Relativistic radiatively damped R -matrix calculations of the electron-impact excitation of helium-like iron and krypton

Electron-impact excitation data for He-like ions are of significant importance for diagnostic applications to both laboratory and astrophysical plasmas. Here we report on the first fully relativistic R -matrix calculations with radiation damping for the He-like ions Fe 24+ and Kr 34+ . Effective collision strengths for these two ions have been determined with and without damping over a wide temperature range for all transitions between the 49 levels through n = 5. We find that damping has a pronounced effect on the effective collision strengths for excitation to some of the low-lying levels, but its effect on excitation to the vast majority of levels is small. At the energy of a resonance peak, we also investigate the effect of radiation damping on the angular distribution of scattered electrons. Finally, we compare our results for Fe 24+ with an earlier intermediate coupling frame transformation R -matrix calculation with radiation damping by Whiteford et al ( J. Phys. B: At. Mol. Opt. Phys. 34 3179) and find good agreement, especially for excitation to the lower levels.

Intermediate-coupling R -matrix calculations of electron-impact excitation of Fe 5+

For applications to laboratory and astrophysical plasmas, there is a great need for accurate electron-impact excitation data between individual levels in the lower charge-state ions of iron. Recently, we have reported on the first intermediate-coupling R -matrix calculation of electron-impact excitation in Fe 4+ , in which the close-coupling expansion of the target included levels from both ground and excited configurations (Ballance et al 2007 J. Phys. B: At. Mol. Opt. Phys. [/0953-4075/40/23/f01] 40 F327 , 2008 Europhys. News 39 14). In this paper, we present the results of two large intermediate-coupling Dirac R -matrix calculations of electron-impact excitation of Fe 5+ . The results from the two calculations, which differ only in the configuration–interaction expansions of the target, are compared. These comparisons provide some indication of the accuracy of the calculations and the resulting data should be useful in modelling plasmas containing iron.

Electron-impact excitation of Fe2: a comparison of intermediate coupling frame transformation, Breit-Pauli and Dirac R-matrix calculations

Modeling the spectral emission of low-charge iron group ions enables the diagnostic determination of the local physical conditions of many cool plasma environments such as those found in H II regions, planetary nebulae, active galactic nuclei etc. Electron-impact excitation drives the population of the emitting levels and, hence, their emissivities. By carrying-out Breit-Pauli and intermediate coupling frame transformation (ICFT) R-matrix calculations for the electron-impact excitation of Fe$^{2+}$ which both use the exact same atomic structure and the same close-coupling expansion, we demonstrate the validity of the application of the powerful ICFT method to low-charge iron group ions. This is in contradiction to the finding of Bautista et al. [Ap.J.Lett, 718, L189, (2010)] who carried-out ICFT and Dirac R-matrix calculations for the same ion. We discuss possible reasons.

Relativistic radiatively damped R-matrix calculation of the electron-impact excitation of W46+

The current design plans for the International Thermonuclear\nExperimental Reactor ( ITER) call for tungsten to be employed for\ncertain plasma facing components in the divertor region. Thus, accurate\natomic collision data are needed for emission modelling of tungsten.\nElectron-impact excitation and radiative rates are of particular\nimportance for Ni-like W, since this ion emits some of the most intense\nspectral lines of all ionization stages. We report on a fully\nrelativistic 115-level R-matrix calculations of W46+, which includes the\neffects of radiation damping. Although radiation damping is very\nimportant in most highly ionized species, its effects are reduced in\nthis case because of the closed-shell Ni-like ground state. The rates\nfrom these relativistic atomic calculations will be employed for\ncollisional-radiative modelling of this ion.

Electron-impact excitation of Fe 4+ : an intermediate-coupling R -matrix calculation

For a number of years, there has been a major effort to calculate electron-impact excitation data for every ion stage of iron embodied by the ongoing efforts of the IRON project by Hummer et al (1993 Astron. Astrophys. 279 298). Due to the complexity of the targets, calculations for the lower stages of ionization have been limited to either intermediate-coupling calculations within the ground configurations or LS -coupling calculations of the ground and excited configurations. However, accurate excitation data between individual levels within both the ground and excited configurations of the low charge-state ions are urgently required for applications to both astrophysical and laboratory plasmas. Here we report on the results of the first intermediate-coupling R -matrix calculation of electron-impact excitation for Fe 4+ for which the close-coupling (CC) expansion includes not only those levels of the 3d 4 ground configuration, but also the levels of the 3d 3 4s, 3d 3 4p, 3d 3 4d and 3d 2 4s 2 excited configurations. With 359 levels in the CC expansion and over 2400 scattering channels for many of the J Π partial waves, this represents the largest electron–ion scattering calculation to date and it was performed on massively parallel computers using a recently developed set of relativistic parallel R -matrix programs.

An R-matrix approach for plasma modelling and the interpretation of astrophysical observation

Over the last decade an Auburn-Rollins-Strathclyde consortium has developed several suites of parallel R-matrix codes [1, 2, 3] that can meet the fundamental data needs required for the interpretation of astrophysical observation and/or plasma experiments. Traditionally our collisional work on light fusion-related atoms has been focused towards spectroscopy and impurity transport for magnetically confined fusion devices. Our approach has been to provide a comprehensive data set for the excitation/ionization for every ion stage of a particular element. As we progress towards a burning fusion plasma, there is a demand for the collisional processes involving tungsten, which has required a revitalization of the relativistic R-matrix approach. The implementation of these codes on massively parallel supercomputers has facilitated the progression to models involving thousands of levels in the close-coupling expansion required by the open d and f sub-shell systems of mid Z tungsten. This work also complements the electron-impact excitation of Fe-Peak elements required by astrophysics, in particular the near neutral species, which offer similar atomic structure challenges. Although electron-impact excitation work is our primary focus in terms of fusion application, the single photon photoionisation codes are also being developed in tandem, and benefit greatly from this ongoing work.

Dirac R -matrix calculations of electron-impact excitation of neon-like krypton

We have employed the Dirac R -matrix method to determine electron-impact excitation cross sections and effective collision strengths in Ne-like Kr 26+ . Both the configuration-interaction expansion of the target and the close-coupling expansion employed in the scattering calculation included 139 levels up through n = 5. Many of the cross sections are found to exhibit very strong resonances, yet the effects of radiation damping on the resonance contributions are relatively small. Using these collisional data along with multi-configuration Dirac–Fock radiative rates, we have performed collisional-radiative modeling calculations to determine line-intensity ratios for various radiative transitions that have been employed for diagnostics of other Ne-like ions.

An R -matrix with pseudo-states calculation of electron-impact excitation in C 2 +

We have performed an R-matrix with pseudo-states (RMPS) calculation of electron-impact excitation in C2+.Collision strengths and effective collision strengths were determined for excitation between the lowest 24 terms, including all those arising from the 2s3l and 2s4l configurations. In the RMPS calculation, 238 terms (90 spectroscopic and 148 pseudo-state) were employed in the close-coupling (CC) expansion of the target. In order to investigate the significance of coupling to the target continuum and highly excited bound states, we compare the RMPS results with those from an R-matrix calculation that incorporated all 238 terms in the configuration- interaction expansion, but only the lowest 44 spectroscopic terms in the CC expansion. We also compare our effective collision strengths with those from an earlier 12-state R-matrix calculation (Berrington et al 1989 J. Phys. B: At.Mol. Opt. Phys. 22 665). The RMPS calculation was extremely large, involving (N +1)-electron Hamiltonian matrices of dimension up to 36 085, and required the use of our recently completed suite of parallel R-matrix programs. The full set of effective collision strengths fromourRMPS calculation is available at theOakRidgeNationalLaboratoryControlledFusion Atomic Data Center web site. 1.

Vibrational excitation of the N2+ first negative (0,0), (1,0) and (2,0) bands by electron impact: a theoretical study using the R-matrix approach

Ab initio cross section calculations for vibronic excitation using the R -matrix approach have been performed on the N 2 + molecular ion complex. A three-state close-coupling expansion is used where the electronic target states; X 2 g + , A 2 u and B 2 u + of the molecular cation are represented by a valence configuration-interaction approximation. A non-adiabatic approximation is invoked to study vibronic excitation for the first three negative bands, (0,0), (1,0) and (2,0) of the X-B transition (B 2 u + v ´ X 2 g + v ´´ ) of N 2 + . Fixed-nuclei and non-adiabatic cross section results are compared with the available experimental data for the (0,0) band and the breakdown of the adiabatic fixed-nuclei approximation is clearly evident for the vibronic excitation of the (1,0) and (2,0) bands in this molecular ion complex.

Electron-impact ionization of argon using the R-matrix with a pseudo-states method

Electron-impact ionization cross sections for argon are calculated using both non-perturbative R-matrix with pseudo-states (RMPS) and perturbative distorted-wave methods. At twice the ionization potential, the 3p(61)S ground-term cross section from a distorted-wave calculation is found to be a factor of 4 above crossed-beams experimental measurements, while with the inclusion of term-dependent continuum effects in the distorted-wave method, the perturbative cross section still remains almost a factor of 2 above experiment. In the case of ionization from the metastable 3p(5)4s(3)P term, the distorted-wave ionization cross section is also higher than the experimental cross section. On the other hand, the ground-term cross section determined from a nonperturbative RMPS calculation that includes 27 LS spectroscopic terms and another 282 LS pseudo-state terms to represent the high Rydberg states, and the target continuum is found to be in excellent agreement with experimental measurements, while the RMPS result is below the experimental cross section for ionization from the metastable term. We conclude that both continuum term dependence and interchannel coupling effects, which are included in the RMPS method, are important for ionization from the ground term, and interchannel coupling is also significant for ionization from the metastable term

A radiation-damped R -matrix approach to the electron-impact excitation of helium-like ions for diagnostic application to fusion and astrophysical plasmas

Electron-impact excitation collision strengths for transitions between all singly excited levels up to the n = 4 shell of helium-Eke argon and the n = 4 and 5 shells of helium-like iron have been calculated using a radiation-damped R-matrix approach. The theoretical collision strengths have been examined and associated with their infinite-energy limit values to allow the preparation of Maxwell-averaged effective collision strengths. These are conservatively considered to be accurate to within 20% at all temperatures, 3 x 10(5)-3 x 10(8) K forAr(16+) and 10(6)-10(9) K for Fe24+. They have been compared with the results of previous studies, where possible, and we find a broad accord. The corresponding rate coefficients are required for use in the calculation of derived, collisional-radiative, effective emission coefficients for helium-like lines for diagnostic application to fusion and astrophysical plasmas. The uncertainties in the fundamental collision data have been used to provide a critical assessment of the expected resultant uncertainties in such derived data, including redistributive and cascade collisional-radiative effects. The consequential uncertainties in the parts of the effective emission coefficients driven by excitation from the ground levels for the key w, x, y and z lines vary between 5% and 10%. Our results remove an uncertainty in the reaction rates of a key class of atomic processes governing the spectral emission of helium-like ions in plasmas.

Valence and L-shell photoionization of Cl-like argon using R-matrix techniques

Photoionization cross-sections are obtained using the relativistic DiracAtomic R-matrix Codes (DARC) for all valence and L-shell energy ranges between 27 and 270 eV. A total of 557 levels arising from the dominant configurations 3s²3p⁴, 3s³p5, 3p⁶, 3s²3p³[3d, 4s, 4p], 3p⁵3d, 3s²3p²3d², 3s³p4³d, 3s³p3³d2 and 2s²2p⁵3s²3p⁵ have been included in the targetwavefunction representation of the Ar III ion, including up to 4p in the orbital basis. We also performed a smaller Breit-Pauli (BP) calculation containing the lowest 124 levels. Direct comparisons are made with previous theoretical and experimental work for both valence shell and L-shell photoionization. Excellent agreement was found for transitions involving the ²P^o initial state to all allowed final states for both calculations across a range of photon energies. A number of resonant states have been identified to help analyse and explain the nature of the spectra at photon energies between 250 and 270 eV.

Photoionization of Cl-like Argon using the Breit-Pauli R-matrix method

Here we present the photoionization cross sections for the ground and metastable states of Cl-like Argon by exploiting the fully relativistic Breit-Pauli R-matrix computer codes to determine these transitions of interest. We compare our work with previous theoretical and experimental results and present a detailed investigation into the model of Ar III, the resonant structure and identification process.

Comparison of Parallelised R-matrix codes for electron impact excitation of Cr II

A comparison of collision strengths and effective collision strengths has been undertaken for the Cr II ion based on the model of Wasson et al [2010 A & A. 524 A35]. Calculations have been completed using the Breit-Pauli, RMATRX II and DARC suites of codes.

Spectra of graphs obtained by a generalization of the join graph operation

Taking a Fiedler’s result on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional consequences are explored, namely regarding the largest eigenvalue and algebraic connectivity.