ITER and other fusion devices.

Single-photon single ionization of W+ ions: experiment and theory

Experimental and theoretical results are reported for photoionization of Ta-like (W+) tungsten ions. Absolute cross sections were measured in the energy range 16–245 eV employing the photon–ion merged-beam setup at the advanced light source in Berkeley. Detailed photon-energy scans at 100 meV bandwidth were performed in the 16–108 eV range. In addition, the cross section was scanned at 50 meV resolution in regions where fine resonance structures could be observed. Theoretical results were obtained from a Dirac–Coulomb R-matrix approach. Photoionization cross section calculations were performed for singly ionized atomic tungsten ions in their J = 1/2, ground level and the associated excited metastable levels with J = 3/2, 5/2, 7/2 and 9/2. Since the ion beams used in the experiments must be expected to contain long-lived excited states also from excited configurations, additional cross-section calculations were performed for the second-lowest term, J = 5/2, and for the 4F term, with J = 3/2, 5/2, 7/2 and 9/2. Given the complexity of the electronic structure of W+ the calculations reproduce the main features of the experimental cross section quite well.

Pseudopotential calculations of photoionization of atoms in the x-ray photon energy range and FEL beam monitor development

A pseudopotential model for calculation of atomic processes under interaction with hard x-ray photons is applied to calculation of Krypton photoionization cross sections by photons with energy in the 20–25 keV range. These cross sections, as well as the mean charge of the resulting ions calculated using the Monte Carlo simulation scheme, are in good agreement with the other theoretical calculations and with the experiment. The obtained results open the doors for new techniques in the design of gas-monitor detectors to control the intensity, coordinates and energy of x-ray free-electron laser (XFEL) beams in the hard x-ray photon energy range. First, Monte Carlo simulations of a scintillation detector application for gas-monitors have been performed.

Hartree-Fock calculation of the differential photoionization cross sections of small Li clusters.

Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li2-8 are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li2 are in a good agreement with the available theoretical data, whereas those computed for Li3-8 clusters can be considered as theoretical predictions.

Configuration-interaction relativistic-many-body-perturbation-theory calculations of photoionization cross sections from quasicontinuum oscillator strengths

Many applications are in need of accurate photoionization cross sections, especially in the case of complex atoms. Configuration-interaction relativistic-many-body-perturbation theory (CI-RMBPT) has been successful in predicting atomic energies, matrix elements between discrete states, and other properties, which is quite promising, but it has not been applied to photoionization problems owing to extra complications arising from continuum states. In this paper a method that will allow the conversion of discrete CI-(R)MPBT oscillator strengths (OS) to photoionization cross sections with minimal modifications of the codes is introduced and CI-RMBPT cross sections of Ne, Ar, Kr, and Xe are calculated. A consistent agreement with experiment is found. RMBPT corrections are particularly significant for Ar, Kr, and Xe and improve agreement with experimental results compared to the particle-hole CI method. The demonstrated conversion method can be applied to CI-RMBPT photoionization calculations for a large number of multivalence atoms and ions.

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.

Valence-shell single photoionization of chlorine-likeK2+ions: Experiment and theory

The absolute single photoionization cross-section was measured for Cl-like K$^{2+}$ over the photon energy range from 44.2 - 69.7 eV at a constant energy resolution of 0.045 eV. The experiments were performed by merging an ion beam with a beam of synchrotron radiation from an undulator. The ground-state ionization threshold was measured at 0.004 eV energy resolution to be 45.717 $\pm$ 0.030 eV. The measurements are rich in resonance structure due to multiple Rydberg series of transitions to autoionizing states. These series are assigned spectroscopically using the quantum defect method, guided by pseudo-relativistic Hartree-Fock calculations for the energies and oscillator strengths of transitions to autoionizing states. The experimental results, which include significant contributions from K$^{2+}$ ions initially in metastable states, are in satisfactory agreement with a linear superposition of semi-relativistic R-matrix calculations of photoionization cross sections from these initial states.

Time-dependent restricted active space Configuration Interaction theory applied to the photoionization of neon

We give a presentation on the time-dependent restricted active space Configuration Interaction method, which has been recently introduced [D. Hochstuhl, M. Bonitz, PRA, in press] to efficiently tackle the few-particle nonequilibrium many-body problem. Particularly, we apply it to the calculation of photoionization cross sections and angular resolved ionization yields of groundstate neon.

Photoionization of Ne-like Ca XI

Relativistic calculations of photoionization cross sections of Ne-like Ca XI using the Breit–Pauli R-matrix method in close-coupling and LS-coupling approximation. In this work, the relativistic distorted-wave method is employed to calculate the fine-structure energy levels, radial functions and continuum wave functions, and the Breit–Pauli R-matrix method is employed to calculate the photoionizaton cross section for photon energy from 43.5 to 73.6 Ry. The resonance structure in the photoionization of Ne-like Ca XI for ejection of a 2p or 2s electron from the ground 2s22p61S0 or excited state 2s22p53s 1,3P has been investigated.

Photoionization cross section of Sc XII

Relativistic calculations of photoionization cross sections of Ne-like Sc XII using the Breit-Pauli R-matrix method in close-coupling and LS-coupling approximation and fully relativistic distorted-wave method are reported. In present work, the relativistic distorted-wave method is employed to calculate the fine-structure energy levels and radial functions, and the Breit-Pauli R-matrix method is employed to calculate the photoionizaton cross sections. In present work, we calculated the photoionization cross sections of Sc XII for ejection of 2p or 2s electron from the ground 2s22p61S0 in jj-coupling and obtained the energy levels and widths of 2s22p5ns3P1, 2s22p5nd1P1 (n = 21−30), 2s2p6np3P1 and 2s2p6np1P1 (n = 5−15). The photoionization cross sections of Sc XII for ejection of 2p electron from the excited state 1s22s22p53s3,1P have been calculated in LS-coupling and obtained the energy levels and widths of 2s2p6ns1,3S and 2s2p6nd1,3D (n = 5−15).

Photoionization of Be-like N3 + and Ne6 + ions: features of Be isoelectronic sequences of Z ⩽ 10

Using a noniterative eigenchannel R-matrix method, we have studied the photoionization for ground 1S and excited 3, 1P initial states of the Be-like N3 + and Ne6 + ions, up to the energy range of the final photo-ionic 3d state. The autoionizing resonance structures arising from the ground and excited states are identified and characterized. Our calculated photoionization cross sections with excellent agreement between length and velocity gauges are compared with the available experimental and previous theoretical results, and good agreement is shown. For the isoelectronic sequences of Z ⩽ 10, the Z-dependent spectral structures and developments of the cross sections are discussed based on the present results of N3 + and Ne6 + ions and the previous results of other ions obtained by the same noniterative eigenchannel R-matrix method. The intermixing among the resonances converging to the final photo-ionic 2p and the various 3l states is increased as Z, resulting in a much more complex pattern of resonances for the photoionization.

Photoionization cross section of Ne-like Cu XX with J=1

Relativistic calculations of photoionization cross sections of Ne-like Cu XX using the Breit–Pauli R-matrix method in close-coupling approximation and fully relativistic distorted-wave method are reported. In the present work, the relativistic distorted-wave method is employed to calculate the fine-structure energy levels and radial functions, and the Breit–Pauli R-matrix method is employed to calculate photoionizaton cross section for photon energy from 124.2Ryd to 208Ryd. Resonance structure in the photoionization of Ne-like Cu XX for ejection of 2p or 2s electron from the ground 2s22p61S0 has been studied.