Maxwellian Averaged Effective Collision Strengths Research Articles

New radiative and collisional atomic data for Sr ii and Y ii with application to Kilonova modelling

Abstract The spectra of singly ionised Strontium and Yttrium (Sr ii and Y ii) have been proposed as identifications of certain spectral features in the AT2017gfo spectrum. With the growing demand for NLTE simulations of Kilonovae, there is a increasing need for atomic data for these and other r-process elements. Our goal is to expand upon the current set of atomic data for r-process elements, by presenting transition probabilities and Maxwellian-averaged effective collision strengths for Sr ii and Y ii. The Breit-Pauli and DARC R-matrix codes are employed to calculate the appropriate collision strengths, which are thermally averaged according to a Maxwellian distribution to calculate excitation and de-excitation rates. The tardis and ColRadPy packages are subsequently used to perform LTE and NLTE modelling respectively. A complete set of transition probabilities and effective collision strengths involving levels for Sr ii and Y ii have been calculated for temperature ranges compatible with kilonova plasma conditions. Forbidden transitions were found to disagree heavily with the Axelrod approximation, an approximation which is currently employed by other models within the literature. Theoretically important spectral lines are identified with both LTE and NLTE modelling codes. LTE simulations in tardis reveal no new significant changes to the full synthetic spectra. NLTE simulations in ColRadPy provide indications of which features are expected to be strong for a range of regimes, and we include luminosity estimates. Synthetic emission spectra over KNe densities and temperatures reveal potentially interesting spectral lines in the NIR.

Electron-Impact Excitation of Ge iii and Photoionisation of Ge ii

Abstract Energy levels, Einstein A-values and oscillator strengths are calculated for doubly-ionised germanium (Ge iii). We have undertaken a study of the electron-impact excitation of Ge iii and have also completed a study of the photoionisation of Ge ii. Ge iii target structures were generated using the relativistic GRASP0 package. Several scattering models were investigated to assess the uncertainty quantification of our results. Initially, the lowest lying 64 jj fine-structure levels were included in the close-coupling expansion resulting from 14 non-relativistic configurations. A second larger model was subsequently generated using the GASP package and incorporated the lowest 589 jj fine-structure levels from 17 non-relativistic configurations. Both the DARC and Breit-Pauli parallel suite of R-matrix collision codes were utilised in the scattering calculations to generate the collision strengths for incident electron-energies between 0 and 5 Rydbergs and subsequently the Maxwellian averaged effective collision strengths for temperatures in the range 1000 to 200000 Kelvin. The photoionisation calculations comprised of two studies, a DARC and a Breit-Pauli calculation incorporating the 250 lowest lying levels. Photoionisation cross sections for Ge ii are presented in the range 0-5 Ryds. Due to the lack of data available in the literature, the present radiative data and electron-impact/photoionisation cross sections are compared between the models presented in this paper. To assess their significance for astrophysics, the data are incorporated into the stellar atmosphere package sterne. Test models for the heavy-metal subdwarf LSIV−14○116 are not affected by the new data, but models for cooler stars may be sensitive to them.

Electron-impact excitation of Ni II

Aims. Energy levels, transition probabilities, and oscillator strengths are calculated for the second most abundant iron peak element Ni II. The difficulty in obtaining an accurate target representation is related to the open d-shell nature of the target, which has a minimum requirement of single and double promotions from the ground state configuration to the n = 4 shells. Therefore, in order to achieve an accurate representation of the target ion, we have also included configurations containing the 4d, 5s, and 5p subshells. We have undertaken a study of the electron impact excitation of Ni II and present here the collision strengths for forbidden and allowed transitions among the lowest 800 fine-structure levels as well as the corresponding Maxwellian-averaged effective collision strengths for a range of astrophysically relevant electron temperatures. Methods. An accurate Ni II target structure was generated using the modified General-purpose Relativistic Atomic Structure Package (GRASP0) for the lowest lying 1220 jj fine-structure levels, comprising the 11 configurations: 3p63d9, 3p63d84s, 3p63d84p, 3p63d84d, 3p63d85s, 3p63d85p, 3p63d74s2, 3p63d75s2, 3p63d74s4p, 3p63d74s4d, and 3p43d94s4d. The relativistic parallel Dirac atomic R-matrix codes (DARC) were utilised in the scattering calculations to generate the collision strengths for incident electron energies between 0 and 2 Ryd and, by employing infinite dipole and non-dipole limit points, we also generated the effective collision strengths for temperatures in the range from 1000 to 400 000 K. Two separate calculations were performed, both comprised of truncated close-coupling expansions of 800 jj-levels with the first calculation retaining the theoretical ab initio energy levels generated in the GRASP0 evaluations, whereas in the second calculation these energies were shifted to their predicted National Institute of Standards and Technology (NIST) values where possible. This should provide a lower estimate on the uncertainty. Results. Comparisons are made between the radiative data and the collisional cross sections with past theoretical and experimental studies. The effective collision strengths when compared with the most recent published calculations, are found to agree to within 10% for the majority of the transitions considered. In addition, the data are used to model the spectrum of Ni II and good agreement is found with previous investigations and observations.

Fine-structure electron-impact excitation of Ne+ and Ne2 + for low-temperature astrophysical plasmas

Collision strengths for electron-impact of fine-structure level excitation within the ground term of Ne$^{+}$ and Ne$^{2+}$ are calculated using the Breit-Pauli, Intermediate Coupling Frame Transformation, and DARC $R$-matrix methods. Maxwellian-averaged effective collision strengths and excitation rate coefficient qij are presented for each. The application of the current calculations is to very low temperature astrophysical plasmas, thus we examine the sensitivity of the effective collision strengths down to 10 K. The use of the various theoretical methods allows us to place estimated uncertainties on the recommended effective collision strengths. We also investigate the sensitivity of the collision strengths to the resonance positions and underlying atomic structure. Good agreement is found with previous R-matrix calculations at higher temperature.

Photoionization of Co+and electron-impact excitation of Co2 +using the DiracR-matrix method

Modelling of massive stars and supernovae (SNe) plays a crucial role in understanding galaxies. From this modelling we can derive fundamental constraints on stellar evolution, mass-loss processes, mixing, and the products of nucleosynthesis. Proper account must be taken of all important processes that populate and depopulate the levels (collisional excitation, de-excitation, ionization, recombination, photoionization, bound-bound processes). For the analysis of Type Ia SNe and core collapse SNe (Types Ib, Ic and II) Fe group elements are particularly important. Unfortunately little data is currently available and most noticeably absent are the photoionization cross-sections for the Fe-peaks which have high abundances in SNe. Important interactions for both photoionization and electron-impact excitation are calculated using the relativistic Dirac Atomic $R$-matrix Codes (DARC) for low ionization stages of cobalt. All results are calculated up to photon energies of 45 eV and electron energies up to 20 eV. The wavefunction representation of Co III has been generated using GRASP0 by including the dominant 3d$^7$, 3d$^6$[4s, 4p], 3p$^4$3d$^9$ and 3p$^6$3d$^9$ configurations, resulting in 292 fine structure levels. Electron-impact collision strengths and Maxwellian averaged effective collision strengths across a wide range of astrophysically relevant temperatures are computed for Co III. In addition, statistically weighted level-resolved ground and metastable photoionization cross-sections are presented for Co II and compared directly with existing work.

ELECTRON-IMPACT EXCITATION COLLISION STRENGTHS AND THEORETICAL LINE INTENSITIES FOR TRANSITIONS IN S III

We present Maxwellian-averaged effective collision strengths for the electron-impact excitation of S III over a wide range of electron temperatures of astrophysical importance, log T(K) = 3.0-6.0. The calculation incorporates 53 fine-structure levels arising from the six lowest configurations, giving rise to 1378 individual lines, and is undertaken using the recently developed RMATRX II plus FINE95 suite of codes. A detailed comparison is made with a previous R-matrix calculation and significant differences are found for some transitions. The atomic data are subsequently incorporated into the modeling code CLOUDY to generate line intensities for a range of plasma parameters, with emphasis on allowed UV and EUV emission lines detected from the Io plasma torus. Electron density-sensitive line ratios are calculated with the present atomic data and compared with those from CHIANTI v7.1, as well as with Io plasma torus spectra obtained by FUSE and EUVE. The present line intensities are found to agree well with the observational results and provide a noticeable improvement upon the values predicted by CHIANTI.

Electron-impact excitation of the astrophysically important singly ionized Fe-peak ions Sc and Ti

In this work we report on the evaluation of electron-impact collision strengths and Maxwellian averaged effective collision strengths for the lowly-ionized Fe-peak elements Sc II and Ti II using the parallel R-matrix package RMATRX II.

Electron-impact excitation of Sc ii: collision strengths and effective collision strengths for fine-structure transitions

Accurate fine-structure atomic data for the Fe-peak elements are essential for interpreting astronomical spectra. There is a severe paucity of data available for Sc ii, highlighted by the fact that no collision strengths are readily available for this ion. We present electron-impact excitation collision strengths and Maxwellian averaged effective collision strengths for Sc ii. The collision strengths were calculated for all 3916 transitions amongst 89 jj levels (arising from the 3d4s, 3d2, 4s2, 3d4p, 4s4p, 3d5s, 3d4d, 3d5p, 4p2 and 3d4f configurations), resulting in a 944 coupled channel problem. The R-matrix package rmatrxii was utilized, along with the transformation code fine and the external region code pstgf, to calculate the collision strengths for a range of incident electron energies in the 0 to 8.3 Rydberg region. Maxwellian averaged effective collision strengths were then produced for 27 temperatures lying within the astrophysically significant range of 30 to 105 K. The collision strengths and effective collision strengths were produced for two different target models. The purpose was to systematically examine the effect of including open 3p correlation terms into the configuration interaction expansion for the wavefunction. The first model consisted of all 36 CI terms that could be generated with the 3p core closed. The second model incorporated an additional six configurations which allowed for single-electron excitations from within the 3p core. Comparisons are made between the two models and the results of Bautista et al., obtained by private communication. It is concluded that the first model produced the most reliable set of collision and effective collision strengths for use in astrophysical and plasma applications.

Electron impact collision strengths in Ne VII

The lines of Ne VII have been observed in many astronomical objects, and some transitions from high energy levels were observed both in Seyfert galaxies and stellar coronae. Thus, the atomic data for these transitions are important for modeling. Using the code FAC we calculated the collision strengths based on the distorted-wave method with large configuration interactions included. The Maxwellian averaged effective collision strengths covering the typical temperature range of astronomical and laboratory hot plasmas are presented. We extend the calculation of the energy levels to n=4 and 5. The energy levels, wavelengths, spontaneous transition rates, weighted oscillator strengths, and effective collision strengths were reported. Compared with the results from experiment or previous theoretical calculations a general agreement is found. It is found that the resonance effects are important in calculating the effective collision strengths.

ELECTRON-IMPACT EXCITATION OF Cr II: A THEORETICAL CALCULATION OF EFFECTIVE COLLISION STRENGTHS FOR OPTICALLY ALLOWED TRANSITIONS

In this paper, we present electron-impact excitation collision strengths and Maxwellian averaged effective collision strengths for the complicated iron-peak ion Cr ii. We consider specifically the allowed lines for transitions from the 3d5 and 3d44s even parity configuration states to the 3d44p odd parity configuration levels. The parallel suite of R-Matrix packages, RMATRX II, which have recently been extended to allow for the inclusion of relativistic effects, were used to compute the collision cross sections. A total of 108 LSπ/280 Jπ levels from the basis configurations 3d5, 3d44s, and 3d44p were included in the wavefunction representation of the target including all doublet, quartet, and sextet terms. Configuration interaction and correlation effects were carefully considered by the inclusion of seven more configurations and a pseudo-corrector type orbital. The 10 configurations incorporated into the Cr ii model thus listed are 3d5, 3d44s, 3d44p, 3d34s2, 3d34p2, 3d34s4p, , , , and , constituting the largest Cr ii target model considered to date in a scattering calculation. The Maxwellian averaged effective collision strengths are computed for a wide range of electron temperatures 2000–100,000 K which are astrophysically significant. Care has been taken to ensure that the partial wave contributions to the collision strengths for these allowed lines have converged with "top-up" from the Burgess–Tully sum rule incorporated. Comparisons are made with the results of Bautista et al. and significant differences are found for some of the optically allowed lines considered.

ELECTRON-IMPACT EXCITATION OF Ni II: EFFECTIVE COLLISION STRENGTHS FOR OPTICALLY ALLOWED FINE-STRUCTURE TRANSITIONS

In this paper, we present collision strengths and Maxwellian averaged effective collision strengths for the electron-impact excitation of Ni II. Attention is expressly concentrated on the optically allowed fine-structure transitions between the 3d 9, 3d 84s, and 3d 74s 2 even parity levels and the 3d 84p and 3d 74s 4p odd parity levels. The parallel RMATRXII R-matrix package has been recently extended to allow for the inclusion of relativistic fine-structure effects. This suite of codes has been utilized in conjunction with the parallel PSTGF and PSTGICF programs in order to compute converged total collision strengths for the allowed transitions with which this study is concerned. All 113 LS terms identified with the 3d 9, 3d 84s, 3d 74s 2, 3d 84p, and 3d 74s 4p basis configurations were included in the target wavefunction representation, giving rise to a sophisticated 295 jj-level, 1930 coupled channel scattering complex. Maxwellian averaged effective collision strengths have been computed at 30 individual electron temperatures ranging from 30 to 1,000,000 K. This range comfortably encompasses all temperatures significant to astrophysical and plasma applications. The convergence of the collision strengths is exhaustively investigated and comparisons are made with previous theoretical works, where significant discrepancies exist for the majority of transitions. We conclude that intrinsic in achieving converged collision strengths and thus effective collision strengths for the allowed transitions is the combined inclusion of contributions from the (N + 1) partial waves extending to a total angular momentum value of L = 50 and further contributions from even higher partial waves accomplished by employing a top-up procedure.

Electron-impact excitation of Ni II

Context. Considerable demand exists for electron excitation data for Ni ii, since lines from this abundant ion are observed in a wide variety of laboratory and astrophysical spectra. The accurate theoretical determination of these data can present a significant challenge however, due to complications arising from the presence of an open 3d-shell in the description of the target ion. Aims. In this work we present collision strengths and Maxwellian averaged effective collision strengths for the electron-impact excitation of Ni ii. Attention is concentrated on the 153 forbidden fine-structure transitions between the energetically lowest 18 levels of Ni ii .E ffective collision strengths have been evaluated at 27 individual electron temperatures ranging from 30–100 000 K. To our knowledge this is the most extensive theoretical collisional study carried out on this ion to date. Methods. The parallel R-matrix package RMATRX II has recently been extended to allow for the inclusion of relativistic effects. This suite of codes has been utilised in the present work in conjunction with PSTGF to evaluate collision strengths and effective collision strengths for all of the low-lying forbidden fine-structure transitions. The following basis configurations were included in the target model – 3d 9 ,3 d 8 4s, 3d 8 4p, 3d 7 4s 2 and 3d 7 4s4p – giving rise to a sophisticated 295 jj-level, 1930 coupled channel scattering problem. Results. Comprehensive comparisons are made between the present collisional data and those obtained from earlier theoretical evaluations. While the effective collision strengths agree well for some transitions, significant discrepancies exist for others.

Electron-impact excitation of Fe-peak ions for astrophysical applications

This paper discusses one of the major outstanding problems in atomic collision physics, namely the accurate theoretical treatment of electron scattering from open d-shell systems, and explores how this issue has been addressed over recent years with the development of the new parallel R-matrix suite of codes. It focuses on one code in particular – the new parallel R-matrix package PRMAT, which has recently been extended to account for relativistic fine-structure effects. This program facilitates the determination of accurate electron-impact excitation rates for complex open 3d-shell systems including the astrophysically important Fe-peak ions such as Ni II, Fe II and Fe III. Results are presented for collision strengths and Maxwellian averaged effective collision strengths for the optically forbidden fine-structure transitions of Ni II. To our knowledge this is the most extensive calculation completed to date for this ion.

Electron-impact excitation of Fe II: Effective collision strengths for optically allowed fine-structure transitions

In this paper, we present collision strengths and Maxwellian averaged effective collision strengths for the electron-impact excitation of Fe II. We consider specifically the optically allowed lines for transitions from the 3d 64s and 3d 7 even parity configuration states to the 3d 64p odd parity configuration levels. The parallel suite of Breit–Pauli codes are utilized to compute the collision cross-sections where relativistic effects are included explicitly in both the target and the scattering approximation. A total of 100 LS or 262- jj levels formed from the basis configurations 3d 64s, 3d 7 and 3d 64p were included in the wavefunction representation of the target, including all doublet, quartet and sextet terms. The Maxwellian averaged effective collision strengths are computed across a wide range of electron temperatures from 100 to 100,000 K, temperatures of importance in astrophysical and plasma applications. A detailed comparison is made with previous works and significant differences were found to occur for some of the transitions considered. We conclude that in order to obtain converged collision strengths and effective collision strengths for these allowed transitions it is necessary to include contributions from partial waves up to L = 50 explicitly in the calculation, and in addition, account for contributions from even higher partial waves through a “top up” procedure.

Relativistic and correlation effects in electron impact excitation of forbidden transitions of OII

We investigate relativistic and correlation effects in electron impact excitation of singly ionized oxygen using the Breit–Pauli R-matrix method. The intermediate coupling close-coupling calculations are carried out using a 16-level target representation dominated by the electronic configurations 1s22s22p3, 1s22s2p4, 1s22s22p23s. Resonance structures are delineated in detail to ascertain the effect on averaged collision strengths. Convergence of the partial wave summation is ensured for non-dipole transitions in the R-matrix calculations. The present results differ significantly from the similar Breit–Pauli R-matrix calculations by McLaughlin and Bell (1998 J. Phys. B: At. Mol. Opt. Phys. 31 4317–29), but are essentially in agreement with the LS coupling results of Pradhan (1976a J. Phys. B: At. Mol. Opt. Phys. 9 433–43, 1976b Mon. Not. R. Astron. Soc. 177 31–8). A comprehensive study of the detailed energy behaviour of all forbidden transitions among the five levels of the ground configuration, i.e. 2s2p3(4So3/2, 2Do5/2,3/2, 2Po3/2,1/2) shows that the finestructure collision strengths do not significantly depart from the values obtained from a purely transformation, and relativistic effects are therefore small. We find that the Maxwellian-averaged effective collision strengths for the ten transitions also differ from the previous work, most likely due to more extensive delineation of resonances in the present work. However, the differences are largely systematic and therefore the OII line intensity ratios are not significantly affected. We also obtain an excellent agreement between the present-calculated cross sections for the 4So − 2Do transition and the experimental merged beam measurements.

O ii] line ratios

Abstract Based on new calculations, we reconfirm the low- and high-density limits on the forbidden fine-structure line intensity ratio [O ii]I(3729)/I(3726): and . Employing [O ii] collision strengths calculated using the Breit–Pauli R-matrix method, we rule out any significant deviation due to relativistic effects from these canonical values. The present results are in substantial agreement with older calculations by Pradhan, and validate the extensive observational analyses of gaseous nebulae by Copetti & Writzel and Wang et al. that reach the same conclusions. The present theoretical results and the recent observational analyses differ significantly from the calculations by McLaughlin & Bell and Keenan et al. The new Maxwellian averaged effective collision strengths are presented for the 10 transitions among the first five levels to enable computations of [O ii] line ratios.

Effective collision strengths for forbidden transitions among the 3s23p3 fine-structure levels of Cl III

Effective collision strengths for the 10 astrophysically important fine-structure forbidden transitions among the 4So, 2Do and 2Po levels in the 3s23p3 configuration of Cl iii are presented. The calculation employs the multichannel R-matrix method to compute the electron-impact excitation collision strengths in a close-coupling expansion, which incorporates the lowest 23 LS target eigenstates of Cl iii. These states are formed from the 3s23p3, 3s3p4, 3s23p23d and 3s23p24s configurations. The Maxwellian-averaged effective collision strengths are presented graphically for all 10 fine-structure transitions over a wide range of electron temperatures appropriate for astrophysical applications [log T(K)=3.3−log T(K)=5.9]. Comparisons are made with the earlier seven-state close-coupling calculation of Butler & Zeippen, and in general excellent agreement is found in the low-temperature region where a comparison is possible [log T(K)=3.3−log T(K)=4.7]. However, discrepancies of up to 30 per cent are found to occur for the forbidden transitions which involve the 4So ground state level, particularly for the lowest temperatures considered. At the higher temperatures, the present data are the only reliable results currently available.