Application of R-matrix method to electron-H<Subscript>2</Subscript>S collisions in the low energy range

Electron-H₂S collision process is studied using the R-matrix method. Nine low-lying states of H₂S molecule are considered in the R-matrix formalism to obtain elastic integral, differential, momentum transfer and excitation cross sections for this scattering system. We have represented our target states using configuration interaction (CI) wavefunctions. We obtained adequate representation of vertical spectrum of the target states included in the scattering calculations. The cross sections are compared with the experiment and other theoretical results. We have obtained good agreement for elastic and momentum transfer cross sections with experiment for entire energy range considered. The differential cross sections are in excellent agreement with experiment in the range 3–15 eV. A prominent feature of this calculation is the detection of a shape resonance in ²B₂ symmetry which decays via dissociative electron attachment (DEA). Born correction is applied for the elastic and dipole allowed transition to account for higher partial waves excluded in the R-matrix calculation. The electron energy range is 0.025–15 eV.     

Resonances in electron-impact integral excitation cross sections of the magnesium atom

The resonance structure of the integral cross sections of excitation of the magnesium atom by low-energy electrons is analyzed in terms of the R-matrix method. The collision strengths are calculated in terms of the close-coupling approximation with consideration of 25 atomic states, including 13 physical target states and 12 pseudostates. The latter simulate the remaining bound and continuum states of the Mg atom that were not included in the close-coupling expansion explicitly. The positions and widths of the resonances found are determined, and the resonances are classified with respect to the mechanism of formation of short-lived states of the negative Mg ion. The results of calculations are compared with available experimental data.     

Effective collision strengths among the fifteen lowest states of FeXVII

Collision strengths have been calculated for electron impact excitation of neon-like Fe XVII for all transitions within its 15 lowest states. Configuration interaction wavefunctions have been used to represent the target states. The standardR-matrix code has been used to calculate the contribution from the lower scattering partial waves (L⩽9), while the no exchange version of the same code has been used to compute efficiently the contribution of higher partial waves (L⩾10). Effective collision strengths for all the 105 transitions are tabulated for elected temperatures in the range logT _e=5.40 to logT _e=7.00 withT _e expressed in °K.     

<Emphasis Type="Italic">R</Emphasis>-matrix calculations of the integral electron-impact excitation cross sections of the ground state of the barium atom

The R-matrix approach has been used to calculate the integral cross sections of excitation of the barium atom by low-energy electrons. The collision strengths have been calculated in the 38-state close coupling approximation, including 16 physical states and 22 pseudostates of the target. The target wave functions have been obtained in terms of the multiconfiguration Hartree-Fock method in the LS coupling scheme. The cross sections calculated exhibit a pronounced resonance structure, which contributes significantly to the total excitation cross sections. The results obtained have been compared to available theoretical and experimental data.     

Collisional excitation among the seven lowest states of TiXII

Collision strengths have been calculated for electron impact excitation of sodium-like TiXII for all 21 transitions amongst its lowest seven states. Configuration interaction wave functions have been used to represent the target states. The standard and no-exchangeR-matrix codes have been used to calculate the contribution of partial waves withL⩽8 andL>8 respectively. Collision strengths are tabulated at selected energies in the range 26 to 50 Ryd. Effective collision strengths are tabulated for electron temperatures in the range logT _e=4.0 to logT _e=6.0, withT _e in K. This is the first detailed calculation on this ion in which the effects of exchange, channel couplings and short-range correlation are taken into account.     

The 17O(p, α)14N reaction: Physics and astrophysics

The nucleus ¹⁸F has been studied using the ¹⁷O(p,α)¹⁴N reaction over the energy range E_p = 400 to 1400 keV with thin Ti¹⁷O₂ targets. New resonances at E_p = 525, 688, 1015, 1276 and 1338 keV have been discovered. The strengths for all resonances in this energy range have been measured and the entire cross section in this region has been fitted using the R-matrix formalism of Lane and Thomas. Some discussion is presented concerning the values of the boundary condition parameters used in the R-matrix fit and two sets of results are presented corresponding to two different treatments of the boundary conditions.The ¹⁷O(p, α)¹⁴N cross section has been extrapolated to astrophysical energies using an R-matrix calculation incorporating the partial widths obtained from the data from E_p = 400 to 1400 keV. These results are compared with previous ¹⁷O(p, α)¹⁴N calculations and the ¹⁷O(p, γ)¹⁸F direct capture calculation of Rolfs and Rodney.     

The dual (p,q)-Alexander-Conway Hopf algebras and the associated universal ℐ-matrix

The dually conjugate Hopf algebrasFun _p,q (R) andU _p,q (R) associated with the two-parametric (p,q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebraU _p,q (R) is extracted. The universal ?-matrix forsFun _p,q (R) is derived. While expressing an arbitrary group element of the quantum group characterized by the noncommuting parameters in a representation independent way, the ?-matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal ?-matrix and the FRT matrix generators,L ^(±), forU _p,q (R) are derived from the ?-matrix.     

Comparison of feshbach and R-matrix reaction theories for C(n,n)C: (I). Shell model

The Feshbach and R-matrix approaches to nuclear structure calculations in the continuum have been applied to the elastic scattering of neutrons from ¹²C below the inelastic threshold. A simple shell model has been used for the positive-parity states of ¹³C and in contrast to the work of Lovas, the predictions of this model disagree significantly with experiment for both theories. The results for the two reaction theories have been compared.     

Reduction of the Lane-Robson “calculable” reaction theory to standard R-matrix form

General dynamical equations derived from the Lane-Robson calculable reaction formalism are cast into a form amenable to standard R-matrix treatment, permitting the resonance content of the equations to be made explicit. Formulae are given which enable the collision matrix and the amplitudes of physical eigenfunctions to be calculated directly from the R-matrix with or without the isolation of resonance contributions. The present methodology permits a significant reduction of effort in numerical investigations of the energy dependence inherent in dynamical models of the nucleus. The formalism is illustrated by calculational results obtained from a potential model fitted to ¹⁶O + n scattering data.     

Application of infinite oscillator shell model calculations to the description of nuclear reactions

A simple R-matrix procedure is proposed to provide a means of using nuclear structure information, from calculations in an infinite oscillator well, to describe reaction cross sections. The procedure uses values for the channel radius parameters of the R-matrix theory that are extracted from knowledge of the structure and reaction properties of the neighbouring closed shell nucleus answering one of the main criticisms expressed concerning the dependence of the R-matrix on unphysical parameters. Application of the model to the scattering of neutrons from ¹⁵N and comparison to previous theoretical predictions are considered.     

Correlation between perturbation and collisional transfers in theA,B, C andb states of CO as revealed by high resolution lifetime measurements

Lifetimes and intensities of theA-X, B-A, C-A andb-a systems in CO have been measured at high spectral resolution using the High Frequency Deflection technique. Of special interest are the pressure effects observed in theA-X andb-a transitions, both as a function of the partial pressure of CO and as a function of added catalyst gas such as argon, helium and CO₂. The nature of these pressure effects are examined with the conclusion that resonance induced collision exchange takes place between theA orb states and other states that strongly perturb them. In particular, the collision exchange cross section estimated for theA state is unusually large, being the order of 10^?7 to 10^?8 cm³/s, mol. In contrast, theB andC (Rydberg) states, which are not known to be highly perturbed, showed no evidence of collision induced exchange. In addition, calculations on Franck-Condon factors and ¯r centroids have been carried out for each of the bands studied. Transition moments and oscillator strengths are also extracted from these calculations and from the new data presented in this paper, and considerable discrepancies to earlier values in the literature are found in some cases.     

Electron impact excitation collision strengths for neon-like Ni XIX calculated using the relativistic R-matrix method

In a recent paper [Pramana — J. Phys. 64, 129 (2005)] results have been presented for electron impact excitation collision strengths for transitions among the fine-structure levels of the 2s²2p⁶ and 2s²2p⁵3s configurations of Ni XIX. In this paper we demonstrate through an independent calculation with the relativistic R-matrix code that those results are unreliable and the conclusions drawn are invalid.     

Electron impact excitation of Ni XIX using theR-matrix method

Collision strengths for all the transitions between the 15 lowest states of neon-like Ni XIX have been calculated for electron impact in the 80–140 Ry energy range. Configuration-interaction wavefunctions have been used to represent the target states. The standardR-matrix code has been used to calculate the lower scattering partial waves (L≤9), while a no-exchange version of the same code has been used to compute efficiently the higher partial waves (L≥10). Effective collision strengths for 105 excitation transitions between the ground state 2s ²2p ^{6 1} S ^e and the 142s ²2p ⁵3l Rydberg states are tabulated for electron temperatures in the range logT=5.40 to logT=7.00, withT expressed in °K.     

Electron impact excitation of the resonance transitions of highly ionized atoms of the Be-, Mg-, and Zn-isoelectronic sequences

Electron impact excitation collision strengths for the ns²¹S - nsnp¹P resonance transitions of highly ionized Be, Mg, and Zn-like ions have been computed in the distorted wave approximation, including the effects of exchange and target state correlation. Good agreement is observed between these data and collision strengths computed in the Coulomb-Born and Born approximations at high incident energies. Analytic fits to the distorted wave data are presented.     

Radiative rates and electron impact excitation rate coefficients for H-like Fe XXVI

In this paper we report on calculations on energy levels, radiative rates, collision strengths, and effective collision strengths for transitions among the lowest 36 levels of the n≤6 configurations of H-like Fe XXVI. Flexible atomic code (FAC) is adopted for the calculation. Energy levels and radiative rates are calculated within relativistic configuration-interaction method. Direct excitation collision strength is calculated using relativistic distorted-wave approximation. Resonance contributions through the relevant He-like doubly excited n^′l^′n^″l^″ configurations with n^′≤7 and n^″≤75 are explicitly taken into account using the isolated process and isolated resonances approximation. We present the radiative rates, oscillator strengths, and line strengths for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among the 36 levels. Furthermore, collision strengths and effective collision strengths are reported for all the 630 transitions among the above 36 levels over a wide energy (temperature) range up to 25 keV . Extensive comparisons are made with earlier available results and the accuracy of the data is assessed.     

On universal R-matrices at roots of unity

It is well-known that quantum algebras at roots of unity are not quasi-triangular. They indeed do not possess an invertible universalR-matrix. They have, however, families of quotients, on which no obstructiona priori forbids the existence an universalR-matrix. In particular, the universalR-matrix of the so-called finite dimensional quotient is already known. We try here to answer the following questions: are most of these quotients equivalent (or Hopf equivalent)? Can the universalR-matrix of one be transformed to the universalR-matrix of another using isomorphisms?     

A generalization of Wigner's R-matrix method

A generalization of the Wigner's non-relativistic R-matrix theory of scattering by a central potential field is proposed. The idea is to use an R-matrix expansion basis generated by a Sturm-Liouville problem with an eigenparameter included both in a differential equation and in a boundary condition (in the standard theory an R-matrix basis is obtained by solving an eigenvalue problem with fixed boundary conditions). A partial fraction expansion of an R^(η)-matrix introduced is derived and shown to converge faster than a partial fraction expansion of Wigner's R-matrix used in the standard theory.     

Radiative capture of low-energy neutrons in the shell-model approach to nuclear reactions

The shell-model approach to photonuclear reactions is applied to the radiative capture of low-energy neutrons. The direct, compound and channel resonant contributions to the collision matrix appear in a natural way. We show that the experimental data in the vicinity of the 3s giant resonance can be quantitatively interpreted in terms of the channel resonant capture. The relationship with the R-matrix approach of Lane and Lynn is discussed.     

Collision-strength dependence of solar emission lines of Si(X) and S(XII)

We have calculated the normalized populations of 15 levels in Si(X) and S(XII) ions in an optically thin medium, under steady-state condition, by using (i) constant collision strengths computed at the incident electron energy kT_e and (ii) incident electron-energy-dependent collision strengths. To calculate intensity ratios for solar emission lines, one may use constant collision strengths at the electron energy E'.     

C 1s near edge X-ray absorption fine structure (NEXAFS) of substituted benzoic acids—A theoretical and experimental study

Ab initio calculations are performed to explain the discrete transitions in experimental C 1s-NEXAFS (near edge X-ray absorption fine structure) spectra of various benzoic acid derivates. Transition energies and oscillator strengths of the contributing C 1s–π^* excitations are computed using the ADC(2) (second-order algebraic-diagrammatic construction) method. This method is demonstrated to be well suited for the finite electronic systems represented by these simple organic acids. There is good agreement between experiment and theory reproducing all the relevant spectral features. Some transitions can only be assigned based on a theoretical foundation. Remaining discrepancies between experimental and computed spectra are discussed.