AUTOSTRUCTURE: Atomic Physics Code

• AUTOSTRUCTURE is an atomic-physics code that computes energy levels, oscillator strengths, and collision data, essential for modeling astrophysical, fusion, and laboratory plasmas.
• The code employs adjustable orbital scaling and model potentials to optimize atomic structures and reaction rates across diverse conditions, from white dwarfs to tokamak environments.
• Its outputs are integrated into NLTE, radiative-transfer, and collisional-radiative workflows, substantially improving spectral diagnostics and elemental abundance analyses.

Searching arXiv for recent and foundational papers on AUTOSTRUCTURE and its applications. AUTOSTRUCTURE is an atomic-physics code used to compute quantities such as energy levels, transition oscillator strengths, radiative decay rates, electron-impact excitation cross sections, collision strengths, photoionization cross sections, autoionization rates, and recombination data. In the literature surveyed here, it appears both as a standalone distorted-wave and structure package and as the target-generation engine for larger close-coupling workflows, with applications spanning white-dwarf atmospheres, planetary nebulae, X-ray photoabsorption, tokamak impurity spectroscopy, solar coronal diagnostics, and kilonova radiative-transfer modeling (Preval et al., 2016, Elabidi, 2013, Preval et al., 2016, Mao et al., 2020, Ferguson et al., 10 Jun 2026).

1. Core computational role

AUTOSTRUCTURE is used in two closely related capacities. First, it provides atomic structure: level energies, wavefunctions, line strengths, oscillator strengths, and radiative transition probabilities. Second, it provides collision and continuum data: electron-impact excitation quantities in distorted-wave form, fine-structure collision strengths, direct and isolated-resonance photoionization cross sections, autoionization rates, and radiative as well as dielectronic recombination rate coefficients (Elabidi, 2013, Mao et al., 2016, Zanna et al., 2024, Preval et al., 2017).

Across the cited studies, the code is employed in configuration average, LS coupling, and intermediate coupling. For heavy highly charged systems, it is also used with relativistic $\kappa$-averaged wavefunctions and quasi-one-electron Dirac treatments in a Thomas–Fermi–Dirac–Amaldi model potential. In tungsten recombination work, intermediate coupling is the principal production mode because relativistic interactions and configuration mixing are important, while configuration average is retained for channel screening and identification of dominant contributions (Preval et al., 2016).

The code is not restricted to a single physical regime. In white-dwarf modeling it supplies non-hydrogenic bound-free opacity through Ni IV–VI photoionization cross sections; in tokamak spectroscopy it supplies wavelengths and radiative data for W$^{5+}$ and Al ions; in solar X-ray work it supplies autoionization and radiative data for Fe XVI satellite lines; and in kilonova research it supplies structure, radiative, autoionization, recombination, and collision data for ions such as Nd, U, and Sr II (Preval et al., 2016, Zhang et al., 2024, Zhang et al., 2023, Zanna et al., 2024, Ferguson et al., 10 Jun 2026, Deprince et al., 9 Sep 2025).

2. Atomic-structure formalism and optimization strategies

A recurring feature of AUTOSTRUCTURE calculations is the use of model potentials with adjustable orbital scaling parameters $\lambda_{nl}$. The literature describes scaled Thomas–Fermi–Dirac–Amaldi statistical model potentials, Slater-Type-Orbital model potentials, and semi-relativistic radial wavefunctions, with $\lambda_{nl}$ chosen variationally or tuned to reproduce spectroscopic benchmarks such as NIST or Kurucz energies (Elabidi, 2013, Mao et al., 2016, Nikolić et al., 2010, Sterling, 2011).

The optimization strategy depends strongly on the target system. In Ni IV–VI work for hot DA white dwarfs, the radial scaling parameters were optimized to reproduce Kurucz 2011 level energies as closely as possible, and the resulting structure was used to compute direct photoionization cross sections in intermediate coupling (Preval et al., 2016). In Mg III and Al IV, the orbitals were optimized by minimizing the sum of target term energies in LS coupling, after which a Breit–Pauli Hamiltonian including one-body fine-structure terms and two-body terms was used to obtain intermediate-coupling level structure (Elabidi, 2013). In Sr II, target energies were improved with a Term Energy Correction, and the resulting AUTOSTRUCTURE energies agreed with NIST to about $0.10\%$ on average (Deprince et al., 9 Sep 2025).

For strongly mixed heavy ions, empirical adjustment is even more important. In Cs IV–VI, term energy corrections based on NIST spectroscopic separations were used to improve Breit–Pauli mixing coefficients, because the ions are strongly mixed and the configuration-interaction model was intentionally modest (Chayer et al., 2022). In open-$f$-shell Nd III and U II–U IV, small changes in the $4f$ or $5f$ scaling parameter were found to move low-lying levels and near-threshold resonances substantially; the structure was therefore optimized specifically against low-lying observed energies, with additional post-processing shifts to place resonances correctly relative to threshold (Ferguson et al., 10 Jun 2026).

This body of work suggests that AUTOSTRUCTURE is most effective when structural optimization is treated as part of the physical model rather than as a purely preparatory step. The degree of sensitivity ranges from modest in mid-$Z$ ions to dominant in open-shell heavy systems (Ferguson et al., 10 Jun 2026, Zanna et al., 2024).

3. Photoionization, scattering, and recombination workflows

AUTOSTRUCTURE is widely used to generate level-resolved or bundled photoionization cross sections that are then converted into recombination data by detailed balance. In radiative-recombination calculations for H-like through Ne-like ions up to Zn, the workflow is explicit: AUTOSTRUCTURE computes level-resolved non-resonant photoionization cross sections; the Milne relation converts them into radiative-recombination cross sections; and Maxwellian integration yields level-resolved and total rate coefficients (Mao et al., 2016).

The rate definitions used in that work are

$$\alpha_i(T)=\int_0^\infty v\,\sigma_i(v)\,f(v,T)\,dv,\qquad \alpha_{\rm t}(T)=\sum_i \alpha_i(T),$$

and the associated electron energy-loss coefficient is

$^{5+}$0

with

$^{5+}$1

The same study introduces the weighted electron energy-loss factor $^{5+}$2, parameterizes it, and archives the data in ADAS adf48 format for use in SPEX (Mao et al., 2016).

For dielectronic recombination, the code is commonly used in the independent-processes, isolated-resonance, distorted-wave approximation. In Ar-like ions from K II to Zn XIII, AUTOSTRUCTURE provides accurate core-excitation thresholds and target wavefunctions, after which multiconfiguration Breit–Pauli calculations yield Maxwellian-averaged DR coefficients that correct earlier low-temperature deficiencies in empirical formulas (Nikolić et al., 2010). In tungsten, both partial final-state-resolved and total DR coefficients are computed, with explicit bundling strategies in $^{5+}$3, $^{5+}$4, and level resolution to support collisional-radiative modeling (Preval et al., 2016, Preval et al., 2017).

The code is also used directly for scattering. Mg III and Al IV fine-structure collision strengths were calculated in Breit–Pauli distorted-wave mode on fixed electron-energy grids, with Burgess-sum-rule and geometric-series top-up for high partial waves (Elabidi, 2013). In Sr II, AUTOSTRUCTURE distorted waves were benchmarked against close-coupling $^{5+}$5-matrix data: the effective collision strengths were generally within a factor of about $^{5+}$6 or less, and the method clearly outperformed ad hoc formulas for forbidden transitions, although it still neglected channel coupling and resonances (Deprince et al., 9 Sep 2025).

In several photoabsorption and K-shell studies, AUTOSTRUCTURE is used in the isolated-resonance approximation as a computationally tractable alternative to BPRM. For trace elements with $^{5+}$7 and $^{5+}$8, it supplies target representations and, where BPRM is infeasible, isolated-resonance cross sections with damping treatments and relativistic non-fine-structure corrections in LS coupling (Mendoza et al., 2017, Mendoza et al., 2018).

4. Embedding in larger modeling frameworks

A distinctive characteristic of AUTOSTRUCTURE is that its outputs are routinely propagated into broader NLTE, CR, and close-coupling pipelines rather than remaining isolated atomic tables. In hot white-dwarf work, Ni IV–VI bound-free and bound-bound data from AUTOSTRUCTURE were inserted into TLUSTY atmosphere models and SYNSPEC spectral synthesis, with superlevels and supercross-sections used to make the data tractable in NLTE radiative transfer (Preval et al., 2016). In the first white-dwarf Cs detection, AUTOSTRUCTURE oscillator strengths for Cs IV–VI were combined with GRASP2K comparisons and then inserted into TLUSTY/SYNSPEC model atoms for abundance analysis (Chayer et al., 2022).

In ADAS-oriented work, AUTOSTRUCTURE outputs are explicitly formatted for downstream plasma modeling. Tungsten DR and RR data were archived as adf09 and adf48 through OPEN-ADAS using a hybrid resolution scheme that retains level resolution for low-lying states and bundles higher manifolds while preserving parentage and branching information (Preval et al., 2016). The RR electron energy-loss dataset for H-like to Ne-like ions was likewise archived in adf48 and incorporated into SPEX (Mao et al., 2016). The N-like iso-electronic sequence calculation used AUTOSTRUCTURE to generate the 725-level target for ICFT $^{5+}$9-matrix calculations, after which the resulting effective collision strengths were archived as adf04 (Mao et al., 2020).

Tokamak spectroscopy provides a different embedding strategy. For W$\lambda_{nl}$0, AUTOSTRUCTURE, HULLAC, and FAC supplied structure and rate data to a fully collisional-radiative model that was then used to derive S/XB ratios and infer tungsten influx in EAST from the 382.13 Å and 394.07 Å lines (Zhang et al., 2024). For aluminum in EAST, AUTOSTRUCTURE wavelengths and radiative data were used together with HULLAC and FAC in CR modeling to identify EUV impurity lines from Al$\lambda_{nl}$1 to Al$\lambda_{nl}$2 (Zhang et al., 2023).

The following applications illustrate the range of embedded uses:

Domain	AUTOSTRUCTURE role	Representative papers
White-dwarf atmospheres	NLTE opacity input, model atoms, abundance fitting	(Preval et al., 2016, Chayer et al., 2022)
ADAS/SPEX plasma data	RR/DR rates, energy-loss data, archival formats	(Mao et al., 2016, Preval et al., 2016)
$\lambda_{nl}$3-matrix target generation	Target structure, $\lambda_{nl}$4-values, high-energy limits	(Mao et al., 2020, Mendoza et al., 2017)
Tokamak CR modeling	Wavelengths, $\lambda_{nl}$5, excitation data, S/XB ratios	(Zhang et al., 2024, Zhang et al., 2023)
Kilonova radiative transfer	Recombination, collision, and line-list inputs	(Ferguson et al., 10 Jun 2026, Fontes et al., 6 Apr 2026, Deprince et al., 9 Sep 2025)

5. Representative scientific impacts

The physical consequences of replacing approximate atomic data with AUTOSTRUCTURE outputs are often large. In the hot DA white dwarf G191-B2B, models using AUTOSTRUCTURE Ni IV–VI photoionization cross sections showed flux attenuation of up to $\lambda_{nl}$6 shortward of $\lambda_{nl}$7 Å relative to hydrogenic cross sections, while the larger Ni line list left the continua essentially unaffected. The same improved PICS changed inferred N and O abundances by as much as $\lambda_{nl}$8, shifted N and O ionization fractions to smaller column masses, and caused N/O IV and V abundance diagnostics to diverge because the higher charge states formed higher in the atmosphere (Preval et al., 2016).

In X-ray solar spectroscopy, AUTOSTRUCTURE calculations of Fe XVI autoionizing states produced satellite-line wavelengths and intensities that increased the modeled $\lambda_{nl}$9–$\lambda_{nl}$0 Å flux by a factor of $\lambda_{nl}$1 relative to CHIANTI v10 at $\lambda_{nl}$2 MK, resolving the shortfall seen in MaGIXS and accounting for the long-standing Fe XVII 3D discrepancy at $\lambda_{nl}$3 Å (Zanna et al., 2024). In the N-like sequence, AUTOSTRUCTURE-based target structures supported a 725-level ICFT $\lambda_{nl}$4-matrix survey whose effective collision strengths changed astrophysical diagnostics, including a Ca XIV density of about $\lambda_{nl}$5 and an Ar XII density of about $\lambda_{nl}$6 in updated CHIANTI modeling (Mao et al., 2020).

In tokamak and fusion contexts, AUTOSTRUCTURE-based tungsten recombination data materially altered ionization balance. For W$\lambda_{nl}$7 to W$\lambda_{nl}$8, the revised steady-state peak abundance temperatures shifted to lower values spanning $\lambda_{nl}$9–$0.10\%$0 keV, a range directly relevant to the pedestal, edge, scrape-off layer, and divertor (Preval et al., 2017). In W$0.10\%$1 to W$0.10\%$2, the inclusion of Maxwell–Jüttner corrections was reported to change both peak abundance temperatures and abundance fractions of several ions (Preval et al., 2016). In EAST W$0.10\%$3, AUTOSTRUCTURE-supported CR modeling gave S/XB ratios of order $0.10\%$4 under edge conditions and, together with a line brightness of about $0.10\%$5, implied a tungsten influx of order $0.10\%$6 at burst peak (Zhang et al., 2024).

In kilonova studies, AUTOSTRUCTURE appears in two different roles. As a recombination engine, it yielded temperature-dependent uranium DR coefficients of order $0.10\%$7–$0.10\%$8, with U III $0.10\%$9 U II giving $f$0 at $f$1 K and $f$2 for the same case (Ferguson et al., 10 Jun 2026). As a source of line lists, it formed one of three Nd atomic datasets whose use in otherwise identical SuperNu simulations changed peak bolometric luminosities by a ratio of nearly $f$3, with the dominant divergence traced to Nd I line statistics and wavelength distributions (Fontes et al., 6 Apr 2026).

The code has also enabled new identifications where no prior radiative data existed. In the first detection of Cs in a white-dwarf atmosphere, AUTOSTRUCTURE provided the first reported $f$4-values and $f$5-values for Cs IV–VI bound-bound transitions used in the analysis, leading to a derived abundance $f$6 (Chayer et al., 2022).

6. Accuracy limits, approximations, and methodological debates

The literature is explicit that AUTOSTRUCTURE results are only as reliable as the structural model and approximation level permit. Several important limitations recur. Distorted-wave calculations neglect channel coupling and, in many applications, resonance effects. In the Sr II benchmark, this was identified as the principal reason AUTOSTRUCTURE distorted waves cannot reach $f$7-matrix accuracy, even though they remain useful for large-scale data production (Deprince et al., 9 Sep 2025). In the white-dwarf Ni proof-of-concept, the photoionization calculation included direct photoionization only and neglected photoexcitation-autoionization resonances (Preval et al., 2016).

Sensitivity to configuration interaction is a second major issue. Fe XVI autoionization rates were found to vary by an order of magnitude under changes in configuration basis or scaling parameters because closely spaced states are strongly mixed, whereas radiative rates were much more stable (Zanna et al., 2024). Open-$f$8-shell Nd III and uranium ions are even more delicate: small changes in $f$9 or $4f$0 scaling can shift near-threshold resonances enough to alter low-temperature DR substantially (Ferguson et al., 10 Jun 2026). Tungsten $4f$1-shell DR provides a related example at the partial-rate level, where intermediate-coupling and configuration-average partial coefficients can differ by as little as $4f$2 and by as much as $4f$3 (Preval et al., 2017).

Uncertainty budgets differ strongly by process. For low-charge Se ions, direct photoionization cross sections near threshold were estimated to have internal uncertainties of $4f$4–$4f$5, RR coefficients about $4f$6, and low-temperature DR from $4f$7–$4f$8 up to two orders of magnitude depending on the ion because of unknown near-threshold autoionizing resonances (Sterling et al., 2011). For low-charge Kr ions, PI cross sections were also described as generally uncertain by $4f$9–$5f$0 near threshold, RR near $5f$1 K as typically uncertain by $5f$2, and DR by factors of $5f$3 to $5f$4 (Sterling, 2011).

Methodological disputes in the literature are not about whether AUTOSTRUCTURE is useful, but about where it is sufficient. For K-shell photoabsorption, BPRM is preferred where feasible because it resolves damping and channel coupling, yet AUTOSTRUCTURE isolated-resonance calculations were judged satisfactory for more complex ions where BPRM becomes computationally intractable (Mendoza et al., 2017, Mendoza et al., 2018). In N-like O II, the use of a single set of orthogonal orbitals in AUTOSTRUCTURE target construction was reported to make the low-charge structure less accurate than approaches with non-orthogonal orbitals or pseudo-states, whereas mid- and high-charge ions were described as much better behaved (Mao et al., 2020). For LS calculations of K-shell cross sections in heavier ions, non-fine-structure relativistic corrections were described as vital to avoid large resonance-position errors (Mendoza et al., 2018).

Taken together, these studies indicate that AUTOSTRUCTURE occupies a specific methodological niche. It is not a universal replacement for close-coupling, multichannel, or experimentally calibrated approaches, but it is a highly adaptable production code whose practical value comes from the combination of configurable structure models, broad process coverage, and direct interoperability with atmosphere, radiative-transfer, collisional-radiative, and plasma-database workflows (Preval et al., 2016, Mao et al., 2020, Ferguson et al., 10 Jun 2026).