Configuration-average Distorted-wave Method Research Articles

Photon and electron ionization of the HeH+ Molecule

With the first detection of HeH+ in nearby interstellar space, various molecular ionization and recombination processes are now being calculated to better understand the dynamics of the first molecule in the universe. We use a configuration-average distorted-wave method to compute the photon and electron ionization cross sections of HeH+ based on an earlier molecular structure tabulation.

Electron ionization of the CN+ molecule

We present electron ionization cross sections for the CN+ molecule. A configuration-average distorted-wave method is used to compute the electron ionization cross sections based on earlier molecular structure tabulations. Electron ionization cross sections are calculated for the outer 4 subshells of the 1σ22σ23σ24σ21π25σ2 ground configuration and for the outer 3 subshells of the 1σ2 2σ23σ24σ21π4 excited configuration. The total electron ionization cross sections are compared with recent total crossed-beams measurements that include production of CN2+, C+, C2+, N+, and N2+. The total theoretical and experimental cross sections are in fairly good agreement, especially at the higher electron energies.

Electron and photon ionization of the BeH molecule

We present electron and photon ionization cross sections for the BeH molecule. A configuration-average distorted-wave method is used to compute the electron and photon ionization cross sections based on earlier molecular structure tabulations. The electron ionization cross sections are compared with previous Deutsch-Mark and binary encounter Bethe calculations. Total single ionization cross sections are found to be larger due to the inclusion of an inner subshell. The photon ionization cross sections are compared with previous molecular-adapted quantum defect orbital calculations. The total single ionization cross sections are again found to be larger due to the inclusion of an inner subshell. We also calculated electron and photon ionization cross sections for a low lying excited configuration of BeH.

Photoionization of the CO and NO molecules

We present photoionization cross sections for two diatomic molecules, CO and NO, using a distorted-wave approximation. Both CO and NO are important atmospheric molecules, particularly in shock-heated atmospheres and in some astrophysical contexts. Photoionization cross sections may be used to compute the bound–free absorption contribution, which although less relevant than the bound–bound absorption that dominates in the near infra-red wavelength band, is still necessary for a complete description of molecular absorption. A configuration-average distorted-wave method is used to compute the photoionization cross sections based on earlier molecular structure tabulations. Our calculations are compared to experiment and good agreement is found at incident energies above 40 eV.

Electron-impact single and double ionization of the Mn2+, Mn3+ and Mn4+ atomic ions

Electron-impact single and double ionization cross sections for Mn2+, Mn3+ and Mn4+ are calculated using a semi-relativistic configuration-average distorted-wave method. The ionization cross sections include contributions from single direct ionization, double direct ionization and excitation–autoionization. Certain excitations may contribute to both single and double ionization as determined by branching ratio calculations. For Mn2+ the ratio of the double to single ionization cross section peak heights is found to be 0.15, while dropping to 0.03 for Mn3+ and 0.01 for Mn3+.

Electron-impact ionization of moderately charged xenon ions

Absolute and energy scanned cross sections for the electron-impact single ionization of Xeq + (q = 10–17) atomic ions are measured by employing a crossed-beams technique in the collision energy range from threshold to 1000 eV. Direct ionization and indirect excitation-autoionization cross sections are calculated using a configuration-average distorted-wave method for the ground and first same parity excited configuration of the Xeq + (q = 10–17) atomic ions. Both the crossed-beams experiment and distorted-wave theory show a steady decrease in the ionization cross section as the charge of the ion increases. The disagreements between experiment and theory are partly attributed to the many metastable levels of ground and excited configurations found in the ion beam.

Dielectronic recombination of W35 +

Accurate data for dielectronic recombination (DR) of the ions of tungsten are of significant interest in the modelling of tungsten impurity transport and radiative power loss in current tokamaks and in ITER. However, the complexity of the atomic structure for many of these ions makes level-resolved DR calculations untenable on currently available computers, especially for open d- and f-subshell ions. The majority of DR data presently available for ITER modelling are based on an average-atom approximation. To improve upon these baseline calculations, we investigate the use of the configuration-average distorted-wave (CADW) method to calculate DR rate coefficients for complex open d-shell systems. The aim is to produce rate coefficients that are sufficiently accurate in terms of modelling, yet greatly reduced in term of computational complexity compared to level-resolved calculations. In this paper, we consider the DR of W35 +. Initially, we carry out several large-scale level-resolved calculations for the DR associated with the 4d → 4f and 4p → 4d excitations in this ion, using both the level-resolved distorted-wave and Dirac R-matrix methods. These calculations allow us to test the validity of the CADW approach on these same excitations by comparing cross sections and rate coefficients. These comparisons demonstrate that the CADW method is relatively accurate in relation to these level-resolved methods for the temperature range for which W35 + should exist in a collisionally ionized plasma. We then present results for CADW rate coefficients for both Δn = 0 and Δn = 1 excitations for this ion. This study indicates that it is now feasible to generate a much improved comprehensive set of DR data for the entire tungsten isonuclear sequence.

Electron-impact ionization of C2

In support of tokamak edge plasma studies, we calculate the electron-impact ionization cross section for the ground state of the diatomic carbon molecule. Bound orbitals for C2 and C+2 are calculated using a single-configuration self-consistent-field method based on a linear combination of Slater-type orbitals. Continuum distorted-wave orbitals are calculated using a two-dimensional lattice (r, θ), which is variable in the radial coordinate and constant in the angular coordinate. Using a perturbative configuration-average distorted-wave method, the first ab initio fully quantal ionization cross sections for C2 at its equilibrium internuclear separation are presented.

Electron-impact ionization ofLi2andLi2+

Electron-impact ionization cross sections for ${\mathrm{Li}}_{2}$ and $\mathrm{Li}_{2}{}^{+}$ are calculated using a configuration-average distorted-wave method. Bound orbitals for the molecule and its ions are calculated using a single-configuration self-consistent-field method based on a linear combination of Slater-type orbitals. The bound orbitals are transformed onto a two-dimensional lattice $(r,\ensuremath{\theta})$, which is variable in the radial coordinate and constant in the angular coordinate, from which Hartree with local exchange potentials are constructed. The single-particle Schr\"odinger equation is then solved for continuum distorted waves with $S$-matrix boundary conditions. Total ionization cross sections for ${\mathrm{Li}}_{2}$ at an equilibrium internuclear separation of $R=5.0\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ and for $\mathrm{Li}_{2}{}^{+}$ at an equilibrium internuclear separation of $R=5.9\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ are presented.

Electron-impact ionization of atoms in high-temperature dense plasmas

Electron-impact ionization cross sections for atoms in high-temperature dense plasmas are calculated in a configuration-average distorted-wave method. For those conditions in which the Coulomb coupling parameter is small, we use the Debye-H\"uckel potential to screen the projectile electron from the nucleus and target electrons. Ionization cross sections are calculated for both ${\text{Ne}}^{4+}$ and ${\text{Au}}^{47+}$ at high temperatures and various electron densities up to $1.0\ifmmode\times\else\texttimes\fi{}{10}^{25}\text{ }{\text{cm}}^{\ensuremath{-}3}$. In general we find that as the density increases, the ionization cross section decreases at all incident energies. We also find that as the charge on the atomic ion becomes larger, the relative density effect becomes smaller.

Electron-impact ionization of atomic ions in the Sn and Xe isonuclear sequences

Electron-impact ionization cross-sections for all atomic ions in the Sn and Xe isonuclear sequences are calculated using a semi-relativistic configuration-average distorted-wave method. Contributions to the cross-sections are included from both direct ionization and indirect excitation-autoionization. Branching ratio calculations are carried out for Cu-like Sn 21+and Xe 25+ and Na-like Sn 39+ and Xe 43+ to determine when best to ignore indirect excitation-autoionization contributions due to radiation damping along the isonuclear sequences. Although experiments exist for Xe through to Xe 6+, Xe 8+, and Xe 43+ the configuration-average distorted-wave results only agree well with the Xe 8+ measurements, once metastable states are taken into account and with the Xe 43+ measurements once radiation damping of the excitation-autoionization contribution is accounted for. Temperature-dependent rate coefficients are calculated for each Sn and Xe ionization stage and then put in a collisional-radiative format that should prove useful in modelling astrophysical and laboratory plasmas.

Electron-impact ionization and recombination ofM-shell atomic ions in the argon isonuclear sequence

Electron-impact ionization and recombination cross sections and rate coefficients are calculated for $M$-shell Ar atomic ions using a configuration-average distorted-wave method. The electron-impact ionization calculations are for all atomic ions in the Ar isonuclear sequence. Ionization contributions include both direct ionization and excitation-autoionization processes. Good agreement is found between theory and experimental crossed-beam measurements for moderately charged ion stages. Comparisons are made with previous theoretical calculations where possible. We also generate rate coefficients for neutral argon ionization, based on recent $R$-matrix with pseudostates calculations. Electron-impact dielectronic recombination is calculated for all $M$-shell ions of argon. For ${\mathrm{Ar}}^{6+}$ and ${\mathrm{Ar}}^{7+}$ the current theoretical results agree well with previous level-resolved distorted-wave calculations. In order to compare with published ionization balance results our dielectronic recombination data are combined with literature values for the higher ion stages and with recent radiative recombination data for all the ion stages. We find significant differences in our equilibrium fractional abundances for the $M$-shell ions, compared with literature values. We relate these differences to the underlying atomic data.

Electron-impact ionization of diatomic molecules using a configuration-average distorted-wave method

Electron-impact ionization cross sections for diatomic molecules are calculated in a configuration-average distorted-wave method. Core bound orbitals for the molecular ion are calculated using a single-configuration self-consistent-field method based on a linear combination of Slater-type orbitals. The core bound orbitals are then transformed onto a two-dimensional $(r,\ensuremath{\theta})$ numerical lattice from which a Hartree potential with local exchange is constructed. The single-particle Schr\odinger equation is then solved for the valence bound orbital and continuum distorted-wave orbitals with $S$-matrix boundary conditions. Total cross section results for ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ are compared with those from semiempirical calculations and experimental measurements.

Electron-impact ionization of atomic ions in the W isonuclear sequence

Electron-impact ionization cross sections for all atomic ions in the W isonuclear sequence are calculated using a variety of theoretical methods. For the direct ionization process, a semirelativistic configuration-average distorted-wave method is used for low to moderately charged ions, while a fully relativistic subconfiguration-average distorted-wave method is used for highly charged ions. For the indirect ionization process of excitation autoionization, a semirelativistic configuration-average distorted-wave method is used for the bulk of the transitions, but a semirelativistic level-resolved distorted-wave method is used for selective strong transitions that may straddle the ionization threshold. For moderately charged ions it is important to include radiation damping of the excitation-autoionization process through explicit calculation of autoionization branching ratios. Checks are made on the theoretical predictions by comparison with available crossed-beams experimental measurements, which only exist for low stages of ionization. The ionization cross sections for the entire W isonuclear sequence are converted to temperature-dependent rate coefficients and put in a collisional-radiative format that should prove useful in modeling laboratory plasmas that contain W impurities.

Electron-impact excitation and ionization ofH2+using a configuration-average distorted-wave method

A configuration-average distorted-wave method is developed to calculate electron-impact excitation and ionization cross sections for diatomic molecules and their ions. The method is based on the construction of bound and continuum orbitals on a two-dimensional numerical lattice in $(r,\ensuremath{\theta})$ center-of-mass polar coordinates. Our first applications are the calculation of $1s\ensuremath{\sigma}\ensuremath{\rightarrow}2p\ensuremath{\sigma}$ and $1s\ensuremath{\sigma}\ensuremath{\rightarrow}2p\ensuremath{\pi}$ excitation cross sections and $1s\ensuremath{\sigma}\ensuremath{\rightarrow}ϵl\ensuremath{\lambda}$ ionization cross sections for $\mathrm{H}_{2}{}^{+}$. Comparisons are made with plane-wave Born, distorted-wave, and $R$-matrix calculations, as well as experimental measurements.

Experimental and theoretical study of electron-impact ionization of atomic ions in the Sm isonuclear sequence

Experimental measurements and theoretical calculations of absolute cross sections are carried out for the electron-impact ionization of atomic ions in the Sm rare-earth-metal isonuclear sequence. Absolute cross sections for ${\mathrm{Sm}}^{q+}$ ions for $q=1\ensuremath{-}12$ were measured using the electron-ion crossed-beam technique and calculated with the configuration-average distorted-wave method for the charge states $q=4\ensuremath{-}12.$ The theory includes both direct ionization and excitation-autoionization contributions, and includes transitions from both ground and metastable levels. We present the cross sections in an electron-impact energy range from threshold up to 1000 eV for all Sm ions up to ${\mathrm{Sm}}^{12+}.$ These systems are extremally complex, but the configuration-average method, when combined with statistical averaging of the cross sections over the many levels, provides results that are in overall good agreement with the experimental measurements. The single-ionization cross sections are dominated by contributions from indirect mechanisms of excitation-autoionization in the low-energy region.

Electron-impact single ionization of low-charged titanium ions

The electron-impact single ionization of low-charged Ti ions was studied both experimentally and theoretically. Absolute cross sections for ions in charge states q = 1 to 6 except 3 were measured using a crossed-beams technique as well as calculated with the configuration-average distorted-wave method, including both direct ionization and excitation-autoionization contributions. For charge states q = 4, 5 and 6, the measurements are in good agreement with the calculations considering that large components of the incident ion beam were in metastable configurations. The cross sections for single ionization of and were determined in part with a high-resolution energy-scan method. Besides contributions of excitation-autoionization mechanisms, a remarkable number of structures arising from resonant-excitation double-autoionization (REDA) processes could be observed.

Absolute cross sections for electron-impact single ionization of Si+ and Si2+

Absolute cross sections for electron-impact single ionization of ${\mathrm{Si}}^{+}$ and ${\mathrm{Si}}^{2+}$ have been measured using crossed beams of ions and electrons and calculated using a configuration-average distorted-wave method. Corrections have been made for metastable components and small fractions of nitrogen impurities in the incident ion beams. Excitation-autoionization measurably enhances the cross sections of both ${\mathrm{Si}}^{+}$ and ${\mathrm{Si}}^{2+}$. Ionization rate coefficients and fitting parameters are presented for the experimental data.