Collision Strengths For Transitions Research Articles

Electron-impact Excitation of Fe i

Abstract The Fe i spectra emitted by astrophysical sources contain information on plasma parameters such as chemical abundances and magnetic fields. However, to determine these parameters requires detailed plasma modeling, which in turn needs accurate atomic data for processes such as radiative decay and electron-impact excitation in Fe i. A lack of fine-structure resolved collision strengths for transitions in Fe i is addressed in this paper with the presentation of data obtained from a Dirac R-matrix calculation. The suitability of our choice of target description is shown, with our energies generally within 7% of literature values. Various A-values are compared with other theoretical and experimental results, and the quality of the collision strengths produced in this work demonstrated. A comparison of 300- and 1000-level close-coupling expansions is made, the latter shown to eliminate pseudoresonances in the collision strengths at electron energies between 0.5 and 1.0 Ry. Maxwell-averaged effective collision strengths are presented, and the convergence of our data is shown in the temperature range 1000–100,000 K.

Density dependence of intensity ratios of the 3d → 2p x-ray anisotropic emission from electron-beam excited Ar13+ ions

We investigate the ratio R of the intensity of the blended lines 3d3/2,5/2 → 2p3/2 over that of the resonance line 3d3/2 → 2p1/2 emitted by boron-like Ar13+ ions after impact excitation by an electron beam. We calculate R as a function of the electron density ne in the range 109–1013 cm−3, for incident-electron energies from 0.46 to 5.5 keV. The calculations take into account the anisotropy in the angular distribution of photon emission by considering several angles of observation θ relative to the electron beam direction. A detailed collisional-radiative model that involves 560 magnetic sublevels arising from the 12 configurations 2s22p, 2s2p2, 2p3, 2s23l, 2s2p3l and 2p23l (l = s, p, d) is used to determine the populations of upper sublevels of the lines. All basic atomic parameters needed in the calculations, including radiative transition probabilities and collision strengths for transitions between magnetic sublevels, are obtained from the flexible atomic code. The ratio R at the angle θ = 0° is found to be higher than that at θ = 90° by up to 43% for ne = 109 cm−3, but this difference drops with increasing density to become less than 10% above ∼8 × 1011 cm−3. The line 3d3/2 → 2p3/2 blended with 3d5/2 → 2p3/2 is found to enhance the anisotropy of R. The present calculations may be extended to non-Maxwellian hot plasmas having cylindrically symmetric electron velocity distributions, which would be useful for electron density diagnostics of such plasmas.

Collisional-radiative calculations for the J = 0−1 lasing line of neon-like germanium under anisotropic excitation conditions

A new asymmetry parameter characterizing the differences between the polarized π and σ gain components of the soft-x-ray J = 0–1 lasing line of neon-like ions is calculated in the case of Ge22+ assuming an electron distribution which is a weighted sum of an isotropic Maxwellian and a monoenergetic beam. Using a quasi steady-state collisional-radiative model, we determine in the weak amplification regime the relative populations of the upper M = 0 and lower magnetic sublevels of the lasing line as a function of electron density from 1020 to cm−3. This model includes inelastic and elastic collisional transitions, as well as spontaneous radiative decay between all the 337 M-sublevels arising from the 75 lowest-lying Ge22+ J-levels. The computations were performed for a temperature of the Maxwellian component between and K, a kinetic energy E0 and a fraction f of the beam component in the ranges and , respectively. The basic atomic data, such as level energies, radiative decay probabilities and inelastic collision strengths, were calculated with the flexible atomic code. However, some modifications of this code were made to get the collision strengths for transitions between M-sublevels due to impact with isotropic electrons as well as due to impact with an electron beam in the case of de-excitation. We find that the newly introduced asymmetry parameter may become significant under certain conditions of electron distribution corresponding to relatively low ( K) and E0 (3–6 keV). The results reported here may be useful in the evaluation of the polarization degree of the J = 0–1 x-ray laser output from a germanium plasma in the presence of fast directional electrons.

Radiative Rates and Electron Impact Excitation Rates for Transitions in He II

We report calculations of energy levels, radiative rates, collision strengths and effective collision strengths for transitions among the lowest 25 levels of the n ≤ 5 configurations of He II. The general-purpose relativistic atomic structure package (grasp) and Dirac atomic R-matrix code (darc) are adopted for the calculations. Radiative rates, oscillator strengths and line strengths are reported for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2) transitions among the 25 levels. Furthermore, collision strengths and effective collision strengths are listed for all 300 transitions among the above 25 levels over a wide energy (temperature) range up to 9 Ryd (10 5.4 K). Comparisons are made with earlier available results, and the accuracy of the data is assessed.

Energy levels, radiative rates and electron impact excitation rates for transitions in Be-like Cl XIV, K XVI and Ge XXIX

Results for energy levels, radiative rates and electron impact excitation (effective) collision strengths for transitions in Be-like Cl XIV, K XVI and Ge XXIX are reported. For the calculations of energy levels and radiative rates the general-purpose relativistic atomic structure package is adopted, while for determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code is used. Oscillator strengths, radiative rates and line strengths are listed for all E1, E2, M1 and M2 transitions among the lowest 98 levels of the configurations. Furthermore, lifetimes are provided for all levels and comparisons made with available theoretical and experimental results. Resonances in the collision strengths are resolved in a fine energy mesh and averaged over a Maxwellian velocity distribution to obtain the effective collision strengths. Results obtained are listed over a wide temperature range up to 10 K, depending on the ion.

Collision strengths for transitions of Ni XXI

In this paper, we use Dirac R-matrix theory to calculate the collision strengths for electron impact excitation of Ni XXI with the Dirac atomic R-matrix code (DARC), which includes contributions of resonances, channel coupling, and relativity. A DARC calculation has been performed for transitions among 86 levels of (1s2) 2s22p4, 2s2p5, 2p6 and 2s22p33l (l = 0, 1, 2) configurations of Ni XXI. The GRASP code has been adopted for the description of target. A comparison is made with the results of Bhatia et al. for the collision strengths of five incident energies, 85, 170, 255, 340, and 425 Ryd, which use distorted wave calculations that do not include channel coupling. Effective collision strengths are calculated by averaging collision strengths over a Maxwellian velocity distribution. The accuracy of our calculations is assessed.

Excitation cross-sections by electron impact for O V and O VI levels

Radiative atomic and electron impact excitation data for O V and O VI ions have been calculated. The radiative atomic data have been calculated with the AUTOSTRUCTURE code. Besides the onebody and the two-body fine structure interactions, the two-body non-fine structure operators of the Breit–Pauli Hamiltonian, namely contact spin–spin, two-body Darwin and orbit–orbit are incorporated in AUTOSTRUCTURE. The scattering problem has been treated in the Breit–Pauli distorted wave approximation using the same code AUTOSTRUCTURE .T he OV atomic calculations have been extended from 46 to 92 levels. We have calculated excitation cross-sections for the O V 2s 2 −2s2p and the O VI 2s−2p transitions at energies near the corresponding excitation threshold regions. We have also calculated collision strengths for transitions from the most important levels for collisional excitation at electron energies up to 120 Ry for O V and up to 140 Ry for O VI. Our results have been compared with the available theoretical/experimental ones and a satisfactory agreement has been found between them.

Energy levels, oscillator strengths, radiative decay rates, and fine structure collision strengths for Kr VII lines

Energy levels, line strengths, oscillator strengths, radiative decay rates and fine structure collision strengths are presented for six-times ionized krypton (Kr VII). The atomic data are calculated with the AUTOSTRUCTURE code, where relativistic corrections are introduced according to the Breit–Pauli distorted wave approach. We present calculations of atomic data for 40 fine-structure levels generated from nine configurations ((1s22s22p63s23p63d10)4s2, 4lnl′, n = 4, 5; l = 0, 1; and l′ ≤ 3) of the Zn-like Kr ion. Fine structure collision strengths for transitions from the ground and the first four excited levels are presented at six electron energies: 8, 15, 30, 45, 60, and 80 Ryd. Our atomic structure data are compared with the available experimental and theoretical results.

Collision strengths for transitions in Ni XIX

In this paper we present calculations of electron impact excitation collision strengths for transitions among the 89 fine-structure levels of the 2s22p6, 2s22p53l, 2s2p63l, 2s22p54l, and 2s2p64l configurations of Ni XIX, for which flexible atomic code (FAC) has been adopted. Comparisons are made with the earlier available results in the literature, and the anomalies observed have been discussed.

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.

New Accurate Oscillator Strengths and Electron Excitation Collision Strengths for N i

The nonorthogonal orbitals technique in a multiconfiguration Hartree-Fock approach is used to calculate oscillator strengths and transition probabilities of N(I) lines. The relativistic effects are allowed by means of Breit-Pauli operators. The length and velocity forms of oscillator strengths show good agreement for most transitions. The B-spline R-matrix with pseudostates approach has been used to calculate electron excitation collision strengths and rates. The nonorthogonal orbitals are used for an accurate description of both target wave functions and the R-matrix basis functions. The 24 spectroscopic bound and autoionizing states together with 15 pseudostates are included in the close-coupling expansion. 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. Thermally averaged collision strengths have been determined by integrating collision strength over a Maxwellian distribution of electron energies over a temperature range suitable for the modeling of astrophysical plasmas. The oscillator strengths and thermally averaged collision strengths are presented for transitions between the fine-structure levels of the 2s(sup 2)p(sup 3) (sup 4)S(sup 0), (sup 2)D(sup 0), (sup 2)P(sup 0), 2s2p(sup 4) (sup 4)P, 2s(sup 2)2p(sup 2)3s (sup 4)P, and (sup 2)P terms and from these levels to the levels of the 2s(sup 2)2p(sup 2)3p (sup 2)S(sup 0), (sup 4)D(sup 0), (sup 4)P(sup 0), (sup 4)S(sup 0), (sup 2)D(sup 0), (sup 2)P(sup 0),2s(sup 2)2p(sup 2)3s(sup 2)D, 2s(sup 2)2p(sup 2)4s(sup 4)P, (sup 2)P, 2s(sup 2)2p(sup 2)3d(sup 2)P, (sup 4)F,(sup 2)F,(sup 4)P, (sup 4)D, and (sup 2)D terms. Thermally averaged collision strengths are tabulated over a temperature range from 500 to 50,000 K.

Density dependence of the polarization of the 23P1 → 11S0 intercombination line emitted by helium-like neon excited by an electron beam

The linear polarization of the x-ray 1s2p3P1 → 1s21S0 intercombination line emitted by helium-like Ne8+ ion collisionally excited by a monoenergetic electron beam has been theoretically studied versus electron densities, from 109 to 5 × 1013 cm−3. In addition to direct excitation from the 1s2 ground level and radiative cascades from 1s3l higher levels, excitation from the 1s2s3S1 metastable level was included in the collisional–radiative model. Collision strengths for transitions between magnetic sublevels were computed at three incident electron energies above the 1s2 → 1s2l excitation threshold (68, 90 and 140 Ry, i.e. 925, 1225 and 1905 eV), using a semi-relativistic distorted-wave approximation for partial waves up to l = 40 and a Coulomb–Bethe top-up for higher l. For electron densities below 1010 cm−3, the intercombination line is found to be polarized between −49.1% and −41.0% in the range of impact energies chosen. With increasing density, the polarization degree rapidly decreases in absolute value to zero, then becomes positive. Similar results for the polarization of the 1s2s3S1 → 1s21S0 forbidden and 1s2p3P2 → 1s2s3S1 dipole-allowed lines are also given.

Effective Collision Strengths for Fine‐Structure Transitions in S i

Electron collisional excitation strengths for transitions between the 3s23p4 3P2,1,0, 1D2, and 1S0 levels and from these levels to the 58 fine-structure levels of the excited configurations of neutral sulfur are calculated using the B-spline R-matrix approach. The nonorthogonal orbitals are used for an accurate representation of both the target states and the R-matrix basis functions. The close-coupling expansion consists of the 27 spectroscopic bound and autoionizing target states that give rise to 63 fine-structure levels. We included the lowest 22 LS states of the 3s23p4, 3s23p34s, 3s23p34p, 3s23p33d, 3s23p34d, 3s23p34f, 3s23p35s, 3s23p35p, 3s23p36s, and 3s3p5 configurations, and five higher lying 3s23p3(2Po)4s 3Po, 1Po, 3s23p3(2Do)3d 3Po, 1Po, and 3s3p5 1Po states that have strong dipole connection with the ground terms. 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. The effective collision strengths are determined by integrating collision strengths over a Maxwellian distribution of electron energies. The effective collision strengths are tabulated for log T from 3.3 to 5.6 K suitable for applications in astrophysical plasma modeling.

Electron impact excitation of Fe XIII

Energy levels and radiative rates for transitions among the lowest 97 fine-structure levels belonging to the (1s 2 2s 2 2p 6 ) 3s 2 3p 2 , 3s3p 3 , 3s 2 3p3d, 3p 4 , 3s3p 2 3d and 3s 2 3d 2 configurations of Fe XIII have been calculated using the fully relativistic GRASP code. Additionally, collision strengths for transitions among these levels have been computed using the Dirac Atomic R-matrix Code (DARC) of Norrington & Grant ([CITE]). Radiative rates and oscillator strengths are tabulated for all allowed transitions among the 97 fine-structure levels, while collision strengths are reported for some transitions at a few energies above thresholds. Comparisons are made with the available results, and the accuracy of the data is assessed.

Effective collision strengths for transitions in singly ionized nitrogen

The R-matrix method has been used to calculate effective collision strengths for the electron-impact excitation of the carbon-like ion N II. The lowest 23 LS target states are included in the expansion of the total wavefunction, consisting of the nine n = 2 states with configurations 2 s 22p 2 and 2s2p 3 , along with 14 n = 3 states with configuration 2s 2 2p3l (l= s,p,d). The fine-structure collision strengths have been obtained by transforming to a jj-coupling scheme using Saraph's JAJOM program, and have been determined at a sufficiently fine energy mesh to delineate properly the resonance structure. Effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities. Results are presented for transitions among the 2s 2 2p 2 3 P, 1 D, 1 S and 2s2p 3 5 S levels for electron temperatures in the range log T e (K) = 2.0-5.1, appropriate for astrophysical applications.

Electron Impact Excitation of O VI

Energy levels and radiative rates for transitions among the lowest 24 fine-structure levels belonging to the 1s2nl (n ≤ 5) configurations of Li-like O VI have been calculated using the fully relativistic GRASP code. Additionally, collision strengths for transitions among these levels have been computed over a wide energy range below 63 Ry, using the Dirac Atomic R-matrix Code. Resonances have been resolved in a fine energy mesh in order to calculate the effective collision strengths. Results for radiative rates, collision strengths, and effective collision strengths are presented for all transitions. Comparisons with other available results are made, and the accuracy of the present data is assessed. Energy levels are expected to be accurate to within 1%, while other parameters are probably accurate to better than 20%.

Electron Impact Excitation of Mo XXXIV

Energy levels and radiative rates for transitions among the lowest 60 fine-structure levels belonging to the (1s2) 2s22p5, 2s2p6, and 2s22p43ℓ configurations of F-like Mo XXXIV have been calculated using the fully relativistic GRASP code. Additionally, collision strengths for transitions among these levels have also been computed over a wide energy range below 3200 Ry, using the Dirac Atomic R-matrix Code. Resonances have been resolved in a fine energy mesh in order to calculate the effective collision strengths. Results for radiative rates, collision strengths, and excitation rates are presented for transitions from the lowest three levels to higher lying states. Comparisons with other available results are made, and the accuracy of the present data is assessed. Energy levels are expected to be accurate to within 1%, while other parameters are probably accurate to better than 20%.

Electron Impact Excitation of C IV

Energy levels and radiative rates for transitions among the lowest 24 fine-structure levels belonging to the 1s2 nℓ (n ≤ 5) configurations of Li-like C IV have been calculated using the fully relativistic GRASP code. Additionally, collision strengths for transitions among these levels have been computed over a wide energy range below 28 Ry, using the Dirac Atomic R-matrix Code. Resonances have been resolved in a fine energy mesh in order to calculate the effective collision strengths. Results for radiative rates, collision strengths, and effective collision strengths are presented for all transitions. Comparisons with other available results are made, and the accuracy of the present data is assessed. Energy levels are expected to be accurate to within 1%, while other parameters are probably accurate to better than 20%.

Excitation rates for transitions in Ca XV

Collision strengths for transitions among the energetically lowest 46 fine-structure levels belonging to the (1s 2 ) 2s 2 2p 2 ,2 s2p 3 ,2 p 4 , and 2s 2 2p3' configurations of Ca XV are computed, over a wide electron energy range below 300 Ryd, using the Dirac Atomic R-matrix Code (DARC) of Norrington & Grant (2003). Resonances in the threshold region have been resolved in a fine energy mesh, and excitation rates are determined over a wide electron temperature range below 10 7 K. The results are compared with those available in the literature, and the accuracy of the data is assessed.

Energy Levels, Radiative Rates, and Collision Strengths for Transitions in Fe xvii

Energy levels and radiative rates have been calculated for fine-structure transitions among the lowest 89 levels of the (1s2) 2s22p6, 2s22p53l, 2s22p54l, 2s2p63l, and 2s2p64l configurations of Fe XVII, using the GRASP code of Dyall et al. Collision strengths have also been calculated, for transitions among the lowest 55 levels, using the recently developed Dirac atomic R-matrix code (DARC) of Norrington & Grant. The results are compared with those available in the literature, and the accuracy of the data is assessed.