arXiv subjects

N. R. Badnell

Publications and source records attributed to N. R. Badnell.

At least 19 recordsLinked to original sources

arXiv2025

Testing strong-field QED to second-order in the highly correlated atomic system berylliumlike Pb78+ by electron-ion recombination spectroscopy

A low-energy storage ring with an ultracold electron cooler has been coupled with a heavy-ion accelerator facilitating high-resolution electron-ion collision spectroscopy of the heaviest few-electron ions. In the present work resonant electron-ion recombination of berylliumlike Pb$^{78+}$ ions was measured in the collision-energy range 9.3-16.5eV and a value of 244.937(30) eV is derived for the Pb$^{78+}$($2s^2\;^1S_0 - 2s\,2p\;^3P_1$) excitation energy. This result agrees with the most recent (less accurate) theoretical value of 244.942(52) eV [Malyshev et al., Physical Review A 110, 062824 (2024)], which has been calculated by applying strong-field QED rigorously up to the second order. The present investigation suggests that further technical improvements can potentially increase the experimental accuracy by an order of magnitude.

physics.atom-ph↗

arXiv2025

H, He-like recombination spectra VI: Quadrupole $l$-changing collisions

We have developed a simple analytic formula that well describes quadrupole $l$-changing collisions of the form $nl \rightarrow nl'$, as confirmed by comparison with numerical quantal Born calculations obtained with the program autostructure (Badnell 2011). Such formulae could easily be included in models of astrophysical plasma emission, such as the hydrogen and helium-like recombination spectra. When compared with the results of previous quantal calculations based upon an analytic solution of the time-dependent Schrödinger equation by Vrinceanu & Flannery (2001), we find relatively good agreement, with the exception of large $l > n/2$ transitions. We provide a tentative explanation for such discrepancies. However, we also show that the rates for quadrupole $l$-changing collisions are typically two orders of magnitude lower than the dipolar ones. Inclusion of the quadrupolar rates in a hydrogenic collisional-radiative model of nebular plasma shows minimal changes to the level populations, typically within 1% in nebular conditions. Simple and complete theories are now available for $l$-changing collisions suitable for astrophysical applications.

physics.atom-ph↗

arXiv2025

UK APAP R-matrix electron-impact excitation cross-sections for modelling laboratory and astrophysical plasma

Systematic R-matrix calculations of electron-impact excitation for ions of astrophysical interest have been performed since 2007 for many iso-electronic sequences as part of the UK Atomic Process for Astrophysical Plasma (APAP) network. Rate coefficients for Maxwellian electron distributions have been provided and used extensively in the literature and many databases for astrophysics. Here, we provide averaged collision strengths to be used to model plasma where electrons are non-Maxwellian, which often occur in laboratory and astrophysical plasma. We also provide for many ions new Maxwellian-averaged collision strengths which include important corrections to the published values. The H- and He-like atomic data were recently made available in Mao+(2022). Here, we provide data for ions of the Li-, Be-, B-, C-, N-, O-, Ne-, Na-, and Mg-like sequences.

physics.atom-ph↗

arXiv2024

Satellite lines from autoionizing states of Fe XVI and the problems with the X-ray Fe XVII lines

We present new calculations of atomic data needed to model autoionizing states of Fe XVI. We compare the state energies, radiative and excitation data with a sample of results from previous literature. We find a large scatter of results, the most significant ones in the autoionization rates, which are very sensitive to the configuration interaction and state mixing. We find relatively good agreement between the autoionization rates and the collisional excitation rates calculated with the R-matrix suite of programs and autostructure. The largest model, which includes J-resolved states up to n=10, produces ab-initio wavelengths and intensities of the satellite lines which agree well with solar high-resolution spectra of active regions, with few minor wavelength adjustements. We review previous literature, finding many incorrect identifications, most notably those in the NIST database. We provide several new tentative identifications in the 15-15.7 A range, and several new ones at shorter wavelengths, where previous lines were unidentified. Compared to the previous CHIANTI model, the present one has an increased flux in the 15--15.7 A range at 2 MK of a factor of 1.9, resolving the discrepancies found in the analysis of the Marshall Grazing Incidence X-Ray Spectrometer (MaGIXS) observation. It appears that the satellite lines also resolve the long-standing discrepancy in the intensity of the important Fe XVII 3D line at 15.26 A.

astro-ph.SR↗

arXiv2023

The 2017 Release of Cloudy

We describe the 2017 release of the spectral synthesis code Cloudy. A major development since the previous release has been exporting the atomic data into external data files. This greatly simplifies updates and maintenance of the data. Many large datasets have been incorporated with the result that we can now predict well over an order of magnitude more emission lines when all databases are fully used. The use of such large datasets is not realistic for most calculations due to the time and memory needs, and we describe the limited subset of data we use by default. Despite the fact that we now predict significantly more lines than the previous Cloudy release, this version is faster because of optimization of memory access patterns and other tuning. The size and use of the databases can easily be adjusted in the command-line interface. We give examples of the accuracy limits using small models, and the performance requirements of large complete models. We summarize several advances in the H- and He-like iso-electronic sequences. We use our complete collisional-radiative models of the ionization of these one and two-electron ions to establish the highest density for which the coronal or interstellar medium (ISM) approximation works, and the lowest density where Saha or local thermodynamic equilibrium can be assumed. The coronal approximation fails at surprisingly low densities for collisional ionization equilibrium but is valid to higher densities for photoionized gas clouds. Many other improvements to the physics have been made and are described. These include the treatment of isotropic continuum sources such as the cosmic microwave background (CMB) in the reported output, and the ability to follow the evolution of cooling non-equilibrium clouds.

astro-ph.GA↗

arXiv2022

Spectroscopic r-Process Abundance Retrieval for Kilonovae I: The Inferred Abundance Pattern of Early Emission from GW170817

Freshly-synthesized r-process elements in kilonovae ejecta imprint absorption features on optical spectra, as observed in the GW170817 binary neutron star merger. These spectral features encode insights into the physical conditions of the r-process and the origins of the ejected material, but associating features with particular elements and inferring the resultant abundance pattern is computationally challenging. We introduce Spectroscopic r-Process Abundance Retrieval for Kilonovae (SPARK), a modular framework to perform Bayesian inference on kilonova spectra with the goals of inferring elemental abundance patterns and identifying absorption features at early times. SPARK inputs an atomic line list and abundance patterns from reaction network calculations into the TARDIS radiative transfer code. It then performs fast Bayesian inference on observed kilonova spectra by training a Gaussian process surrogate for the approximate posteriors of kilonova ejecta parameters, via active learning. We use the spectrum of GW170817 at 1.4 days to perform the first inference on a kilonova spectrum, and recover a complete abundance pattern. Our inference shows that this ejecta was generated by an r-process with either (1) high electron fraction Y_e ~ 0.35 and high entropy s/k_B ~ 25, or, (2) a more moderate Y_e ~ 0.30 and s/k_B ~ 14. These parameters are consistent with a shocked, polar dynamical component, and a viscously-driven outflow from a remnant accretion disk, respectively. We also recover previous identifications of strontium absorption at ~8000 AA, and tentatively identify yttrium and/or zirconium at < 4500 AA. Our approach will enable computationally-tractable inference on the spectra of future kilonovae discovered through multi-messenger observations.

astro-ph.HE↗

arXiv2022

R-matrix electron-impact excitation data for the H- and He-like ions with Z=6-30

Plasma models built on extensive atomic data are essential to interpreting the observed cosmic spectra. H-like Lyman series and He-like triplets observable in the X-ray band are powerful diagnostic lines to measure the physical properties of various types of astrophysical plasmas. Electron-impact excitation is a fundamental atomic process for the formation of H-like and He-like key diagnostic lines. Electron-impact excitation data adopted by the widely used plasma codes (AtomDB, CHIANTI, and SPEX) do not necessarily agree with each other. Here we present a systematic calculation of electron-impact excitation data of H-like and He-like ions with the atomic number Z=6-30 (i.e., C to Zn). Radiation damped R-matrix intermediate coupling frame transformation calculation was performed for each ion with configurations up to $n=6$. We compare the present work with the above three plasma codes and literature to assess the quality of the new data, which are relevant for current and future high-resolution X-ray spectrometers.

physics.atom-ph↗

arXiv2021

H, He-like recombination spectra IV; H, He-like recombination spectra IV: clarification and refinement of methodology for $l$-changing collisions

Precise spectral diagnostic modelling of H~{\sc i} and He~{\sc ii} recombination spectra can constrain theoretical models which describe many astrophysical environments. Simple analytic expressions are of interest for collisional $l$-changing rate coefficients that are used by large-scale population modelling codes. We review, clarify and improve-upon the modified Pengelly \& Seaton formulae of Guzmán \etal We show that the recent poor results for it shown by Vrinceanu \etal are due to their misinterpretation of its usage. We also detail efficient numerical algorithms which should enable the full quantum mechanical expression for such rate coefficients to be used much more routinely by modelling codes. We illustrate with some collisional-radiative population modelling for hydrogen.

astro-ph.SR↗

arXiv2021

R-matrix electron-impact excitation data for the O-like iso-electronic sequence

Astrophysical plasma codes are built on atomic databases. In the current atomic databases, R-matrix electron-impact excitation data of O-like ions are limited. The accuracy of plasma diagnostics with O-like ions depends on the availability and accuracy of the atomic data. This is particularly relevant in the context of future observatories equipped with the next generation of high-resolution spectrometers. To obtain level-resolved effective collision strengths of O-like ions from \ion{Ne}{III} to \ion{Zn}{XXIII} (i.e., Ne$^{2+}$ to Zn$^{22+}$) over a wide range of temperatures. This includes transitions up to $nl=5d$ for each ion. We also aim to assess the accuracy of the new data, as well as their impact on solar atmosphere plasma diagnostics, compared to those available within the CHIANTI database. A large-scale R-matrix intermediate coupling frame transformation calculations were performed systematically for the O-like iso-electronic sequence. For each ion, 630 fine-structure levels were included in both the configuration interaction target and close-coupling collision expansions. The present results (energy levels, oscillator strengths, and effective collision strengths) of selected ions across the iso-electronic sequence are compared with those in archival databases and the literature. For selected ions across the iso-electronic sequence. We find general agreement with the few previous R-matrix calculations of collision strengths. We illustrate the improvements for a few solar plasma diagnostics over existing CHIANTI atomic models based on distorted wave data. The electron-impact excitation data are archived according to the Atomic Data and Analysis Structure (ADAS) data class adf04 and will be available in OPEN-ADAS.

astro-ph.SR↗

arXiv2021

The influence of photo-induced processes and charge transfer on carbon and oxygen in the lower solar atmosphere

To predict line emission in the solar atmosphere requires models which are fundamentally different depending on whether the emission is from the chromosphere or the corona. At some point between the two regions, there must be a change between the two modelling regimes. Recent extensions to the coronal modelling for carbon and oxygen lines in the solar transition region have shown improvements in the emission of singly- and doubly-charged ions, along with Li-like ions. However, discrepancies still remain, particularly for singly-charged ions and intercombination lines. The aim of this work is to explore additional atomic processes that could further alter the charge state distribution and the level populations within ions, in order to resolve some of the discrepancies. To this end, excitation and ionisation caused by both the radiation field and by atom-ion collisions have been included, along with recombination through charge transfer. The modelling is carried out using conditions which would be present in the quiet Sun, which allows an assessment of the part atomic processes play in changing coronal modelling, separately from dynamic and transient events taking place in the plasma. The effect the processes have on the fractional ion populations are presented, as well as the change in level populations brought about by the new excitation mechanisms. Contribution functions of selected lines from low charge states are also shown, to demonstrate the extent to which line emission in the lower atmosphere could be affected by the new modelling.

astro-ph.SR↗

arXiv2021

Quantitative comparison of opacities calculated using the $R$-matrix and Distorted-Wave methods: Fe XVII

We present here a detailed calculation of opacities for Fe~XVII at the physical conditions corresponding to the base of the Solar convection zone. Many ingredients are involved in the calculation of opacities. We review the impact of each ingredient on the final monochromatic and mean opacities (Rosseland and Planck). The necessary atomic data were calculated with the $R$-matrix and the distorted-wave (DW) methods. We study the effect of broadening, of resolution, of the extent of configuration sets and of configuration interaction to understand the differences between several theoretical predictions as well as the existing large disagreement with measurements. New Dirac $R$-matrix calculations including all configurations up to the $n=$ 4, 5 and $6$ complexes have been performed as well as corresponding Breit--Pauli DW calculations. The DW calculations have been extended to include autoionizing initial levels. A quantitative contrast is made between comparable DW and $R$-matrix models. We have reached self-convergence with $n=6$ $R$-matrix and DW calculations. Populations in autoionizing initial levels contribute significantly to the opacities and should not be neglected. The $R$-matrix and DW results are consistent under the similar treatment of resonance broadening. The comparison with the experiment shows a persistent difference in the continuum while the filling of the windows shows some improvement. The present study defines our path to the next generation of opacities and opacity tables for stellar modeling.

astro-ph.SR↗

arXiv2020

R-matrix electron-impact excitation data for the N-like iso-electronic sequence

Spectral lines from N-like ions can be used to measure the temperature and density of various types of astrophysical plasmas. The atomic databases of astrophysical plasma modelling codes still have room for improvement in their electron-impact excitation data sets for N-like ions, especially $R$-matrix data. This is particularly relevant for future observatories (e.g. Arcus) which will host high-resolution spectrometers. We aim to obtain level-resolved effective collision strengths for all transitions up to $nl=5d$ over a wide range of temperatures for N-like ions from O II to Zn XXIV (i.e., O$^{+}$ to Zn$^{23+}$) and to assess the accuracy of the present work. We also examine the impact of our new data on plasma diagnostics by modelling solar observations with CHIANTI. We have carried-out systematic $R$-matrix calculations for N-like ions which included 725 fine-structure target levels in both the configuration interaction target and close-coupling collision expansions. The $R$-matrix intermediate coupling frame transformation method was used to calculate the collision strengths, while the AUTOSTRUCTURE code was used for the atomic structures. We compare the present results for selected ions with those in archival databases and the literature. The comparison covers energy levels, oscillator strengths, and effective collision strengths. We show examples of improved plasma diagnostics when compared to CHIANTI models which use only distorted wave data as well as some which use previous $R$-matrix data. The electron-impact excitation data are archived according to the Atomic Data and Analysis Structure (ADAS) data class it adf04 and will be available in OPEN-ADAS. The data can be used to improve the atomic databases for astrophysical plasma diagnostics.

astro-ph.SR↗

arXiv2020

Effects of density on the oxygen ionisation equilibrium in collisional plasmas

The ion populations most frequently adopted for diagnostics in collisional plasmas are derived from the density independent, coronal approximation. In higher density, lower temperature conditions, ionisation rates are enhanced once metastable levels become populated, and recombination rates are suppressed if ions recombine into Rydberg levels. As a result, the formation temperatures of ions shift, altering the diagnostics of the plasma. To accurately model the effect of ionisation from metastable levels, new electron impact, ionisation cross sections have been calculated for oxygen, both for direct ionisation and excitation--auto-ionisation of the ground and metastable levels. The results have been incorporated into collisional radiative modelling to show how the ionisation equilibrium of oxygen changes once metastable levels become populated. Suppression of dielectronic recombination has been estimated and also included in the modelling, demonstrating the shifts with density in comparison to the coronal approximation. The final results for the ionisation equilibrium are used in differential emission measure modelling to predict line intensities for many lines emitted by O II-VI in the solar transition region. The predictions show improved agreement by 15-40% for O II, O VI and the inter-combination lines of O III-V, when compared to results from coronal approximation modelling. While there are still discrepancies with observations of these lines, this could, to a large part, be explained by variability in the observations.

astro-ph.SR↗

arXiv2020

Fe III emission in quasars: evidence for a dense turbulent medium

Recent improvements to atomic energy-level data allow, for the first time, accurate predictions to be made for the Fe III line emission strengths in the spectra of luminous, $L_\text{bol}=10^{46}-10^{48}$ erg/s, Active Galactic Nuclei. The Fe III emitting gas must be primarily photoionized, consistent with observations of line reverberation. We use CLOUDY models exploring a wide range of parameter space, together with 26,500 rest-frame ultraviolet spectra from the Sloan Digital Sky Survey, to constrain the physical conditions of the line emitting gas. The observed Fe III emission is best accounted for by dense ($n_H=10^{14}$ cm$^{-3}$) gas which is microturbulent, leading to smaller line optical depths and fluorescent excitation. Such high density gas appears to be present in the central regions of the majority of luminous quasars. Using our favoured model, we present theoretical predictions for the relative strengths of the Fe III UV34 $λλ$1895,1914,1926 multiplet. This multiplet is blended with the Si III] $λ$1892 and C III] $λ$1909 emission lines and an accurate subtraction of UV34 is essential when using these lines to infer information about the physics of the broad line region in quasars.

astro-ph.GA↗

arXiv2020

Helium line emissivities in the solar corona

We present new collisional-radiative models (CRMs) for helium in the quiescent solar corona, and predict the emissivities of the He and He$^+$ lines to be observed by DKIST, Solar Orbiter, and Proba-3. We discuss in detail the rates we selected for these models, highlighting several shortcomings we have found in previous work. As no previous complete and self-consistent coronal CRM for helium existed, we have benchmarked our largest model at a density of 10$^{6}$ cm$^{-3}$ and temperature of 20,000 K against recent CRMs developed for photoionised nebulae. We then present results for the outer solar corona, using new dielectronic recombination rates we have calculated, which increase the abundance of neutral helium by about a factor of two. We also find that all the optical triplet He I lines, and in particular the well known He I 10830 and 5876 A lines are strongly affected by both photo-excitation and photo-ionisation from the disk radiation, and that extensive CRM models are required to obtain correct estimates. Close to the Sun, at an electron density of 10$^{8}$ cm$^{-3}$ and temperature of 1 MK, we predict the emissivity of the He I 10830 A to be comparable to that of the strong Fe XIII coronal line at 10798 A. However, we expect the He I emissivity to sharply fall in the outer corona, with respect to Fe XIII. We confirm that the He$^+$ Lyman $α$ at 304 A is also significantly affected by photo-excitation and is expected to be detectable as a strong coronal line up to several solar radii.

physics.atom-ph↗

arXiv2020

PSTGF : time-independent R-Matrix atomic electron-impact code

STGF is a community code employed for outer-region R-matrix calculations, describing electron-impact collisional processes. It is widely recognised that the original version of STGF was written by M. J. Seaton in 1983, but through constant refinement over the next decades by worldwide contributors has evolved into its current form that more reflects modern coding practice and current computer architectures. Despite its current wide acceptance, it was never formally published. Therefore, we present an updated high-performance parallel version of PSTGF, that balances the requirements of small university clusters, yet can exploit the computational power of cutting edge supercomputers. There are many improvements over the original STGF, but most noticeably, the full introduction of MQDT options that provide subsequent integration with ICFT (Intermediate Coupling Frame Transformation) codes, and for either Breit-Pauli / DARC (Dirac Atomic R-matrix Codes), better load balancing, high levels of vectorisation and simplified output. Semantically, the program is full fortran 90 in conjunction with MPI (Message Passing Interface) though has CUDA fortran options for the most numerically intensive code sections.

physics.comp-ph↗

arXiv2019

R-matrix electron-impact excitation data for the C-like iso-electronic sequence

Emission and absorption features from C-like ions serve as temperature and density diagnostics of astrophysical plasmas. $R$-matrix electron-impact excitation data sets for C-like ions in the literature merely cover a few ions, and often only for the ground configuration. Our goal is to obtain level-resolved effective collision strength over a wide temperature range for C-like ions from \ion{N}{II} to \ion{Kr}{XXXI} (i.e., N$^{+}$ to Kr$^{30+}$) with a systematic set of $R$-matrix calculations. We also aim to assess their accuracy. For each ion, we included a total of 590 fine-structure levels in both the configuration interaction target and close-coupling collision expansion. These levels arise from 24 configurations $2l^3 nl^{\prime}$ with $n=2-4$, $l=0-1$, and $l^{\prime}=0-3$ plus the three configurations $2s^22p5l$ with $l=0-2$. The AUTOSTRUCTURE code was used to calculate the target structure. Additionally, the $R$-matrix intermediate coupling frame transformation method was used to calculate the collision strengths. We compare the present results of selected ions with archival databases and results in the literature. The comparison covers energy levels, transition rates, and effective collision strengths. We illustrate the impact of using the present results on an \ion{Ar}{xiii} density diagnostic for the solar corona. The electron-impact excitation data is archived according to the Atomic Data and Analysis Structure (ADAS) data class adf04 and will be available in OPEN-ADAS. The data will be incorporated into spectral codes, such as CHIANTI and SPEX, for plasma diagnostics.

astro-ph.SR↗

arXiv2019

H-, He-like recombination spectra III: $n$-changing collisions in highly-excited Rydberg states and their impact on the radio, IR and optical recombination lines

At intermediate to high densities, electron (de-)excitation collisions are the dominant process for populating or depopulating high Rydberg states. In particular, the accurate knowledge of the energy changing ($n$-changing) collisional rates is determinant for predicting the radio recombination spectra of gaseous nebula. The different datasets present in the literature come either from impact parameter calculations or semi-empirical fits and the rate coefficients agree within a factor of two. We show in this paper that these uncertainties cause errors lower than 5% in the emission of radio recombination lines (RRL) of most ionized plasmas of typical nebulae. However, in special circumstances where the transitions between Rydberg levels are amplified by maser effects, the errors can increase up to 20%. We present simulations of the optical depth and H$nα$ line emission of Active Galactic Nuclei (AGN) Broad Line Regions (BLRs) and the Orion Nebula Blister to showcase our findings.

astro-ph.GA↗