R-matrix Approach Research Articles

Superelastic scattering of electrons from highly charged ions with inner shell vacancies.

We report the measurement of electrons scattered superelastically from highly charged ions having an initial K-shell vacancy. In this process, the scattered electron gains approximately 725 eV of energy from the deexcitation of an excited He-like F7+(1s2s 3S) metastable ion to its ground state. Theoretical calculations based on an R-matrix approach agree well in position, shape, and magnitude with the experimental data.

Photoionization of the excited 3s3p 1,3Po states of atomicmagnesium

Calculational results for the photoionization cross sections leading to theionic Mg+(\\rm3s,3p,4s and 3d) states from theexcited3s3p 1,3Po states of atomic magnesium are reported in the energyregion from the first ionization threshold up to the Mg+(4p)threshold limit. For these calculations, we have used an enhancednon-iterative variational R-matrix approach combined withmultichannel quantum-defect theory at the R-matrix surface.Autoionizing doubly excited 1,3S, 1,3P and 1,3D resonancestructures converging to the Mg+(3p, 4s, 3d and 4p)thresholds are discussed with resonant energies Er, effective quantumnumbers n* and widths Γ. The present photoionizationcross sections are in good agreement with previous available calculations.There is excellent agreement between length andvelocity gauges in our calculations.

Electron Impact Excitation Collision Strengths for Fe x

Electron collision excitation strengths for transitions between fine-structure levels of the 3s23p5, 3s3p6, 3s23p43d, 3s3p53d, and 3s23p44s configurations in Fe X are calculated using semirelativistic R-matrix approach which takes into account parts of the Breit-Pauli Hamiltonian. We included 49 fine-structure levels in our scattering calculation. These levels are represented by configuration-interaction wave functions. Rydberg series of resonances converging to the excited state thresholds are explicitly included in the calculation. Present results of collision strength are compared with available distorted wave calculations. Some differences are noted. Effective collision strengths are evaluated by averaging the electron collision strengths over a Maxwellian distribution of electron energies. Results are listed over a wide temperature range (3 × 104- 6 × 106 K) applicable to many astrophysical plasmas.

Effective Collision Strengths of Fine‐Structure Transitions in Fex, Fexi, and Fexiii

Electron excitation collision strengths for fine-structure transitions in Fe X, Fe XI, and Fe XIII are calculated using full Breit-Pauli R-matrix approach. We included 49 fine-structure levels of Fe X, 38 fine-structure levels of Fe XI, and 26 fine-structure levels of Fe XIII in our scattering calculations. These levels are represented by configuration-interaction wave functions. The relativistic effects are included in the Breit-Pauli approximation via one-body mass correction, Darwin, and spin-orbit interaction terms in the scattering equations. Rydberg series of resonances converging to the excited state thresholds are explicitly included in the calculations. The effective collision strengths are determined by integrating collision strengths and assuming a Maxwellian distribution of electron energies.

Geometry dependence of resonance background separationwithin the R-matrix approach in the e- + CF3Cl system

Elastic electron scattering off CF3Cl is studied fordifferent nuclear geometries by separating the resonantprocesses from the scattering background. This separation isperformed within the Feshbach projection operator formalism,applied to R-matrix theory. In the energy region below 13 eVtwo resonances of 2A1 symmetry and one of 2E symmetryare found. In background scattering the target appears asnearly spherical and the effect of the C-Cl distance is verysmall over a range of 0.8 Bohr. This means that in the presentexample the molecular structure as it appears in low-energyelectronically elastic electron scattering is entirely providedby resonant processes.

Observation of an α-cluster structure in 36Ar

Excitation functions for 32S+α elastic scattering are measured by a new method based on inverse kinematics and a thick gas target. Data corresponding to the 36Ar excitation range 12–16 MeV are treated within the R-matrix approach. Spin-parity assignments are given for over 40 new levels.

Rate coefficients for electron impact excitation ofhelium-like ions within the Dirac R-matrix approach

The Dirac R-matrix theory is used to calculate the collisionstrengths for electron impact excitation of He-like ions(S14+, Ca18+ and Fe24+) using the Dirac atomicR-matrix code, which has been developed mainly byNorrington and Grant (Norrington P H and Grant I P 1987 J. Phys. B: At. Mol. Phys. 20 4869). The lowest 31 target levels are includedin the calculation. Rate coefficients are obtained fortransitions from the ground 1s2 1S0 state to thefine-structure levels of all excited states of 1s2ℓ(ℓ = 0,1) and 1s3ℓ (ℓ = 0,1,2) configurations.We compare our results for rate coefficients with the resultsof previous calculations, and indicate where significantdifferences arise because of our more accurate representation ofresonance and relativistic effects.

Fusion ofq-tensor operators: Quasi-hopf-algebraic point of view

We discuss the fusion of tensor operators for Uq{itJ} by means of the R-matrix approach. The problem is reducedxz to construction of the twisting elementF which appears in Drinfeld's description of quasi-Hopf algebras. The discussion is illustrated by explicit calculations for the case of Uq(sl(2)). Bibliography: 20 titles.

Study of electron polarization and correlation effects in resonant and background electron scattering off CF 3Cl

We report on ab initio calculations for electron–CF 3Cl scattering based on the R-matrix approach. Eigenphases and cross-sections are presented for collision energies up to 15 eV in static exchange and static exchange plus polarization (SEP) approximation. The SEP results for integral cross-sections agree satisfactorily with experimental total cross-sections. Moreover, the partial cross-sections confirm the symmetry assignment of the lowest three resonances as has been found in experiments carried out by Mann and Linder. Electron polarization and correlation effects are studied separately for resonant and background scattering. For this separation, the Feshbach projection operator technique formulated within the R-matrix framework is applied. We found that the description of resonant scattering is considerably affected by configuration interaction. The background scattering appears to be appropriately described on the SEP level.

Duality for coloured quantum groups

Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L± functionals are constructed and the dual algebra is derived explicitly. These functionals are then employed to give a coloured generalisation of the differential calculus on quantum GL(2) within the framework of the R-matrix approach.

Collision Strengths for Electron Collision Excitation of Fine‐Structure Levels in Siii

Electron collisional excitation strengths for transitions between the 3s23p2 3P0,1,2, 1D2, and 1S0 levels and from these levels to the fine-structure levels of the excited 3s3p3, 3s23p3d, 3s23p4s, 3s23p4p, and 3s23p4d configurations of S III are calculated in R-matrix approach. We considered 49 fine-structure levels arising from the 27 LS 3s23p2 3P, 1D, 1S, 3s3p3 5, 3So, 1, 3Do, 1, 3Po, 3s23p3d 1, 3Po, 1,3Do, 1, 3Fo, 3s23p4s 1,3Po, 3s23p4p 1,3S, 1,3P, 1,3D, 3s23p4d 1,3Po, and 1,3Do states. These target levels are represented by fairly extensive configuration-interaction wave functions. The collision strengths for transitions between fine-structure levels are calculated by transforming the LS-coupled K-matrices to K-matrices in an intermediate coupling scheme. Complicated resonance structures converging to excited state thresholds are explicitly included in collision strengths. The effective collision strengths are obtained from the total collision strengths by integrating over a Maxwellian velocity distribution. These are tabulated over a wide electron temperature range (0.5-10) × 104 K.

R-matrix calculation of the photoabsorption of K II, Ca III and Sc IV

The R-matrix approach is employed to study the photoionization of the argon-like ions K II, Ca III and Sc IV. The 3s3p6np 1Po Rydberg series is identified for each ion. Excellent agreement with previously published resonance positions is observed but the q-reversal reported for Ca III by van Kampen et al is not replicated in this calculation. Good agreement with experimental data is observed for K II but not for Ca III. The differences in shape of the total cross sections along the sequence are attributed to the relative positions of the 3s and 3p Cooper minima.

Absolute cross sections for near-threshold electron-impact excitation of Be-like C 2+, N 3+, and O 4+ ions

Absolute total cross sections for electron-impact excitation of the Be-like C 2+, N 3+, and O 4+ ions have been measured near threshold using the merged electron-ion beams energy-loss (MEIBEL) technique and calculated using a close-coupling R-matrix (CCR) approach. The 2 s 2 1 S → 2 s2 p 1 P 0 dipole-allowed transition from the ground state was investigated for all three ions and satisfactory agreement between experiment and theory is found. In addition, calculations and measurements for the 2 s2 p 3 P 0 → 2 p 2 3 P allowed transition from the metastable level of C 2+ are in excellent agreement. The sum of the cross sections for the 2 s 2 1 S → 2 s2 p 3 P 0 and 2 s2 p 3 P 0 → 2 s2 p 1 P 0 spin-forbidden transitions, not completely resolved by the MEIBEL technique, are measured for C 2+ and O 4+ and compared to CCR calculations scaled to account for the ground state and metastable fractions of the target ion beams. The results for these unresolved transitions are in reasonable agreement except for a resonance feature measured in the 2 s2 p 3 P 0 → 2 s2 p 1 P 0 transition in C 2+ that is not predicted by theory.

Electron Impact Excitation of Fine‐Structure Levels in Sulfur‐like Fe xi

Collision strengths for electron impact excitation of fine-structure levels in sulfur-like Fe XI are calculated in a semirelativistic R-matrix approach. The 38 fine-structure levels arising from the 20 LS states 3s23p43P,1D,1S; 3s3p53Po,1Po; 3s23p3(4So)3d3Do, 3s23p3(2Po)3d1,3Po,1,3Do,1,3Fo, 3s23p3(2Do)3d1,3So,1,3Po,1,3Do,1,3Fo are included in our calculation. The target levels are represented by configuration interaction wave functions. The relativistic effects are considered in the Breit-Pauli approximation by including one-body mass correction, Darwin term, and spin-orbit terms in the scattering equations. Collision strengths for transitions from the 3s23p43P2,1,0 levels to the fine-structure levels of the 3s23p33d configuration are compared with the distorted-wave results of Bhatia & Doschek at 8.0, 16.0, 24.0 ryd. There are some significant discrepancies between the two calculations, mostly caused by the difference in target wave functions. The collision strengths are integrated over a Maxwellian distribution of electron energies to obtain effective collision strengths over the temperature range from 5 × 105 to 5 × 106 K.

Effective Collision Strengths for Electron Impact Excitation of Fine‐Structure Levels in Fexi

Collision strengths for transitions between the 3s23p4 P2, 1, 03, 1D2, and 1S0 levels and from these levels to the 3s3p5 P02, 1, 03 and 1P01 levels of Fe XI are calculated using a semirelativistic R-matrix approach. The 38 fine-structure levels arising from the 20 LS 3s23p4 P3, 1D, 1S, 3s3p5 P03, 1P0, 3s23p3(4S0)3d D03, 3s23p3(2P0)3d P01,3, 1, 3D0, 1, 3F0, 3s23p3(2D0)3d S01,3, 1, 3P0, 1, 3D0, 1, 3F0 states are included in our calculation. These target levels are represented by configuration-interaction wave functions. The relativistic effects are considered in the Breit-Pauli approximation by including one-body mass correction, Darwin term, and spin-orbit terms in the scattering equations. Complicated resonance structures are found to enhance the collision strengths significantly for many transitions in the threshold energy regions. Our collision strengths are compared with the available results of Bhatia & Doschek at 8.0, 16.0, and 24.0 ryd. The collision strengths are integrated over a Maxwellian distribution of electron energies to give effective collision strengths over a wide temperature range.

Integral Representation for the Eigenfunctions of a Quantum Periodic Toda Chain

An integral representation for the eigenfunctions of a quantum periodic Toda chain is constructed for the N-particle case. The multiple integral is calculated using the Cauchy residue formula. This gives the representation which reproduces the particular results obtained by Gutzwiller for the N=2,3 and 4-particle chain. Our method of solving the problem combines the ideas of Gutzwiller and the R-matrix approach of Sklyanin with the classical results in the theory of Whittaker functions. In particular, we calculate Sklyanin's invariant scalar product from the Plancherel formula for the Whittaker functions derived by Semenov-Tian-Shansky thus obtaining a natural interpretation of the Sklyanin measure in terms of the Harish-Chandra function.

Photoabsorption of atomic oxygen in the vicinity of the K-edge

Ab initio cross section calculations using the R-matrix approach have been performed for the inner-shell photoabsorption of atomic oxygen in the photon energy region 520-555 eV. The prominent (1s2(P)np ) resonance series, converging to the series limit of atomic oxygen, dominate the cross section in the vicinity of the K-edge. A comparison of the calculations with two recent sets of experimental measurements taken at the Advanced Light Source and at the Wisconsin synchrotron facility is made.

Computational aspects of the two-dimensional propagation of R-matrices on MPPs

The simulation of electron collisions, at intermediate energies, with atoms, ions and molecules in highly excited Rydberg states is a physically important and computationally challenging problem. A suitable computational technique, to meet this challenge for the general two-electron problem, involves an adaptation of the intermediate energy R-matrix approach, in which the ( r 1, r 2) plane of the inner region is partitioned into a set of connected subregions and a global -matrix is propagated, in two dimensions, across this plane. In this paper we examine the computational aspects of this technique and, in particular, describe a parallel strategy for exploiting the architecture of distributed memory parallel computers.

Collision Strengths for Electron Impact Excitation of Fine‐Structure Levels in Fexiii

Electron collisional excitation strengths for transitions among the fine-structure levels of the ground 3s23p2 configuration and from the levels of 3s23p2 configuration to the levels of the excited 3s3p3 and 3s23p3d configurations in Fe XIII are calculated using a semirelativistic R-matrix approach. We considered 14 LS 3s23p23P,1D,1S, 3s3p33Do,3Po,1Do,3So,1Po, 3s23p3d3Po,1Do,3Do,3Fo,1Fo, and 1Po states of Fe XIII in the present calculation. The 14 LS states give rise to 26 fine-structure levels that are represented by configuration-interaction wave functions. The relativistic effects are included in the Breit-Pauli approximation via one-body mass correction, Darwin, and spin-orbit interaction terms in the scattering equations. Complicated resonance structures are explicitly included in the collision strengths. The collision strengths are integrated over a Maxwellian distribution of electron energies to give effective collision strengths over a wide temperature range from 5 × 105 to 5 × 106 K.

Characterization of metastable anionic states within the R-matrix approach

Metastable anionic states are very useful for describing resonances in electron-molecule scattering processes. However, a rigorous definition of such metastable states does not exist and their numerical representation, in particular in cases of very broad resonances, is difficult. In the present paper, the formalism of the R-matrix theory is employed to develop a general concept for constructing metastable electronic states. The discretization of the scattering continuum by the R-matrix formalism allows us to define metastable anionic states similar to diabatic states in cases of avoided crossings of potential curves in molecules. This present technique also allows the solution of the background scattering problem and the determination of the energy-dependent decay width of resonances. The concept is demonstrated for the state of , the state of and the state of .