Close-coupling Approximation Research Articles

Electron-impact study of PO2using theR-matrix method

The $R$-matrix approach is used to study the electron scattering from ${\text{PO}}_{2}$ radical at low electron impact energies. The elastic scattering phenomenon is studied in static-exchange, one-state and many-states close-coupling approximation. The elastic differential cross sections, corresponding momentum-transfer cross sections, and collision frequency are calculated in the one-state configuration interaction approximation only. Calculations reveal a stable bound state of ${\text{PO}}_{2}^{\ensuremath{-}}$ having symmetry ${}^{1}{A}_{1}$, a configuration of $\ensuremath{\cdots}8{a}_{1}^{2},\ensuremath{\cdots}2{b}_{1}^{2},\ensuremath{\cdots}5{b}_{2}^{2},\ensuremath{\cdots}1{a}_{2}^{2}$, and vertical electron affinity of $2.94$ eV. The excited state of anion ${\text{PO}}_{2}^{\ensuremath{-}}$ having symmetry ${}^{3}{B}_{1}$ is also just bound relative to the ground state of ${\text{PO}}_{2}$ at its equilibrium geometry. The shape, core-excited, and Feshbach resonances are analyzed in different symmetries up to 7 eV. The partial waves up to $l=4$ are used to represent continuum electron. The converged cross sections are obtained for the partial waves having $l$ greater than 4 by applying Born correction. Certain interesting spectroscopic properties of radical are also reported.

Inclusion of a Coulomb interaction potential in a variational model for positronium–helium scattering

While carrying out investigations on Ps–He scattering it was discovered that it would be possible to improve the results of a previous work on zero-energy scattering of ortho-positronium by helium atoms. The previous work used a model to account for exchange and also attempted to include the effect of short-range Coulomb interactions in the close-coupling approximation. The three terms that were then included did not produce a well-converged result but served to give some justification to the model. Now we improve the calculation by using a simple variational wave function, and derive a much better value of the scattering length. The new result is compared with other computed values, and when an approximate correction due to the van der Waals potential is included the total is consistent with an earlier conjecture.

Electron impact ionization cross sections of beryllium and beryllium hydrides

We report calculated electron impact ionization cross sections (EICSs) for beryllium (Be) and some of its hydrides from the ionization threshold to 1 keV using the Deutsch-Mark (DM) and the Binary-Encounter-Bethe (BEB) formalisms. The positions of the maxima of the DM and BEB cross sections are very close in each case while the DM cross section values at the maxima are consistently higher. Our calculations for Be are in qualitative agreement with results from earlier calculations (convergent close-coupling, R matrix, distorted-wave and plane-wave Born approximation) in the low energy region. For the various beryllium hydrides, we know of no other available data. The maximum cross section values for the various compounds range from 4.0 × 10−16 to 9.4 × 10−16 cm2 at energies of 44 to 56 eV for the DM cross sections and 3.0 × 10−16 to 5.4 × 10−16 cm2 at energies of 40.5 to 60 eV for the BEB cross sections.

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.

Oscillator strengths and effective collision strengths for electron excitation of Mg VI

Aims. Electron impact excitation collision strengths and oscillator strengths for the astrophysically important lines in Mg VI are reported. Thermally averaged collision strengths are presented as a function of electron temperature for application to solar and other astrophysical plasmas.Methods. The collision strengths were calculated in a close-coupling approximation using the B-spline Breit-Pauli R-matrix method. The multiconfiguration Hartree-Fock method with term-dependent, non-orthogonal orbitals was employed for an accurate representation of the target wave functions. The close-coupling expansion includes 74 bound levels of Mg VI covering the n = 2 and n = 3 terms. The present calculations led to a total of 2701 forbidden, intercombination, and allowed transitions between fine-structure levels. The effective collision strengths were obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities.Results. The accuracy of present oscillator strengths is evaluated by the agreement between the length and velocity formulations combined with the agreement between the calculated and measured excitation energies. The calculated excitation energies are in excellent agreement with experiments and other extensive configuration-interaction calculations. The oscillator strengths for all E1 transitions are listed. The effective collision strengths are tabulated for all 2701 transitions among the 74 fine-structure levels at 11 electron temperatures in the range from 10 000 to 200 000 K. The present results are compared with other close-coupling and distorted-wave calculations. Overall good agrement is generally found with the calculations by Ramsbottom & Bell and by Landi & Bhatia for many transitions, but significant differences are also noted for some transitions.

State-selective charge exchange in slow collisions of Si3+ ions with H atoms: A molecular state close coupling treatment*)

Charge transfer cross sections are calculated by employing both the quantal and semiclassical ε(R) molecular orbital close coupling (MOCC) approximations in the adiabatic representation and compared with other theoretical and experimental results

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).

TRANSITION PROBABILITIES AND COLLISION STRENGTHS FOR ELECTRON-IMPACT EXCITATION OF Cl III

We report transition probabilities and effective collision strengths for electron-impact excitation of the astrophysically important Cl III ion. The collision strengths are calculated in the close-coupling approximation using the B-spline Breit-Pauli R-matrix method. The multiconfiguration Hartree-Fock method with term-dependent non-orthogonal orbitals is employed for an accurate description of the target wave functions. The 68 fine-structure levels belonging to the 32 LS states of 3s {sup 2}3p{sup 3}, 3s3p{sup 4}, 3s {sup 2}3p {sup 2}3d, 3s {sup 2}3p {sup 2}4s, and 3s {sup 2}3p {sup 2}4p configurations are included in the close-coupling expansion. The effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities, and those are tabulated for all 2278 possible fine-structure transitions at electron temperatures in the range from 5000 to 1,000,000 K. Our results are compared with previous theoretical results and available experimental data. Overall, we reached a good agreement with the 23 state calculation of Ramsbottom et al., but some discrepancies are seen for some transitions.

H+ + NO(vi = 0) → H+ + NO(vf = 0–2) at ELab = 30 eV with canonical and Morse coherent states

H++NO(vi=0)=H++NO(vf=0–2) at ELab=30eV is investigated with the simplest-level electron nuclear dynamics (SLEND) method. In a direct, time-dependent, variational, and non-adiabatic framework, SLEND adopts nuclear classical mechanics and an electronic single-determinantal wavefunction. A coherent-states (CS) procedure recovers quantum vibrational properties from classical mechanics. Besides canonical CS, SU(1,1), SU(2), and Gazeau–Klauder Morse CS are innovatively introduced to treat anharmonicity. SLEND vibrational differential cross, rainbow scattering angles, and H+ energy loss spectra compare well with experimental data and with vibrational close-coupling rotational infinite-order sudden approximation results obtained at a higher computational cost.

R-matrix study of elastic and inelastic electron collisions with cytosine and thymine

Ab initio scattering calculations for low-energy electron collisions with gas-phase DNA pyrimidine bases (cytosine and thymine) are performed using the R-matrix method. The low-lying resonant states of the anions, formed due to electron capture by the bases, are identified using different levels of theory, including static exchange, static exchange plus polarization, and close-coupling approximations. For both the bases, all of our scattering models find three shape resonances of 2A″ (π) symmetry lying below 10 eV, in accordance with other calculations and experimental observations. In addition to these, a fourth 2A″ resonance is found in all models for thymine and in our best model, i.e. the uncontracted close-coupling approximation, for cytosine. This model places the fourth 2A″ resonance in both systems in the 6–7 eV range. No evidence is found for the presence of low-lying Feshbach resonances in either system. Integral cross sections for electronically elastic and inelastic collisions are also presented.

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.

Differential cross sections and electron impact coherence parameters for elastic electron scattering from laser-excited 138Ba

We have measured and calculated differential cross sections and the P3 collision Stokes parameter for elastic electron scattering from the laser-excited (…6s6p 1P1) and cascade-populated (…6s5d 3D1, 2) levels of barium at 5, 10, and 20 eV impact energy. Measurements were performed using a crossed-beam apparatus, where excited-state atomic targets were prepared with resonant laser radiation incident on the electron–atom interaction region. Calculations were performed in the convergent close-coupling (CCC), relativistic CCC, and optical-model potential approximations. We present measured and calculated partial differential cross sections, which relate to differential cross sections and electron impact coherence parameters through the target state anisotropy introduced by the laser geometry.

Photoionization and electron–ion recombination of Fe XVII for high temperature plasmas

Earlier studies on electron–ion recombination of Fe XVII, e+FeXVIII→FeXVII, concentrated on low temperature region. However, due to its higher abundance, recombination in the high temperature region is of great importance. Total and level-specific recombination cross sections and rates of Fe XVII are presented from the detailed study in the high temperature. The calculations were carried out using the unified method which incorporates both the radiative recombination (RR) and dielectronic recombination (DR) including the interference effects. The method also yields self-consistent set of recombination rates and photoionization cross sections. Unified method is implemented through relativistic Breit–Pauli R-matrix (BPRM) method and close coupling (CC) approximation. For the details of the high energy and high temperature features a CC wave function expansion consisting of 60 levels from n=2 and 3 complexes of the core Fe XVIII was considered. Earlier study included core excitations to n=2 levels only. It is found that the resonances due to core excitations to n=3 levels are much more extensive and stronger than those to n=2 levels and increase the recombination considerably in the high temperature region. While earlier study of 3-level calculations agree very well with the experimentally derived low temperature recombination, the high temperature rate shows a broad peak at about 5×106K, near the maximum abundance of the ion, due to dominance of DR via PEC (photo-excitation-of-core) resonances of n=3 levels. Level-specific recombination rate coefficients, which include both the RR and DR, are presented for 454 levels (n≤10, l≤9, 0 ≤J≤8 with even and odd parities) of Fe XVII. This is the first large-scale BPRM calculations for recombination of a complex atomic system beyond He- and Li-like ions. The results are expected to be accurate with 10–20% uncertainty and provide accurate modelings of ultraviolet to X-ray spectra.

Electron-impact study of an NCO molecule using theR-matrix method

We have carried out a comprehensive study of electron impact on an open shell NCO molecule by using the $R$-matrix method. Elastic (integrated and differential), momentum-transfer, excitation, and ionization cross sections, along with effective collision frequencies over a wide electron temperature range $(500--30\phantom{\rule{0.16em}{0ex}}000\phantom{\rule{4.pt}{0ex}}\text{K})$ have been presented. The target states are represented by including correlations via a configuration interaction formalism. The results of the static-exchange, correlated 1-state and 13-state close-coupling approximation are presented. Our study has detected five core excited shape resonances in the 13-state model. All calculations are done in the ${C}_{2v}$ point group. We also detect a stable bound state of ${\text{NCO}}^{\ensuremath{-}}$ of ${}^{1}\phantom{\rule{-0.16em}{0ex}}{A}_{1}$ symmetry having configuration $\ensuremath{\cdots}7{a}_{1}^{2},1{b}_{1}^{2}2{b}_{1}^{2},1{b}_{2}^{2}2{b}_{2}^{2}$ with a vertical electronic affinity value of $3.035\phantom{\rule{4.pt}{0ex}}\text{eV}$ which is in good agreement with the experimental (adiabatic) value of $3.609\ifmmode\pm\else\textpm\fi{}0.0005\phantom{\rule{4.pt}{0ex}}\text{eV}$. The ionization cross sections are calculated using the binary-encounter-Bethe model in which molecular orbitals at self-consistent Hartree-Fock level are used to calculate kinetic and binding energies of the occupied molecular orbitals. For scattering calculations we have used partial waves up to $l=4$ to represent the continuum electron in our $R$-matrix approach. A Born top-up procedure is invoked for dipole allowed transitions to account for the contribution of partial waves higher than $l=4$ to obtain converged cross sections.

Low-energy rotational inelastic collisions of H+ + CO system

The quantum mechanical state-to-state rotational excitation cross sections have been computed using the ab initio ground electronic state potential energy surface of the system [M. Mladenovic and S. Schmatz, J. Chem. Phys. 109, 4456 (1998)] computed at coupled-cluster single and double and triple perturbative excitations method using correlation-consistent polarized valence quadruple zeta basis set where the asymptotic potential have been computed using the dipole moment, quadrupole moment, and the molecular polarizability components and fitted to this interaction potential. The anisotropy of the surface has been analyzed in terms of the multipolar expansion coefficients for the rigid-rotor surface. The integral cross sections for rotational excitations have been computed by solving close-coupled equations at very low collision energies (5-200 cm(-1)) and the corresponding rates have been obtained for a range of low temperatures (5-175 K). The j = 0 → j(') = 1 rotational excitation cross section (and rate) is found to be the dominant followed by the j = 0 → j(') = 2 in these collision energies. The close-coupling, coupled-state, and infinite-order sudden approximations coupling calculations have been performed in the energy range of 0.1-1.0 eV using vibrational ground potential. The rotational cross sections have been obtained by performing computationally accurate close-coupling calculations at 0.1 eV using vibrationally averaged potential (ν = 1) and compared with the results of vibrational ground potential.

Low-energy electron collisions with formamide using theR-matrix method

Low-energy electron collisions with formamide are studied using the $R$-matrix method within the static-exchange, static-exchange-polarization, and close-coupling approximations. Twenty target states are included in the close-coupling formalism. The elastic integral, differential, and momentum transfer cross sections and the excitation cross sections from the ground state to the first four low-lying electron excited states are presented in the energy region of 0--10 eV. Besides the low-lying ${}^{2}\phantom{\rule{-0.16em}{0ex}}{A}^{\ensuremath{'}\ensuremath{'}}$ shape resonance indicating good agreement between the present results and the values available in literature, one core-excited resonance (${}^{2}\phantom{\rule{-0.16em}{0ex}}{A}^{\ensuremath{'}\ensuremath{'}}$) and three Feshbach resonances (${}^{2}\phantom{\rule{-0.16em}{0ex}}{A}^{\ensuremath{'}\ensuremath{'}}$, ${}^{2}\phantom{\rule{-0.16em}{0ex}}{A}^{\ensuremath{'}}$, and ${}^{2}\phantom{\rule{-0.16em}{0ex}}{A}^{\ensuremath{'}}$) at the higher energies are predicted, and they could be responsible for the fragments observed in a recent experiment of the dissociative electron attachments to formamide.

Fine-structure photoionization cross sections of Fe II

We present the first calculation of fine-structure photoionization cross sections for the ground state of singly ionized Fe. These large-scale ab initio calculations, limited to the near-threshold region, were performed in the close-coupling approximation using a Dirac–Coulomb R-matrix method implemented within a modified version of the DARC package. Our calculated cross sections reproduce in detail the resonance structures observed in previous experimental determinations.

The calculation of excitation cross-sections of collisions between Ne isotope atoms with HF molecule

In this paper, we use the Huxley potential function to fit the interaction energy data, which have been calculated at the theoretical level of the QCISD(T)/aug-cc-pVTZ. Differential and partial cross-sections of 16Ne, 20Ne, 34Ne atoms and HF molecule collisions are calculated by the accurate close-coupling approximation method when the incident energy is 100meV. We study the changing tendencies of Ne-HF collisional cross-sections with Ne isotopic substitution.

EFFECTIVE COLLISION STRENGTHS FOR ELECTRON-IMPACT EXCITATION OF Fe VIII

New extensive calculations are reported for electron collision strengths, rate coefficients, and transition probabilities for the astrophysically important lines of Fe VIII. The collision strengths have been calculated in the close-coupling approximation using the B-spline Breit-Pauli R-matrix method. The multiconfiguration Hartree-Fock method with term-dependent non-orthogonal orbitals is employed for an accurate representation of the target wave functions. The close-coupling expansion includes 102 fine-structure levels of Fe VIII covering all possible terms of the ground 3p 63d and singly excited 3p 53d 2, 3p 64l, 3p 53d4s, 3s3p 63d 2, and 3p 65l configurations. The present calculations are more extensive than the previous ones, leading to a total 5151 transitions between fine-structure levels. The effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities and these are tabulated for all fine-structure transitions at electron temperatures in the range from 5 × 103 to 5 × 106 K. There is an overall good agreement with the previous 77-state calculations by Griffin, Pindzola, & Badnell, but significant differences are also noted for some transitions.

Lowest lying doubly-excited P-and D-state resonances of Ps− in weakly coupled plasmas

The lowest-lying 1, 3Po and 1De resonances of positronium negative ion, Ps−, in weakly coupled plasmas have been investigated employing the close-coupling approximation. Three different basis sets have been employed in the present study. The plasma screening condition obtained from the Debye-Huckel type potential is used to represent the interaction between the charged particles. The resonance energies and the corresponding widths of one 1Po, two 3Po, and one 1De resonant states associated with the n = 2 threshold of the positronium atom for various Debye lengths ranging from infinity to small values are reported. The 1Po resonance as well as the higher lying 3Po resonant state transforms to a shape resonance for denser plasma conditions. The 1De resonant state also changes to a shape-type resonance for very dense plasmas.