Oleg Zatsarinny

The B-spline R-matrix method for atomic processes: application to atomic structure, electron collisions and photoionization

The basic ideas of the B-spline R-matrix (BSR) approach are reviewed, and the use of the method is illustrated with a variety of applications to atomic structure, electron?atom collisions and photo-induced processes. Special emphasis is placed on complex, open-shell targets, for which the method has proven very successful in reproducing, for example, a wealth of near-threshold resonance structures. Recent extensions to a fully relativistic framework and intermediate energies have allowed for an accurate treatment of heavy targets as well as a fully nonperturbative scheme for electron-impact ionization. Finally, field-free BSR Hamiltonian and electric dipole matrices can be employed in the time-dependent treatment of intense short-pulse laser?atom interactions.

BSR: B-spline atomic R-matrix codes☆

Abstract BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron–atom and electron–ion scattering, and radiative processes such as bound–bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit–Pauli Hamiltonian. New version program summary Title of program: BSR Catalogue identifier: ADWY Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWY Program obtainable from: CPC Program Library, Queens University of Belfast, N. Ireland Computers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PC Operating systems under which the new version has been tested: UNIX, Windows XP Programming language used: FORTRAN 95 Memory required to execute with typical data: Typically 256–512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problem No. of bits in a word: 8 No. of processors used: 1 Has the code been vectorized or parallelized?: no No. of lines in distributed program, including test data, etc.: 69 943 No. of bytes in distributed program, including test data, etc.: 746 450 Peripherals used: scratch disk store; permanent disk store Distribution format: tar.gz Nature of physical problem: This program uses the R-matrix method to calculate electron–atom and electron–ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit–Pauli terms in the Hamiltonian. Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput. Phys. Comm. 92 (1995) 290].

The Virtual Atomic and Molecular Data Centre (VAMDC) Consortium

The Virtual Atomic and Molecular Data Centre (VAMDC) Consortium is a worldwide consortium which federates atomic and molecular databases through an e-science infrastructure and an organisation to support this activity. About 90% of the inter-connected databases handle data that are used for the interpretation of astronomical spectra and for modelling in many fields of astrophysics. Recently the VAMDC Consortium has connected databases from the radiation damage and the plasma communities, as well as promoting the publication of data from Indian institutes. This paper describes how the VAMDC Consortium is organised for the optimal distribution of atomic and molecular data for scientific research. It is noted that the VAMDC Consortium strongly advocates that authors of research papers using data cite the original experimental and theoretical papers as well as the relevant databases.

The use of basis splines and non-orthogonal orbitals in R-matrix calculations: application to Li photoionization

We present a new extended version of the R -matrix method for the calculation of continuum properties in which non-orthogonal orbitals are extensively used for describing both the target states and the R -matrix basis functions. In particular, a B -spline basis is used for the description of continuum states in the inner region and the target states may be obtained from independent calculations. This leads to a generalized eigenvalue problem but has the advantage of requiring much smaller bases for accurate representation of target wavefunctions and to achieve convergence in the close-coupling expansion. The present approach and its code are both applicable to a general atom and their efficiency for low-energy scattering processes is demonstrated by calculating the photoionization of Li. A detailed analysis of the resonance structure is given. Very good agreement with experimental data has been obtained, and considerable improvement in the description of resonances has been achieved in comparison with the standard R -matrix calculations.

A general program for computing angular integrals of the Breit-Pauli Hamiltonian with non-orthogonal orbitals

Abstract The BREIT_NO program performs the angular integrations necessary for expressing the matrix elements of the Breit–Pauli Hamiltonian as a linear combination of radial integrals. Any amount of non-orthogonality between the orbitals may be present leading to overlap factors in the matrix elements. The calculations follow the method based on the representation of configuration wave functions through the Slater determinants. All matrix elements for a given list of configuration states may be evaluated or for a selected subset. The program effectively reuses data obtained previously through the creation of a data bank for angular coefficients.

B-spline calculations of oscillator strengths in neutral argon

B-spline box-based multi-channel calculations of transition probabilities in Ar I are reported for energy levels up to n = 12. An individually optimized, term-dependent set of non-orthogonal valence orbitals is used to account for the strong term dependence in the one-electron orbitals. Energy levels and oscillator strengths for transitions from the 3p6 ground-state configuration as well as for transitions between excited states have been computed in the Breit–Pauli approximation. The agreement in the length and velocity gauges of the transition data and the accuracy of the binding energies are used to estimate the accuracy of our results, which are also compared with experimental and other theoretical data. It is shown that the present method can be used for accurate calculations of oscillator strengths for states with intermediate and high n-values, for which it is difficult to apply standard multi-configuration Hartree–Fock methods.

Near-infrared collisional radiative model for Xe plasma electrostatic thrusters: the role of metastable atoms

Mestastable Xe atoms play an important role in the collisional radiative processes of dense xenon plasmas, including those of electric thrusters for space vehicles. Recent measurements and calculations of electron-excitation processes out of the 5p56s J = 2 metastable state (1s5 state in Paschen notation) have allowed for the development of a collisional radiative model for Xe near-infrared (NIR) emissions based on the population of the metastable level through 2p?1s5 radiative transitions, and based on depopulation through electron-impact excitation. A modified plasma radiative model incorporating newly computed electron-impact excitation cross sections using both relativistic distorted wave and semi-relativistic Breit?Pauli B-Spline R-matrix methods is presented. The model applies to optically thin, low-density regions of the thruster plasma and is most accurate at electron temperatures below 10?eV. The model is tested on laboratory spectral measurements of the D55 TAL and BHT-200 Hall thruster plasma NIR radiation. The metastable neutral fraction is determined to rise from 0.1 to slightly above 1% as the electron temperature increases from ~2 to 10?eV, reaching a maximum around 15?eV. Electron temperatures derived with the modified model are approximately 20% lower than a previous version of the model that used an approximate approach to account for metastable population and line intensity enhancement.

Differential cross sections for low-energy elastic electron scattering from the CF3 radical

We report measurements of differential cross sections for elastic electron scattering from CF3. These experiments were performed at nine incident electron energies in the range 7?50?eV and over a scattered electron angular range of 20??135?. Where possible, results from the present measurements are compared with those from earlier R-matrix and Schwinger multichannel computations, as well as those from an extended independent atom model approach that were calculated as a part of the present study. Agreement with theory is generally good at energies above 20?eV, but for 20?eV and below the magnitude of the measured differential cross sections are significantly larger than those predicted by all the theories.

A B-spline Galerkin method for the Dirac equation

The B-spline methods Johnson and Sapirstein (1, 2) introduced into relativistic many-body perturbation the- ory have produced results of unprecedented accuracy (3). Essentially, the local non-orthogonal B-spline basis was transformed to an orthogonal orbital basis by the ap- plication of the Galerkin method to the Dirac equation over a finite interval (4). The resulting basis was fi- nite and effectively complete. Though the low-energy bound states were good approximations to solutions of the Dirac equation, no physical interpretation was impor- tant for continuum states. Rapidly oscillating solutions were observed but played a negligible role in the sum- mation over states in their applications (2). However, these spurious states perturbed the spectrum and slowed the convergence of quantum electrodynamic (QED) cal- culations. This led Shabaev et al. (5) to propose a dual kinetic balance basis similar to the basis Quiney et al. (6) employed with analytic Slater type functions. Bound- ary conditions were for the case of a finite nuclear-charge distribution, with the point nucleus considered as a lim- iting case. Different boundary conditions at the origin were proposed for positive and negative values ofand both large and small components were set to zero at the large r boundary. Recently Igarashi (7) investigated a variety of methods and boundary conditions. He pointed out that the four boundary conditions used by Froese Fischer and Parpia (8) were excessive and explored the use of B-splines of different order, kp and kq, as a way of avoiding spurious solutions. In a subsequent paper he concluded that kinetic balance also provided a good basis (9). No best method was identified. All his methods em- ployed analytic weighting factors to B-spline expansions in order to control the asymptotic properties of large and small components. R-matrix methods (see Ref.s (10, 11) for recent re- views) differ from the applications considered by the above authors in that zero boundary conditions at large r, such as proposed by Shabaev et al. (5), cannot be used. R-matrix theory assumes an inner region r a where exchange with an outer electron can be neglected. What is needed is a basis for the inner region that satisfies certain conditions at the r = a boundary. B-splines were very successfully employed in the non-relativistic R-matrix calculations (12), however, they cannot be used in the Dirac-based calculations when spurious states in the continuum spectrum are present. At the same time, the kinetically balanced bases lead to extensive compu- tational difficultes in many-electron calculations. Spline methods are based on approximation theory. The grid that is selected along with boundary condi- tions determine a piecewise polynomial space with a finite basis. The unique B-spline basis has many advantages (12, 13), but there are many possible bases. The trans- formation from a non-orthogonal basis to an orthogonal orbital basis depends on how the Galerkin method is ap- plied. In this letter we propose a simple method for the Dirac matrix equation and apply it to the calculation of the R-matrix boundary condition. All calculations are for a point nucleus so that results can be compared with exact solutions. Special attention is given to the bound- ary conditions. We also show the relationship between kinetic balance and the use of splines of different order. At large values of r, the non-relativistic Schrodinger equation has the same form as

B-spline R-matrix with pseudostates approach for electron impact excitation of atomic nitrogen

The B-spline R-matrix with pseudostates approach has been used to calculate excitation cross sections for the forbidden 2s22p34So–2Do, 2Po, 2s22p32Do–2Po and resonance 2s22p34So–2s22p23s4P, 2s2p44P, 2s22p24s4P and 2s22p23d4P transitions in atomic nitrogen for incident electron energies from threshold to 120 eV. The excitation of these transitions gives rise to prominent lines in the spectra of solar and planetary atmospheres. The 24 spectroscopic bound and autoionizing states together with 15 pseudostates are included in the close-coupling expansion. The pseudostates are chosen to approximate the loss of flux into the infinite number of bound and continuum states that are dipole coupled with ground configuration terms. The contribution of the ionization continuum is significant for resonance transitions. An accurate description of target wavefunctions has been obtained on the basis of non-orthogonal spectroscopic and pseudo-orbitals to adequately account for the correlation corrections and interactions. A comparison of calculated cross sections with the measured absolute direct excitation cross sections is presented. A good agreement with measured integral cross sections is noted except at 5 eV for the forbidden transition and 30 eV for the resonance transitions.