State-specific Recombination Research Articles

State-to-state study of non-equilibrium recombination of oxygen and nitrogen molecules.

Rapidly cooled mixtures are of interest for several applications, including hypersonic flows due to the presence of strong cooling temperature gradients in regions such as hypersonic boundary layers and expanding nozzles. There have been very few studies of rapidly cooled mixtures using the high-fidelity rovibrational databases afforded by abinitio potential energy surfaces. This work makes use of existing rovibrational state-specific databases to study rapidly cooled mixtures. In particular, we seek to understand the importance of thermal non-equilibrium in recombining mixtures using both rovibrational and vibrational state-to-state methods for oxygen and nitrogen molecules. We find that although there is significant non-equilibrium during recombination, it is well captured by the vibrational state-specific approach. Finally, we compare the global recombination rate computed based on the state-specific recombination rate coefficients and the global recombination rate computed based on the time local dissociation rate coefficient, which is reversed using the principle of detailed balance. The local dissociation rate coefficient is computed by weighting the state-specific dissociation rate coefficients with the state-specific distribution of energy states. We find a large difference between these rates, highlighting a potential source of errors in hypersonic flow predictions.

Total and state-specific electron-ion recombination rates and photoionization of Ca XV for high temperature plasma

The inverse processes of photoionization and electron-ion recombination of (Ca XV + hν↔ Ca XVI + e), are studied using the unified method of Nahar and Pradhan for a large number of bound states, 582 in total with n≤10 and l≤9, for their characteristic features particularly in the high energy region that can impact plasmas at high temperature. The unified method which implements close-coupling (CC) approximation and the R-matrix method includes both the radiative recombination (RR) and dielectronic recombination (DR) for the total recombination and yields self-consistent sets of results for both the inverse processes. The present study, carried out in large scale computations, employs a large CC wavefunction expansion of 29 LS states belonging to n=2,3 complexes of the core ion Ca XVI, and appeared to be the first detailed study for the electron-ion recombination of the ion. The present results include (i) state-specific photoionization cross sections (σPI(nLS)) leaving the core ion in the ground state, (ii) state-specific recombination rate coefficients (αRC(nLS,T)) that include both the RR and DR, (iii) total recombination rate coefficients (αRC) with temperature that include contributions of infinite number of recombined states, and (iv) a spectrum of total electron-ion recombination cross sections and rates with respect to photoelectron energy. The study finds that the core ion excitations from the ground to high n=3 states have introduced Rydberg resonances which are stronger and Seaton resonances which are more enhanced in the high energy region of σPI compared to those introduced by excitations to the n=2 states. Such features have contributed to the shape of the temperature dependent state-specific αRC(nLS,T), and have resulted in three DR bumps/ shoulders in the high temperature region of the total αRC(T) where the third DR bump at temperature of ∼ 4 MK has raised αRC(T) at high T above all previous rates. The results are expected to be accurate within 10%–15% and provide more complete and precise spectral modelings for the high temperature plasmas where the highly charged Ca XV is more abundant.

State selective study of H3+recombination in Cryo-FALP and SA-CRDS experiments at 77 K

Rate coefficients for nuclear spin state-specific recombination of H + ions with thermal electrons were measured using FALP and SA techniques at temperatures 77-300K. For this purpose H2 gas with both thermal and enriched population of the para nuclear spin configuration was used. Measurements have shown that at 77K para-H + exhibits five times higher binary recombination rate coefficient than ortho-H + : (1.5 ± 0.4) × 10 −7 vs. (3 ± 2) × 10 −8 cm 3 s −1 .

Generalized Chemistry–Internal Energy Coupling Model Using Prior Recombination Distribution

In this work, the interaction between the internal energy states and the dissociation/recombination process for a diatomic molecule is studied in detail. In particular, the state-specific recombination and dissociation rate constants are derived as a function of internal energy distribution and other molecular parameters. As a special case, applying this result with specific vibrational energy distributions, we obtain the classic Marrone and Treanor models. An information theory approach to obtain the initial recombination distribution for any diatomic molecule is also presented. The general idea is to incorporate the vibrational and the rotational effects in the dissociation and recombination process without a full vibrational-rotational state-specific model. The effect of this rovibrational coupling is to produce an initial recombination distribution that is biased to the high internal energy states. These initial recombination distributions are then thermally averaged to obtain temperature-dependent expressions for different diatomic molecules to characterize the internal energy distribution of recombining molecules.

Photoionization and electron–ion recombination of Cr I

Using the unified method, the inverse processes of photoionization and electron–ion recombination are studied in detail for neutral chromium, ( Cr I + h ν ↔ Cr II + e ), for the ground and excited states. The unified method based on close-coupling approximation and R-matrix method (i) subsumes both the radiative recombination (RR) and dielectronic recombination (DR) for the total rate and (ii) provides self-consistent sets of photoionization cross sections σ PI and recombination rates α RC . The present results show in total photoionization of the ground and excited states an enhancement in the background at the first excited threshold, 3 d 4 4 s 5 D state of the core. One prominent phot-excitation-of-core (PEC) resonance due to one dipole allowed transition ( 6 S - 6 P o ) in the core is found in the photoionization cross sections of most of the valence electron excited states. Structures in the total and partial photoionization, for ionization into various excited core states and ground state only, respectively, are demonstrated. Results are presented for the septet and quintet states with n ≤ 10 and l ≤ 9 of Cr I. These states couple to the core ground state 6 S and contribute to the recombination rates. State-specific recombination rates are also presented for these states and their features are illustrated. The total recombination rate shows two DR peaks, one at a relatively low temperature, at 630 K, and the other around 40,000 K. This can explain existence of neutral Cr in interstellar medium. Calculations were carried out in LS coupling using a close-coupling wave function expansion of 40 core states. The results illustrate the features in the radiative processes of Cr I and provide photoionization cross sections and recombination rates with good approximation for this astrophysically important ion.

Electron–ion recombination and photoionization of Fe XXI

Results for electron–ion recombination and photoionization of ( Fe XXI + h ν ↔ Fe XXII + e ) , with emphasis in high-temperature region, are presented from ab initio unified method. The unified method, based on close coupling (CC) approximation and R-matrix method, (i) subsumes both the radiative recombination (RR) and dielectronic recombination (DR), (ii) enables self-consistent sets of photoionization and recombination cross sections from using an identical wavefunction for both the processes, and (iii) provides state-specific recombination rates of a large number of bound states. A large CC wavefunction expansion, which includes the ground and 28 core excitations of n = 2 and 3 complexes and span a wide energy range, has been used. Compared to Δ n = 2 – 2 , Δ n = 2 – 3 core excitations are found to introduce strong resonant structures and enhance the background photoionization cross sections ( σ PI ) in the high-energy region. These features along with prominent photoexcitation-of-core (PEC) resonances at n = 3 core thresholds have increased the unified total recombination rate coefficients ( α R ( T ) ) at temperatures T > 10 6 K , region of maximum abundance of the ion in collisional equilibrium, by a factor of 1.6 over previous calculations. State-specific recombination rate coefficients α R ( nLS ) , which include both the RR and DR, are presented for the first time for 685 bound states with n ⩽ 10 and l ⩽ 9 . The unified total recombination rate with photoelectron energy α R ( E ) is presented and the role of low-energy near-threshold fine structure resonances is illustrated. The present results should provide a reasonably complete self-consistent set of recombination rates and photoionization cross sections for astrophysical modelings of high-temperature plasmas from optical to far-ultraviolet wavelength regions.

Electron‐Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. VIII. Ar xiii with New Features

Ar xiii is found to be unique with new features in electron-ion recombination not seen in any other ion. The ion has been studied with the unified method, which provides a theoretically self-consistent set of atomic parameters for the inverse processes of photoionization and total electron-ion recombination. Unified method subsumes both the radiative recombination (RR) and dielectronic recombination (DR) within the framework of close-coupling formulations using the R-matrix method. A set of four DR ‘‘bumps,’’ two in the low-temperature and two in the high-temperature regions, is found to exist in the recombination rates of Ar xiv þ e ! Ar xiii. This is in contrast to two typical DR ‘‘bumps,’’ one at high temperature common for most ions and one at low temperature depending on the presence of near threshold autoionizing resonances in the bound-free process. Large-scale ab initio calculations have been carried out for photoionization and electron-ion recombination cross sections of Ar xiii. The ion is represented by a large close-coupling eigenfunction expansion of 37 core Ar xiv states from n ¼ 2 and 3 complexes. This enables core excitations of type n ¼ 0 and 1. The n ¼ 1 transitions have much higher radiative decay rates than those of n ¼ 0 and cause the fourth DR bump around 2 ;10 6 K. For a large number of bound states, Ar xiii exhibits more extensive resonant structures and wider PEC (photoexitation-of-core) resonances for n ¼ 3 core states than those of n ¼ 2 states. Hence, the high-energy regions of photoionization and recombination are dominated by these structures. A total of 684 bound states with valence electron n � 10 and l � 9 are found for Ar xiii. Total and partial photoionization cross sections of all bound states, state-specific recombination rates of 561 bound states, and total recombination rate coefficients at a large temperature range are presented for Ar xiii. Subject headingg atomic data — atomic processes

Electron‐Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. VI. Ni ii

We present the first detailed ab initio quantum mechanical calculations for total and state-specific recombination rate coefficients for e + Ni III --> Ni II. These rates are obtained using a unified treatment for total electron-ion recombination that treats the nonresonant radiative recombination and the resonant dielectronic recombination in a self-consistent unified manner in the close coupling approximation. Large-scale calculations are carried out using a 49-state wavefunction expansion from core configurations 3d^8, 3d^74s, and 3d^64p that permits the inclusion of prominent dipole allowed core transitions. These extensive calculations for the recombination rates of Ni II required hundreds of CPU hours on the Cray T90. The total recombination rate coefficients are provided for a wide range of temperature. The state-specific recombination rates for 532 bound states of doublet and quartet symmetries, and the corresponding photoionization cross sections for leaving the core in the ground state, are presented. Present total recombination rate coefficients differ considerably from the currently used data in astrophysical models.

The XSTAR Atomic Database

We report on the XSTAR atomic database that contains a large quantity of atomic rates for use in spectral modeling of astrophysical plasmas. The database includes atomic energy levels, line wavelengths, radiative transition probabilities, electron impact excitation rates, photoionization cross section, recombination rate coefficients, electron impact ionization rates, and fluorescence and Auger yields. The species considered are all the ions of H, He, C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, and Ni. The database collects recent data from many sources including CHIANTI, TOPbase, ADAS, NIST, and the IRON Project. Two particular features of the database are the incorporation of photoionization cross sections from the Opacity Project for all levels of every ion, and state-specific recombination rates. State-specific collisional ionization and three-body recombination are also included. The collection of data is used to build excitation-ionization models of each ion for calculation of their spectra for electron densities of up to 1018 cm-3 and temperatures between 100 and 109 K. In addition, every ion model is designed to converge to LTE under appropriate conditions. These models and data are implemented in the photoionization modeling code XSTAR v.2.

Electron‐Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. III. Si‐Sequence Ions: Si i , S iii , Ar v , Ca vii , and Fe xiii

Photoionization cross sections, σPI, and electron-ion recombination rate coefficients, αR, for silicon-like ions are calculated. Calculations are carried out in the close coupling approximation using the R-matrix method. Each ion has a large number of bound states with n ≤ 10 and l ≤ 9: 433 for Ar V, 631 for Ca VII, and 1223 for Fe XIII. Both the partial photoionization cross sections leaving the core ion in the ground state and the total cross sections for ionization in the ground state as well as the excited core states are obtained for all bound states. The electron-ion recombination rates are obtained using a unified method, based on the close coupling R-matrix method, that incorporates both the radiative and dielectronic recombination processes in a self-consistent and unified manner. Total recombination rate coefficients are presented for a wide range of temperatures for practical applications. State-specific recombination rate coefficients for individual bound states are also presented. Results of Si I and S III, derived from earlier works, are also presented for completeness.

Electron-ion recombination of Fe IV

Ab initio calculations are presented for total and partial recombination cross sections and rate coefficients for $e+\mathrm{Fe}V\ensuremath{\rightarrow}\mathrm{Fe}\mathrm{IV},$ employing a unified treatment that incorporates both the radiative and dielectronic recombinations (RR and DR) in a self-consistent and accurate manner. The theoretical treatment is based on the close-coupling approximation using the R-matrix method. Recombination calculations for heavy atoms such as Fe IV, with $3d$ open-shell ground configuration, require an extensive eigenfunction expansion for the target ion, as well as a carefully optimized basis set of electron-ion bound configurations that represent short range correlation effects. The large-scale calculations are preceded by electron scattering and photoionization calculations using a 31-term eigenfunction expansion dominated by the configurations ${3d}^{4},$ ${3d}^{3}4s,$ and ${3d}^{3}4p$ of Fe V. Photorecombination cross sections and DR collision strengths are thereby obtained, including individual photorecombination cross sections for a large number of bound states of Fe IV that couple to the ground state ${3d}^{4}{}^{5}D$ of the target ion Fe V---all possible bound states up to $n=10 (740 \mathrm{LS}$ terms of Fe IV). The cross sections include autoionizing resonances, also up to the $n=10$ complex, accounting for the unified (RR + DR) contribution into the $n<~10$ (low-$n)$ bound states of Fe IV. Recombination into the high-$n$ states, $10<~n<~\ensuremath{\infty},$ is obtained through the DR collision strengths for the corresponding series of resonances in the electron-ion continua. The convergence of the close-coupling expansion, with respect to the target ion states and the (electron plus ion) correlation functions is discussed with reference to other highly complex atomic systems. Maxwellian average at a range of temperatures yields the total rate coefficient, as well as partial contributions directly to state-specific recombination rate coefficients. The new close-coupling rates differ considerably from those heretofore obtained from simpler approximations. We expect the present data to be of importance in the modeling of astrophysical and laboratory plasmas where iron is often a prominent constituent.

Electron-ion recombination of FetII

A complete treatment of electron-ion recombination of e+Fe III\ensuremath{\rightarrow}Fe II employing a unified method is presented. The treatment incorporates both the radiative and dielectronic recombinations in a self-consistent manner. Total recombination rate coefficients are obtained from photoionization cross sections, and from collision strengths for dielectronic recombination calculated using the precise theory of Bell and Seaton [J. Phys. B 18, 1589 (1985)]. Large-scale computations for both of these quantities are carried out in the close coupling approximation using the R-matrix method with an eigenfunction expansion that includes 83 states of Fe III dominated by the ground ${3\mathrm{d}}^{6}$, and the excited ${3\mathrm{d}}^{5}$4s and ${3\mathrm{d}}^{5}$4p configurations. Both the total and state-specific recombination rate coefficients are obtained. Comparison of the present results with the previous ones shows considerable difference for most of the temperature regions. The present results provide accurate and self-consistent recombination rates, in the temperature range of practical applications (T${10}^{5}$ K), for ionization balance in photoionization models employing the detailed photoionization cross sections from the Opacity Project.

Electron‐Ion Recombination of Fe v

Ionization balance in the low-ionization stages of iron is important in a variety of astrophysical plasmas. Accurate recombination rates are needed but are difficult to compute in a detailed quantum mechanical treatment. The main difficulty lies in the complexity of strong electron-electron correlation arising due to the open 3d shell. We present the total electron-ion recombination rate coefficients for the process, e+Fe VI → Fe V, obtained in an ab initio manner. Large-scale computations are carried out in the close coupling (CC) approximation using the R-matrix method employing a unified treatment that considers the infinite number of states of the recombined ion and incorporates both the radiative recombiantion (RR) and the dielectronic recombination (DR) processes in a self-consistent manner. It involves calculations of detailed photoionization cross sections, σPI, with autoionizing resonances of a large number of bound states with n≤nmax, such as 1054 bound states for the present case of Fe V. The number also equals the total number of state-specific recombination rates obtained for the ion. The high-n states are treated through the DR theory by Bell & Seaton. The same wavefunction expansion is employed in all photoionization/recombination calculations, thereby ensuring self-consistency. Rates are presented at a wide range of temperature for all practical applications. Present rates for total recombination differ considerably from currently used values obtained using simpler approximations. Application of the new recombination rate coefficients and photoionization cross sections for the ionization structure of iron in planetary nebulae show that under typical conditions the relative fractions of Fe V and Fe VI change by nearly a factor of 2.

Total electron-ion recombination of Fe

It is shown that a method for calculating unified total electron-ion recombination rates, incorporating both the radiative and dielectronic recombination processes, can be applied to substantially complex atomic systems where a large number of recombination channels need to be coupled in an ab initio manner. Calculations are carried out for the astrophysically important ion Fe III, and total and state-specific recombination rate coefficients are obtained for e+ Fe IV \ensuremath{\rightarrow} Fe III, in the close coupling approximation employing the R-matrix method. The calculations correspond to a 49-state eigenfunction expansion for the Fe IV core that includes states from the ground configuration 3${\mathit{d}}^{5}$ and the excited configurations 3${\mathit{d}}^{4}$4s and 3${\mathit{d}}^{4}$4p for proper treatment of the electron correlation effects. This is an accurate and detailed atomic calculation for the recombination rates for Fe III. The present rates are up to an order of magnitude lower than the previous values obtained through the Burgess general formula at electron temperatures where dielectronic recombination dominates. \textcopyright{} 1996 The American Physical Society.