Close-coupling Approximation Research Articles

Inelastic Triatom-Atom Quantum Close-Coupling Dynamics in Full Dimensionality: All Rovibrational Mode Quenching of Water Due to the H Impact on a Six-Dimensional Potential Energy Surface.

The rovibrational level populations, and subsequent emission in various astrophysical environments, are driven by inelastic collision processes. The available rovibrational rate coefficients for water have been calculated using a number of approximations. We present a numerically exact calculation for the rovibrational quenching for all water vibrational modes due to collisions with atomic hydrogen. The scattering theory implements a quantum close-coupling (CC) method on a high level ab initio six-dimensional (6D) potential energy surface (PES). Total rovibrational quenching cross sections for excited bending levels were compared with earlier results on a 4D PES with the rigid-bender close-coupling (RBCC) approximation. General agreement between 6D-CC and 4D-RBCC calculations are found, but differences are evident including the energy and amplitude of low-energy orbiting resonances. Quenching cross sections from the symmetric and asymmetric stretch modes are provided for the first time. The current 6D-CC calculation provides accurate inelastic data needed for astrophysical modeling.

Photoionization of hydrogen halides using the R-matrix method

Abstract In this study, we use the UK Molecular R-matrix (UKRMol) codes in the close-coupling approximation to examine the photoionization of hydrogen halides (hydrogen fluoride, hydrogen chloride, and hydrogen bromide). This article reports the total and partial photoionization cross sections for the X2Π, A2Σ+, and B2Σ+ ionic states of these halides. The calculated cross sections are compared with the available literature, which does not accurately represent the effective cross sections near the threshold region, which is dominated by the Rydberg series autoionization resonances converging to the A2Σ+ ionic state. There seems to have been minimal effort to investigate the Rydberg-bound states of these halides. Meanwhile, the R-matrix approaches have traditionally excelled at characterizing such studies. This indicates the effectiveness of this method for molecular photoionization as well as for understanding the resonant contribution to the photoionization cross sections. The detailed cross sections calculated comprise the complex autoionizing resonance structures capable of significantly contributing to the computations of total photoionization rates, which are necessary to maintain a steady state of ionization in astrophysical plasmas. Comparisons with the experimental measurements and the theoretical data generally show reasonable agreement across the reported energy range.

Photoionization of the Propargyl Radical Using the R-Matrix Method.

The absolute photoionization cross section of the propargyl radical measured by Savee et al. [J. Chem. Phys. 2012, 136, 134307] is about 2-3 times larger than the experimental result from Robinson et al. [J. Chem. Phys. 2003, 119, 5311]. Meanwhile, there is a significant discrepancy in the shapes of the propargyl photoionization spectra between these two measurements and the result measured by Zhang et al. [J. Chem. Phys. 2006, 124, 074302]. To estimate the accuracy of the various results, we carried out comprehensive calculations with the multichannel R-matrix method, which uses multiconfigurational wave functions to generate accurate initial and final states. Three scattering models including static-exchange, correlated 1 state, and 80 state close-coupling (CC) approximations are employed to reveal the dynamic interaction. The autoionization peaks near the ionization threshold are predicted for the first time. Two resonances are detected with the photon energy around 41.4 and 49.6 eV in the 80 state CC model. We checked the sensitivity of the results to change descriptions of the active spaces, the different partial waves, and the R-matrix radii in the theoretical model. Our best results are compared with the experimental measurements, and discussions are provided. The cross sections and asymmetry parameters for the valence orbitals are reported for photon energies from ionization thresholds of 70 eV.

Elastic and inelastic low-energy electron scattering from pyridine.

A comprehensive investigation of elastic and inelastic electron scattering from molecular pyridine is reported using the ab initio R-matrix method with the static exchange plus polarization and close-coupling approximations for incident energies up to 10eV. The two well-known low-lying 1 2B1 and 1 2A2 shape resonances as well as a 2 2B1 mixed-character resonance compare well with the theoretical and experimental results. We also detect five core-excited resonances (1 2A1, 1 2B2, 3 2B1, 2 2A2, and 4 2B1), which lie above the first electronic excitation threshold. The total elastic cross sections and momentum transfer cross sections agree reasonably with previous reference data. Comparisons of the differential elastic cross sections of pyridine with those measured for benzene, pyrazine, and pyrimidine show remarkable agreement at scattering angles above 40° but behave differently for forward scattering below 40° below 6eV, due to the dominant effect of the permanent dipole moment on the differential cross section in the low energy region with narrow scattering angles. Inelastic electronic excitation cross sections are presented, showing the influence of core-excited resonances below the ionization threshold for the first time.

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.

Study of Charged Particles Scattering with Atomic Target

In this paper, we have reported the calculated results of anisotropy parameter (Pl) and angular momentum transfer parameter (L) for positron (electron) scattering by Calcium (Ca) atom using close coupling approximation method in the framework of R-matrix theory at 20eV. Since this theory has deep root in nuclear physics, it also provides better results in atomic and molecular physics. The authors have compared the reviewed results with available theoretical results. A good agreement between these results shows that the present method gives better understanding for the positron (electron)-atom scattering.

Photoejection from Various Systems and Radiative-Rate Coefficients

Photoionization or photodetachment is an important process. It has applications in solar- and astrophysics. In addition to accurate wave function of the target, accurate continuum functions are required. There are various approaches, like exchange approximation, method of polarized orbitals, close-coupling approximation, R-matrix formulation, exterior complex scaling, the recent hybrid theory, etc., to calculate scattering functions. We describe some of them used in calculations of photodetachment or photoabsorption cross sections of ions and atoms. Comparisons of cross sections obtained using different approaches for the ejected electron are given. Furthermore, recombination rate coefficients are also important in solar- and astrophysics and they have been calculated at various electron temperatures using the Maxwell velocity distribution function. Approaches based on the method of polarized orbitals do not provide any resonance structure of photoabsorption cross sections, in spite of the fact that accurate results have been obtained away from the resonance region and in the resonance region by calculating continuum functions to calculate resonance widths using phase shifts in the Breit–Wigner formula for calculating resonance parameters. Accurate resonance parameters in the elastic cross sections have been obtained using the hybrid theory and they compare well with those obtained using the Feshbach formulation. We conclude that accurate results for photoabsorption cross sections can be obtained using the hybrid theory.

Elastic electron scattering with CH2Br2 and CCl2Br2: The role of the polarization effects

We present elastic electron scattering cross sections with holmethane molecules CH2Br2 and CCl2Br2 in the low-energy region ranging from 0.01 eV to 20 eV. The calculations are performed with the R-matrix method in static-exchange plus polarization (SEP) and close-coupling (CC) approximations. The integral, differential, and momentum transfer cross sections are calculated. The convergence of the obtained cross sections is checked at four different levels of SEP approximation. The predicted positions of the resonances agree well with available results. The precise resonance parameters are found to be sensitive to the treatment of polarization effects employed. We find that the polarization has a substantial effect on the cross sections, and this effect becomes even more important for lower impact energies.

Transition Probabilities and Collision Strengths for Fine-structure Levels Excitation of Ti II

Abstract Several spectral features from the stellar and nebular objects arise due to the iron-peak Ti II fine-structure excitations. Transition probabilities and electron excitation collision strengths of iron-peak elements are important for a meaningful interpretation and analysis of the observed astrophysical spectra. Accurate description of atomic structure with open 3d-shell elements is the key to the reliable and accurate computation of radiative and collision rates. The term-dependent one-electron orbitals in the multiconfiguration Hartree–Fock approach with adjustable configuration expansions and semi-empirical fine-tuning for energy corrections have been used in achieving highly accurate target description. A total of 314 Ti II fine-structure levels of the ground 3d 24s and excited 3d 3, 3d4s 2, 3d 24p, 3d 25s, 3d4s4p, 3d 24d, 3d 25p, and 3d 24f configurations have been included in the calculations of these atomic parameters. The present calculation of collision strengths has been performed in a close-coupling approximation based on the B-spline Breit–Pauli R-matrix method with inclusion of spin–orbit interaction term in the Hamiltonian matrices. Effective collision strengths over a Maxwellian distribution of electron velocities at temperatures in the range from 103 to 105 K have been reported for transitions between the 314 fine-structure levels. These wide array of transitions give rise to many main Ti II infrared, optical, and ultraviolet lines from a variety of astrophysical objects. Our calculated parameters are compared with the available other theoretical and experimental results, and through this comparison likely uncertainties in our results have been estimated, especially for transitions among the low-lying fine-structure levels of astrophysical importance.

Scattering and Its Applications to Various Atomic Processes: Elastic Scattering, Resonances, Photoabsorption, Rydberg States, and Opacity of the Atmosphere of the Sun and Stellar Objects

A scattering process can be a natural process or a process carried out in a laboratory. The scattering of particles from targets has resulted in important discoveries in physics. We discuss various scattering theories of electrons and positrons and their applications to elastic scattering, resonances, photoabsorption, excitation, and solar and stellar atmospheres. Among the most commonly employed approaches are the Kohn variational principle, close-coupling approximation, method of polarized orbitals, R-matrix formulation, and hybrid theory. In every formulation, an attempt is made to include exchange, long-range and short-range correlations, and to make the approach variationally correct. The present formulation, namely, hybrid theory, which is discussed in greater detail compared to other approximations, includes exchange, long-range correlations, and short-range correlations at the same time, and is variationally correct. It was applied to calculate the phase shifts for elastic scattering, the resonance parameters of two-electron systems, photoabsorption in two-electron systems, excitation of atomic hydrogen by an electron and positron impact, and to study the opacity of the Sun’s atmosphere. Calculations of polarizabilities, Rydberg states, and bound states of atoms are also discussed.

Database NORAD-Atomic-Data for Atomic Processes in Plasma

The online atomic database of NORAD-Atomic-Data, where NORAD stands for Nahar OSU Radiative, is part of the data sources of the two international collaborations of the Opacity Project (OP) and the Iron Project (IP). It contains large sets of parameters for the dominant atomic processes in astrophysical plasmas, such as, (i) photo-excitation, (ii) photoionization, (iii) electron–ion recombination, (iv) electron–impact excitations. The atomic parameters correspond to tables of energy levels, level-specific total photoionization cross-sections, partial photoionization cross-sections of all bound states for leaving the residual ion in the ground state, partial cross-sections of the ground state for leaving the ion in various excited states, total level-specific electron–ion recombination rate coefficients that include both the radiative and dielectronic recombination, total recombination rate coefficients summed from contributions of an infinite number of recombined states, total photo-recombination cross-sections and rates with respect to photoelectron energy, transition probabilities, lifetimes, collision strengths. The database was created after the first two atomic databases, TOPbase under the OP and TIPbase under the IP. Hence the contents of NORAD-Atomic-Data are either new or from repeated calculations using a much larger wave function expansion making the data more complete. The results have been obtained from the R-matrix method using the close-coupling approximation developed under the OP and IP, and from atomic structure calculations using the program SUPERSTRUCTURE. They have been compared with available published results which have been obtained theoretically and experimentally, and are expected to be of high accuracy in general. All computations were carried out using the computational facilities at the Ohio Supercomputer Center (OSC) starting in 1990. At present it contains atomic data for 154 atomic species, 98 of which are lighter atomic species with nuclear charge Z ≤ 28 and 56 are heavier ones with Z > 28. New data are added with publications.

Electron Scattering Cross Sections for Anthracene and Pyrene.

UK molecular R-matrix calculations have been carried out for electron scattering from anthracene and pyrene. These molecules belong to the family of polycyclic hydrocarbons (PAHs) and are found in a nebula known as the Red Rectangle. Static exchange (SE), static exchange plus polarization (SEP), and close coupling (CC) approximations are used for scattering calculations. Different elastic and inelastic cross sections are computed in the present work in the energy range of 0.1-15 eV. Dissociative electron attachment cross sections are also calculated for both the molecules. Various shape, Feshbach/core-excited, and mixed resonances are detected for these molecules below 10 eV. All of the resonances detected in the present study are in agreement with the existing experimental and theoretical results. Due to the complexity of the present targets, electron collision cross sections are essentially unknown and hence most of the results are presented for the first time.

Low-energy electron scattering from methylene radicals: multichannel-coupling effects

SynopsisWe reported elastic and excitation cross sections for electron collisions with methylene radical using R-matrix method for electron energies ranging from 0.01 to 15 eV in close-coupling (CC) approximation. We discuss the multi-channel-coupling effects on the calculated cross sections and resonances, and how the number of excited states included in the target state impacts the convergence of the elastic and the X3B1 → 11A1 and X3B1 → 11B1 excitation cross sections, especially at higher impact energy. Finally, we estimate the accuracy of the 11A1and 11B1 excitation cross sections.

Vibrationally-resolved excitation and dissociation collision strengths of AlO+ by electron-impact using the R-matrix method

The electron-impact calculations are reported for excitation and dissociation of AlO+ ion using the R-matrix method. Calculations are performed in the static-exchange (SE) and close-coupling (CC) approximation. Each target state in CC approximation is represented by a configuration interaction (CI) wavefunction that takes into account the correlation and polarisation effects. In CC approximation 14-target states are included in the trial wavefunction of the entire scattering system. Potential energy curves (PECs) for the first four low-lying states are generated using the basis functions 6-311G* wherein we obtain X1Σ+ as the ground state contrary to a3Π as stated elsewhere in literature. Scattering calculations are then performed to yield vibrationally-resolved electronic excitation collision strengths to the first three lowest excited states a3Π, A1Π and b3Σ+. Using more accurate PECs we calculated the Franck–Condon factors which were then employed to get the vibrationally-resolved electronic excitations and dissociation collision strengths for the fragment channel Al++O of the lowest three excited states a3Π, A1Π and b3Σ+. All scattering calculations are performed at the experimental bond length 1.6178 A of AlO+. Rotational excitation cross sections (0→j, j = 1, 2 … 5) have also been calculated and the corresponding rate coefficients have been evaluated for excitation and de-excitation by using the Maxwellian distribution function for electron temperature upto 5000 K. There are many Feshbach resonances detected in this work. We have analysed only the low-lying resonances below the excitation threshold of A1Π excited state. Beyond this threshold the resonance structure is too complex to analyse due to many overlapping resonances.

State-selective quantum interference studied in the photo-recombination of Ar17+ ion

We investigate the total and partial cross sections of the state-selective photo-recombination (PR) from the ground state 1sS01 of H-like Ar17+ ion to the 1s2S01, 1s2sS01,S13 and 1s2pP0,1,23,P11 states of He-like Ar16+ ion. The analysis is performed based on the close-coupling approximation and the fully relativistic Dirac R-matrix method, in which the unified treatments of the combined electron-ion PR process, including radiative and dielectronic recombination (DR) as coherent, interfering components are considered. The KLL PR resonance group are determined and identified according to the calculated energies and transition rates using the multiconfiguration Dirac–Fock (MCDF) method. The DR cross sections are also presented for comparison purposes. Our results show that the quantum interference between direct recombination and resonant recombination processes will strongly influence the intensity and shape of the PR cross sections, especially for the 2s2pP11 and 2p2D21 resonant regions. Comparison of our computed results with previously published experimental and theoretical values, when available, is made.

Photoionization of fine structure levels of Ne III

Detailed study on the characteristic features in photoionization of Ne III, (hν + Ne III → Ne VI + e) is reported. The calculations were carried out in relativistic Briet–Pauli R-matrix (BPRM) method and close-coupling (CC) approximation. The CC expansion for the wavefunction of Ne III includes 58 fine structure levels of Ne IV from configurations 2s22p3, 2s2p4, 2p5, 2s22p23s, 2s22p23p, 2s22p23d. The photoionization cross section (σPI) features exhibit i) presence of prominent resonances in the low energy region near the ionization thresholds of low lying levels, ii) lower energy region of extensive narrow Rydberg resonances and slow decaying background cross section in the high energy region for equivalent electron levels, and iii) presence of strong Seaton resonances due to photo-excitation-of-core (PEC) in the high energy region. The relativistic effects have almost no impact on the σPI in the high energy regions. However, for a number of low lying levels the coupling of fine structure channels, which is not allowed in LS coupling, introduces high-peak narrow resonances with almost zero background below the excitation threshold of 2s22p3(2Do) level of the residual ion. These will enhance quantities such as electron-ion recombination, opacity at very low temperature. The Seaton resonances due to n=3 PECs in the high energy region, which was not studied before, are more prominent than those for n=2 PECs. For complete modeling of astrophysical and laboratory plasmas, photoionization cross sections are presented for a large number of excited levels, in total 392, with n ≤ 10 and l ≤ 9.

Electron-impact excitation of forbidden and allowed transitions in Fe ii

Extensive calculations are reported for electron collision strengths, rate coefficients, and transitions probabilities for a wide range of transitions in Fe ii. The collision strengths were calculated in the close-coupling approximation using the B-spline Breit-Pauli R-matrix method. The multiconfiguration Hartree-Fock method in connection with adjustable configuration expansions and a semiempirical fine-tuning procedure is employed for an accurate representation of the target wave functions. The energy correction was also used in the scattering calculations by adding to Hamiltonian matrices prior to transformation to intermediate coupling. The spin-orbit interaction term was added to the final Hamiltonian matrices in scattering calculations. The close-coupling expansion contains 340 fine-structure levels of Fe ii and includes all levels of the $3{d}^{6}4s$, $3{d}^{5}4{s}^{2}$, $3{d}^{7}$, and $3{d}^{6}4p$ configurations, plus a few lowest levels of the $3{d}^{5}4s4p$ configuration. The effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities at electron temperatures in the range from ${10}^{2}$ to ${10}^{5}$ K and are reported for all possible inelastic transitions between the 340 fine-structure levels. The present results are more extensive than the previous calculations and considerably expand the existing data sets for Fe ii, allowing a more detailed treatment of the available measured spectra from different space observatories. Comparison with other calculations for collision rates and available experimental radiative rates is used to place uncertainty bounds on our collision strengths and to assess the likely uncertainties in the existing data sets.

Collision Strengths and Effective Collision Strengths for Allowed Transitions among the n ≤ 5 Degenerate Levels of Atomic Hydrogen

We report calculations of collision strengths and effective collision strengths for 26 allowed transitions among the n≤ 5 degenerate levels of atomic hydrogen for which the close-coupling (CC) and Born approximations have been used. Results are listed over a wide range of energies (up to 100 Ryd) and temperatures (up to 107 K), sufficient for applications over a variety of plasmas, including fusion. Similar results have also been calculated for deuterium, but they negligibly differ with those of hydrogen.

Electron-impact coherence parameters for 41P1 excitation of zinc

We present electron-impact coherence parameters (EICP) for electron-impact excitation of 41P1 state of zinc atoms for collision energies 40 eV and 60 eV. The experimental results are presented together with convergent close-coupling and relativistic distorted-wave approximation theoretical predictions. The results are compared and discussed with EICP data for collision energies 80 eV and 100 eV.

Excitation of the 2S State of Atomic Hydrogen by Electron Impact

The excitation cross sections of the 2S state of atomic hydrogen at 10 low incident electron energies (10.30 and 54.5 eV) have been calculated using the variational polarized method. Nine partial waves are used to get convergence of cross sections in the above energy range. The maximum of the cross section is 0.137 π a 0 2 at 11.14 eV which is close to the experimental result 0.163 ± 0.2 π a 0 2 at 11.6 ± 0.2 eV. The present results are compared with other calculations, many of them are based on the close-coupling approximation, including the R-matrix method. Differential cross sections at 13.6 eV incident energy have also been calculated. Spin-flip cross sections have been calculated and compared with those obtained using the close-coupling approximation.