Breit-Pauli R-matrix Research Articles

Oscillator strengths and transition probabilities from the Breit–Pauli R-matrix method: Ne IV

The atomic parameters–oscillator strengths, line strengths, radiative decay rates (A), and lifetimes–for fine structure transitions of electric dipole (E1) type for the astrophysically abundant ion Ne IV are presented. The results include 868 fine structure levels with n≤ 10, l≤ 9, and 1/2≤J≤ 19/2 of even and odd parities, and the corresponding 83,767 E1 transitions. The calculations were carried out using the relativistic Breit–Pauli R-matrix method in the close coupling approximation. The transitions have been identified spectroscopically using an algorithm based on quantum defect analysis and other criteria. The calculated energies agree with the 103 observed and identified energies to within 3% or better for most of the levels. Some larger differences are also noted. The A-values show good to fair agreement with the very limited number of available transitions in the table compiled by NIST, but show very good agreement with the latest published multi-configuration Hartree–Fock calculations. The present transitions should be useful for diagnostics as well as for precise and complete spectral modeling in the soft X-ray to infra-red regions of astrophysical and laboratory plasmas.

ELECTRON IMPACT EXCITATION COLLISION STRENGTHS FOR EXTREME ULTRAVIOLET LINES OF Fe VII

Extensive calculations have been performed for electron impact excitation collision strengths and oscillator strengths for the Fe VII extreme ultraviolet lines of astrophysical importance. The collision strengths for fine-structure transitions are calculated in the B-spline Breit-Pauli R-matrix approach. The target wavefunctions have been calculated in the multiconfiguration Hartree-Fock method with term-dependent non-orthogonal orbitals. The close-coupling expansion includes 189 fine-structure levels of Fe VII belonging to terms of the ground 3p 63d 2 and excited 3p 53d 3, 3p 63d4l, 3p 63d5s, and 3p 63d5p configurations. The effective collision strengths are determined from the electron excitation collision strengths by integration over a Maxwellian distribution of electron velocities. The effective collision strengths are provided for 17766 fine-structure transitions at electron temperatures from 104 to 107 K. Our results normally agree with the previous R-matrix frame-transformation calculations by Witthoeft & Badnell. However, there are important differences for some transitions with the previous calculations. The corrections to the previous results are mainly due to more extensive expansions for the Fe VII target states.

EFFECTIVE COLLISION STRENGTHS FOR FINE-STRUCTURE TRANSITIONS IN Si VII

The effective collision strengths for electron-impact excitation of fine-structure transitions in Si vii are calculated as a function of electron temperature in the range 5000–2,000,000 K. The B-spline Breit–Pauli R-matrix method has been used to calculate collision strengths by electron impact. The target wave functions have been obtained using the multi-configuration Hartree–Fock method with term-dependent non-orthogonal orbitals. The 92 fine-structure levels belonging to the 46 LS states of 2s22p4, 2s2p5, 2p6, 2s22p33s, 2s22p33p, 2s22p33d, and 2s2p43s configurations are included in our calculations of oscillator strengths and collision strengths. There are 4186 possible fine-structure allowed and forbidden transitions among the 92 levels. The present excitation energies, oscillator strengths, and collision strengths have been compared with previous theoretical results and available experimental data. Generally, a good agreement is found with the 6 LS-state close-coupling approximation results of Butler & Zeippen and the 44 LS-state distorted wave calculation of Bhatia & Landi.

Photoionization of fine structure levels of Ne IV

Study of characteristic features in photoionization of a large number of excited levels of Ne IV, (hν+Ne IV→Ne V+e), using ab initio Breit–Pauli R-matrix (BPRM) method, is presented. This is the second large atomic system, after Fe XVII, for which BPRM method has been used for a full scale computation of photoionization cross sections for a large number of bound levels (N⩽10). The study include features, such as, of Seaton resonances due to photo-excitation-of-core and new near threshold resonant features. Coupling of fine structure channels due to relativistic effects is found to introduce low energy resonances near threshold, not allowed in LS coupling approximation. These resonances play crucial role for low temperature recombination rates. Photoionization cross sections (σPI) for the largest set of levels of Ne IV, a total of 868, with n⩽10 and l⩽9 are presented. A wave function expansion optimized with 24 configurations with orbitals going up to 4p of core Ne V was used. Resonances due to Rydberg series of autoionizing states belonging to various core excited core levels are resolved with fine energy mesh. Details of resonant structures and enhanced background due to Seaton resonances are elaborated in this first study of the ion with relativistic effects.

Inner-shell photoionization of atomic chlorine

Relative partial cross sections have been measured following photoexcitation of atomic chlorine near the Cl 2p and Cl 1s ionization thresholds. In addition, Breit-Pauli R-matrix calculations have been carried out in the region of the 2p thresholds, and the results are compared with experiment. Owing to angular-momentum considerations, it was found that the resonances associated with the higher 2p(-1) thresholds should be significantly wider than the lower ones, and this is borne out in both the experimental and the theoretical results. It is shown that a large number of resonance series contribute to the cross section, which make it difficult to untangle, and suggestions for further work to better understand the spectra are presented.

Fine-structure energy levels and autoionizing width calculations of magnesium-like Ni XVII

We have calculated highly excited fine-structure energy levels and their autoionizing width of 3pns3P1 (n = 11–26), 3pns1P1 (n = 10–22), 3pnd3D1 (n = 11–26), 3pnd3P1 (n = 10–21), 3pnd1P1(n = 10–21), 3dnp3D1 (n = 7–30), 3dnp3P1 (n = 7–28), 3dnp1P1 (n = 7–28), 3dnf3D1 (n = 7, 9–27), 3dnf3P1 (n = 7, 9–27), and 3dnf1P1 (n = 7, 9–27) for magnesium-like Ni XVII. The calculations are based upon the relativistic Breit-Pauli R-matrix approximation combining with the QB method of Quigley-Berrington (L. Quigley, K. A. Berrington, Pelan J. Comput. Phys. Commun. 114, 225 (1998)). We have reported the many unpublished energy values and autoionizing width of the J = 1 odd states of magnesium-like Ni XVII.

Evaluation of Electron Impact Excitation Data Along Isoelectronic Sequences

R-matrix calculations of electron impact excitations have been done for several isoelectronic sequences under the program of the Atomic Processes for Astrophysical Plasmas network in the United Kingdom. The intermediate-coupling framework transformation R-matrix approach was used to generate data in this program since it is less resource (time/memory) demanding than the full Breit-Pauli R-matrix method, without reduction of accuracy. A detailed accuracy assessment was done for four/five/six selected ions spanning the isoelectronic sequence, which provides insight into the behavior of the whole sequence of ions. For each ion, we adopted the following procedure: First, the target structure was assessed by comparing the calculated level energies with available experimental data and with previous calculations using different methods. Second, weighted oscillator strengths or line strengths or radiative decay rates were compared with various available theoretical works for several transitions. Usually, a “survey” comparison with another database has been done for all available transitions by way of a scatter plot. Finally, direct comparison for the excitation (effective) collision strength is done with available measurements or with previously published data. A survey comparison with another database is usually presented to investigate the spread of the consistency or inconsistency among the different calculations.

Photoionization and photoabsorption of Li-like neon near 1s2p(1P)2s 2P autoionizing states

Davies–Seaton radiative damping theory (Davies and Seaton 1969 J. Phys. B: At. Mol. Phys. 2 757) is precisely applied to Li-like neon photoionization/photoabsorption data computed by the Breit–Pauli R-matrix code, for photon energies near the 1s2p(1P)2s 2P autoionizing states. Damping effects are responsible for the separation between photoionization and photoabsorption cross-sections of 1s2ns 2S1/2 n = 2, 3, 4, 5…. The R-matrix code presently used, enables us to compare with similar data for photoionization obtained by the complex potential method of Robicheaux et al (1995 Phys. Rev. A 52 1319), and photoabsorption obtained by the Hickman–Robicheaux method (Gorczyca and Robicheaux 1999 Phys. Rev. A 60 1216).

Photoionization and photoabsorption cross sections for the aluminum iso-nuclear sequence

K-shell photoionization and photoabsorption cross sections are presented for Li-like to Na-like Al. The calculations are performed using the Breit–Pauli R-matrix method where the effects of radiation and Auger dampings are included. We provide electronic data files for the raw cross sections as well as those convolved with a Gaussian of width ΔE/E=10−4. In addition to total cross sections for photoabsorption and photoionization, partial cross sections are available for photoionization.

Photoionization of Ar XVI and Ar XVII

Photoionization of Li-like argon, (hν+ArXVI→ArXVII+e), and He-like argon, (hν+ArXVII→ArXVIII+e), are studied using the relativistic Breit–Pauli R-matrix (BPRM) method. Results include both the partial and total photoionization cross-sections of fine structure levels with 1/2≤J≤17/2, n≤10 and 0≤l≤9 of Ar XVI and with 0≤J≤10, n≤10 and 0≤l≤9 of Ar XVII. They correspond to 98 bound levels of Ar XVI and 191 of Ar XVII. The close coupling wave function expansion for Ar XVI included 17 core levels up to n=3 thresholds and that of Ar XVII 16 core levels up to n=4 thresholds. Because of high-lying core excitations of these ions, the photoionization cross-section, σPI(nSLJ), decreases monotonically without features until at high energies where narrow high-peak resonances of Rydberg series of autoionizing states belonging to excited n=2 thresholds begin to appear. The dominant photoexcitation-of-core (PEC) or Seaton resonances also appear in the excited level cross-sections. The background of the total cross-section shows enhancement at n=2 thresholds due to resonant 1s–2p core excitations. However, the resonances become much weaker beyond n=2 thresholds. Radiation damping of resonances, important for these highly charged He- and Li-like ions, is included. These cross-sections are much improved over the existing TOPbase cross-sections where resonances, and background enhancements for Ar XVII were not included. With consideration of these effects, the present results should be accurate up to 10%–30% for various applications in modeling, recombination rates, opacities and diagnostic spectral analysis in the ultraviolet and X-ray regions. Cross-sections for H-like Ar are also included for completeness.

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.

Fine structure transitions in Fe XIV

Results are reported for Fe XIV energy levels and transitions obtained from the ab initio relativistic Breit–Pauli R-matrix (BPRM) method. BPRM method developed under the Iron Project is capable of calculating very large number of fine structure energy levels and corresponding transitions. However, unlike in the atomic structure calculations, where levels are identified spectroscopically based on the leading percentage contributions of configurations, BPRM is incapable of such identification of the levels and hence the transitions. The main reason for it is that the percentage contributions can not be determined exactly from the large number of channels in the R-matrix space. The present report describes an identification method that uses considerations of quantum defects of channels, contributions of channel from outer regions, Hund’s rule, and angular momenta algebra for addition and completeness of fine structure components. The present calculations are carried out using a close coupling wave function expansion that included 26 core excitations from configurations 2s22p63s2, 2s22p63s3p,2s22p63p2,2s22p63s3d, and 2s22p63p3d. A total of 1002 fine structure levels with n⩽10, l⩽9, and 0.5⩽J⩽9.5 with even and odd parities and the corresponding 130,520 electric dipole allowed (E1) fine structure transitions, a most complete set for astrophysical modelings of spectral analysis and opacities, is presented. Large number of new energy levels are found and identified. The energies agree very well, mostly in less than 1% with the highest being 1.9%, with the 68 observed fine structure levels. While the high lying levels may have some uncertainty, an overall accuracy of energy levels should be within 10%. BPRM transitions have been benchmarked with the existing most accurate calculated transition probabilities with very good agreement for most cases. Based on the accuracy of the method and comparisons, most of the transitions can be rated with A (⩽10%) to C (⩽30%).

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.

Photoionization Cross-Section of Chlorine-like Iron

Semi-relativistic calculations are performed for the photoionization of Fe X (an important coronal ion) from its ground state 3s23p\(^{5}(^{2}P^{0}_{3/2})\) and the first two excited states 3s23p\(^{5}(^{2}P^{0}_{1/2})\) and 3s3p\(^{6}(^{2}S_{1/2})\) using the Breit–Pauli R-matrix method. A lowest 41 state eigenfunction expansion for Fe XI is employed to ensure an extensive treatment of auto ionizing resonances that affect the effective cross-sections. In the present calculations, we have considered all the important physical effects like channel coupling, exchange and short range correlation. The present calculations using the lowest 41 target levels of Fe XI in the LSJ coupling scheme are reported and we expect that the present results should enable more accurate modelling of the emission spectrum of highly excited plasma from the optical to the far UV region.

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.

Improved collision strengths and line ratios for forbidden [O iii] far-infrared and optical lines

ABSTRACT Far-infrared and optical [O iii] lines are useful temperature–density diagnostics of nebular as well as dust obscured astrophysical sources. Fine-structure transitions among the ground state levels 1 s22 s22 p33 P 0,1,2 give rise to the 52- and 88-m lines, whereas transitions among the 3 P 0,1,2, 1 D 2, 1 S 0 levels yield the well-known optical lines λλ4363, 4959 and 5007 Å. These lines are excited primarily by electron impact excitation. However, despite their importance in nebular diagnostics collision strengths for the associated fine-structure transitions have not been computed taking full account of relativistic effects. We present Breit–Pauli R-matrix calculations for the collision strengths with highly resolved resonance structures. We find significant differences of up to 20 per cent in the Maxwellian averaged rate coefficients from previous works. We also tabulate these to lower temperatures down to 100 K to enable determination of physical conditions in cold dusty environments such photodissociation regions and ultraluminous infrared galaxies observed with the Herschel Space Observatory. We also examine the effect of improved collision strengths on temperature- and density-sensitive line ratios.

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.

Breit-Pauli oscillator strengths and electron excitation collision strengths for Si VIII

Aims. Oscillator strengths and electron impact excitation collision strengths for transitions between the 68 fine-structure levels of the 2s22p3, 2s2p4, 2p5, 2s22p23s, 2s22p23p, 2s22p23d and 2s2p33s configurations in Si VIII are calculated. Thermally averaged collision strengths are presented as a function of electron temperature for application to solar and other astrophysical plasmas. Methods. The collision strengths have been calculated using the B-spline Breit-Pauli R-matrix method for allowed and forbidden transitions in Si VIII. The relativistic effects have been incorporated through mass, Darwin and spin-orbit one-body operators in the Breit-Pauli Hamiltonian in the scattering calculation, while in the calculation of oscillator strengths the one-body and two-body relativistic operators are included. Flexible non-orthogonal sets of spectroscopic and correlation radial functions are used to obtain accurate description of Si VIII levels and to represent the scattering functions. The 68 fine-structure levels of the 2s22p3, 2s2p4, 2p5, 2s22p23s, 2s22p23p, 2s22p23d and 2s2p33s configurations have been considered in both the radiative and scattering calculations. The present scattering calculations are more extensive than previous ones, leading to a total 2278 transitions between fine-structure levels. Results. The calculated excitation energies are in excellent agreement with experiment and represent an improvement over the previous calculations. The present collision strengths show reasonable agreement with the previously available R-matrix and distorted-wave calculations. The oscillator strengths for E1 transitions normally compare very well with previous calculations. The effective collision strengths are obtained by integrating total resonant and non-resonant collision strengths over a Maxwellian distribution of electron energies and these are presented over a wide temperature range from 104 to 4.0 × 106 K.