- Open Access
Calibrated lanthanide atomic data for kilonova radiative transfer: Atomic structure and opacities
Phys. Rev. D 113, 063041 – Published 23 March, 2026
DOI: https://doi.org/10.1103/jxqw-7ynk
Abstract
The early spectra of the kilonova AT2017gfo following the binary neutron star merger GW170817 exhibit numerous features shaped by r-process nucleosynthesis products. Although a few species were tentatively detected, no third-peak elements were unambiguously identified, as the amount of atomic data required for radiative transfer modeling is immense. Although comprehensive atomic data, including atomic opacities, is now available for many elements, wavelength-calibrated data remain limited to a few selected ions. To examine the atomic opacities of all singly and doubly ionized lanthanides, from La () to Yb (), we perform atomic structure calculations using the fac code. Our calculations incorporate an innovative optimization of the local central potential and the number of configurations considered, alongside a calibration technique aimed at enhancing agreement between theoretical and experimental atomic energy levels. We assess the accuracy of the computed data, including energy levels and electric dipole (E1) transition strengths, as well as their impact on kilonova opacities. We find that strong transitions [] are in good agreement with both experiments and semiempirical calculations. For ions with substantial experimental data, the computed opacities exhibit good agreement with prior calculations. By calibrating low-lying energy levels with experimental data, we have identified 66 722 transitions with experimentally calibrated wavelength information, rendering future lanthanide line identifications through radiative transfer modeling feasible. In total, our calculations encompass 28 ions, yielding 146 849 energy levels below the ionization threshold and 29 337 507 transitions among these levels.
Physics Subject Headings (PhySH)
- Atomic & molecular structure
- Atomic spectra
- Electronic excitation & ionization
- Electronic structure of atoms & molecules
- Electronic transitions
- Fine & hyperfine structure
- Nuclear physics of explosive environments
- Nucleosynthesis in explosive environments
- Optical, UV, & IR astronomy
- Photoemission
- Transient & explosive astronomical phenomena
- Neutron stars & pulsars
- Composition of astronomical objects
- Electronic structure
- Hartree-Fock methods
Article Text
References (204)
- D. A. Coulter et al., Swope Supernova Survey 2017a (SSS17a), The optical counterpart to a gravitational wave source, Science 358, 1556 (2017).
- P. S. Cowperthwaite et al., The electromagnetic counterpart of the binary neutron star merger LIGO/Virgo GW170817. II. UV, Optical, and near-infrared light curves and comparison to kilonova models, Astrophys. J. Lett. 848, L17 (2017).
- S. J. Smartt et al., A kilonova as the electromagnetic counterpart to a gravitational-wave source, Nature (London) 551, 75 (2017).
- M. R. Drout et al., Light curves of the neutron star merger GW170817/SSS17a: Implications for r-process nucleosynthesis, Science 358, 1570 (2017).
- Y. Utsumi et al., J-GEM observations of an electromagnetic counterpart to the neutron star merger GW170817, Publ. Astron. Soc. Jpn. 69, 101 (2017).
- B. P. Abbott et al., Multi-messenger observations of a binary neutron star merger, Astrophys. J. Lett. 848, L12 (2017).
- B. P. Abbott et al., GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119, 161101 (2017).
- J. M. Lattimer and D. N. Schramm, Black-hole-neutron-star collisions, Astrophys. J. Lett. 192, L145 (1974).
- E. Symbalisty and D. N. Schramm, Neutron star collisions and the r-process, Astrophys. Lett. 22, 143 (1982), https://ui.adsabs.harvard.edu/abs/1982ApL....22..143S/abstract.
- D. Eichler, M. Livio, T. Piran, and D. N. Schramm, Nucleosynthesis, neutrino bursts and -rays from coalescing neutron stars, Nature (London) 340, 126 (1989).
- C. Freiburghaus, S. Rosswog, and F. K. Thielemann, R-process in neutron star mergers, Astrophys. J. Lett. 525, L121 (1999).
- S. Goriely, A. Bauswein, and H.-T. Janka, R-process nucleosynthesis in dynamically ejected matter of neutron star mergers, Astrophys. J. Lett. 738, L32 (2011).
- A. Bauswein, T. W. Baumgarte, and H. T. Janka, Prompt merger collapse and the maximum mass of neutron stars, Phys. Rev. Lett. 111, 131101 (2013).
- S. Wanajo, Y. Sekiguchi, N. Nishimura, K. Kiuchi, K. Kyutoku, and M. Shibata, Production of all the r-process nuclides in the dynamical ejecta of neutron star mergers, Astrophys. J. Lett. 789, L39 (2014).
- L.-X. Li and B. Paczyński, Transient events from neutron star mergers, Astrophys. J. Lett. 507, L59 (1998).
- S. R. Kulkarni, Modeling supernova-like explosions associated with gamma-ray bursts with short durations, arXiv:astro-ph/0510256.
- B. D. Metzger, G. Martínez-Pinedo, S. Darbha, E. Quataert, A. Arcones, D. Kasen, R. Thomas, P. Nugent, I. V. Panov, and N. T. Zinner, Electromagnetic counterparts of compact object mergers powered by the radioactive decay of r-process nuclei, Mon. Not. R. Astron. Soc. 406, 2650 (2010).
- D. Kasen, N. R. Badnell, and J. Barnes, Opacities and spectra of the r-process ejecta from neutron star mergers, Astrophys. J. 774, 25 (2013).
- M. Tanaka and K. Hotokezaka, Radiative transfer simulations of neutron star merger ejecta, Astrophys. J. 775, 113 (2013).
- B. D. Metzger and R. Fernández, Red or blue? A potential kilonova imprint of the delay until black hole formation following a neutron star merger, Mon. Not. R. Astron. Soc. 441, 3444 (2014).
- D. Kasen, B. Metzger, J. Barnes, E. Quataert, and E. Ramirez-Ruiz, Origin of the heavy elements in binary neutron-star mergers from a gravitational-wave event, Nature (London) 551, 80 (2017).
- J. Barnes, D. Kasen, M.-R. Wu, and G. Martínez-Pinedo, Radioactivity and thermalization in the ejecta of compact object mergers and their impact on kilonova light curves, Astrophys. J. 829, 110 (2016).
- M. Tanaka, D. Kato, G. Gaigalas, P. Rynkun, L. Radžiūtė, S. Wanajo, Y. Sekiguchi, N. Nakamura, H. Tanuma, I. Murakami, and H. A. Sakaue, Properties of kilonovae from dynamical and post-merger ejecta of neutron star mergers, Astrophys. J. 852, 109 (2018).
- M. Tanaka, D. Kato, G. Gaigalas, and K. Kawaguchi, Systematic opacity calculations for kilonovae, Mon. Not. R. Astron. Soc. 496, 1369 (2020).
- M. Bulla, POSSIS: Predicting spectra, light curves, and polarization for multidimensional models of supernovae and kilonovae, Mon. Not. R. Astron. Soc. 489, 5037 (2019).
- L. J. Shingles, C. E. Collins, V. Vijayan, A. Flörs, O. Just, G. Leck, Z. Xiong, A. Bauswein, G. Martínez-Pinedo, and S. A. Sim, Self-consistent 3D radiative transfer for kilonovae: Directional spectra from merger simulations, Astrophys. J. Lett. 954, L41 (2023).
- C. E. Collins, L. J. Shingles, A. Bauswein, S. A. Sim, T. Soultanis, V. Vijayan, A. Flörs, O. Just, G. Leck, G. Lioutas, G. Martínez-Pinedo, A. Sneppen, D. Watson, and Z. Xiong, Towards inferring the geometry of kilonovae, Mon. Not. R. Astron. Soc. 529, 1333 (2024).
- A. Kitamura, K. Kawaguchi, M. Tanaka, and S. Fujibayashi, Linking analytic light-curve models to physical properties of kilonovae, Astrophys. J. 982, 97 (2025).
- J. Barnes, Y. L. Zhu, K. A. Lund, T. M. Sprouse, N. Vassh, G. C. McLaughlin, M. R. Mumpower, and R. Surman, Kilonovae across the nuclear physics landscape: The impact of nuclear physics uncertainties on r-process-powered emission, Astrophys. J. 918, 44 (2021).
- J. Barnes and D. Kasen, Effect of a high opacity on the light curves of radioactively powered transients from compact object mergers, Astrophys. J. 775, 18 (2013).
- D. Kasen, R. Fernández, and B. D. Metzger, Kilonova light curves from the disc wind outflows of compact object mergers, Mon. Not. R. Astron. Soc. 450, 1777 (2015).
- C. J. Fontes, C. L. Fryer, A. L. Hungerford, P. Hakel, J. Colgan, D. P. Kilcrease, and M. E. Sherrill, Relativistic opacities for astrophysical applications, High Energy Density Phys. 16, 53 (2015).
- S. Banerjee, M. Tanaka, K. Kawaguchi, D. Kato, and G. Gaigalas, Simulations of early kilonova emission from neutron star mergers, Astrophys. J. 901, 29 (2020).
- H. Carvajal Gallego, J. C. Berengut, P. Palmeri, and P. Quinet, Large-scale atomic data calculations in Ce V—X ions for application to early kilonova emission from neutron star mergers, Mon. Not. R. Astron. Soc. 509, 6138 (2022).
- H. Carvajal Gallego, J. C. Berengut, P. Palmeri, and P. Quinet, Atomic data and opacity calculations in La V-X ions for the investigation of kilonova emission spectra, Mon. Not. R. Astron. Soc. 513, 2302 (2022).
- S. Banerjee, M. Tanaka, D. Kato, G. Gaigalas, K. Kawaguchi, and N. Domoto, Opacity of the highly ionized lanthanides and the effect on the early eilonova, Astrophys. J. 934, 117 (2022).
- H. Carvajal Gallego, J. Deprince, J. C. Berengut, P. Palmeri, and P. Quinet, Opacity calculations in four to nine times ionized Pr, Nd, and Pm atoms for the spectral analysis of kilonovae, Mon. Not. R. Astron. Soc. 518, 332 (2023).
- S. Banerjee, M. Tanaka, D. Kato, and G. Gaigalas, Diversity of early kilonova with the realistic opacities of highly ionized heavy elements, Astrophys. J. 968, 64 (2024).
- H. Carvajal Gallego, J. Deprince, L. Maison, P. Palmeri, and P. Quinet, Overview of the contributions from all lanthanide elements to kilonova opacity in the temperature range from 25 000 to 40 000 K, Astron. Astrophys. 685, A91 (2024).
- G. Gaigalas, P. Rynkun, L. Radžiūtė, D. Kato, M. Tanaka, and P. Jönsson, Energy level structure and transition data of , Astrophys. J. Suppl. Ser. 248, 13 (2020).
- H. Carvajal Gallego, P. Palmeri, and P. Quinet, Multiconfiguration Dirac-Hartree-Fock radiative parameters for emission lines in Ce II-IV ions and cerium opacity calculations for kilonovae, Mon. Not. R. Astron. Soc. 501, 1440 (2021).
- J. H. Gillanders, M. McCann, S. A. Sim, S. J. Smartt, and C. P. Ballance, Constraints on the presence of platinum and gold in the spectra of the kilonova AT2017gfo, Mon. Not. R. Astron. Soc. 506, 3560 (2021).
- R. F. Silva, J. M. Sampaio, P. Amaro, A. Flörs, G. Martínez-Pinedo, and J. P. Marques, Structure calculations in Nd III and U III relevant for kilonovae modelling, Atoms 10, 18 (2022).
- A. Flörs, R. F. Silva, J. Deprince, H. Carvajal Gallego, G. Leck, L. J. Shingles, G. Martínez-Pinedo, J. M. Sampaio, P. Amaro, J. P. Marques, S. Goriely, P. Quinet, P. Palmeri, and M. Godefroid, Opacities of singly and doubly ionized neodymium and uranium for kilonova emission modeling, Mon. Not. R. Astron. Soc. 524, 3083 (2023).
- G. Gaigalas, P. Rynkun, N. Domoto, M. Tanaka, D. Kato, and L. Kitovienė, Theoretical investigation of energy levels and transitions for Ce III with applications to kilonova spectra, Mon. Not. R. Astron. Soc. 530, 5220 (2024).
- C. J. Fontes, C. L. Fryer, A. L. Hungerford, R. T. Wollaeger, and O. Korobkin, A line-binned treatment of opacities for the spectra and light curves from neutron star mergers, Mon. Not. R. Astron. Soc. 493, 4143 (2020).
- L. Radžiūtė, G. Gaigalas, D. Kato, P. Rynkun, and M. Tanaka, Extended calculations of energy levels and transition rates for singly ionized lanthanide elements. I. Pr-Gd, Astrophys. J. Suppl. Ser. 248, 17 (2020).
- L. Radžiūtė, G. Gaigalas, D. Kato, P. Rynkun, and M. Tanaka, Extended calculations of energy levels and transition rates for singly ionized lanthanide elements. II. Tb-Yb, Astrophys. J. Suppl. Ser. 257, 29 (2021).
- C. J. Fontes, C. L. Fryer, R. T. Wollaeger, M. R. Mumpower, and T. M. Sprouse, Actinide opacities for modelling the spectra and light curves of kilonovae, Mon. Not. R. Astron. Soc. 519, 2862 (2023).
- D. Kato, M. Tanaka, G. Gaigalas, L. Kitovienė, and P. Rynkun, Systematic opacity calculations for kilonovae—II. Improved atomic data for singly ionized lanthanides, Mon. Not. R. Astron. Soc. 535, 2670 (2024).
- J. Deprince, G. Wagle, S. Ben Nasr, H. Carvajal Gallego, M. Godefroid, S. Goriely, O. Just, P. Palmeri, P. Quinet, and S. Van Eck, Kilonova ejecta opacity inferred from new large-scale hfr atomic calculations in all elements between Ca () and Lr (), Astron. Astrophys. 696, A32 (2025).
- W. Even, O. Korobkin, C. L. Fryer, C. J. Fontes, R. T. Wollaeger, A. Hungerford, J. Lippuner, J. Miller, M. R. Mumpower, and G. W. Misch, Composition effects on kilonova spectra and light curves. I, Astrophys. J. 899, 24 (2020).
- N. R. Badnell, autostructure: General program for calculation of atomic and ionic properties, Astrophysics Source Code Library, record ascl:1612.014 (2016), https://ascl.net/1612.014.
- M. F. Gu, The flexible atomic code, Can. J. Phys. 86, 675 (2008).
- C. Froese Fischer, G. Gaigalas, P. Jönsson, and J. Bieroń, grasp2018-A Fortran 95 version of the general relativistic atomic structure package, Comput. Phys. Commun. 237, 184 (2019).
- A. Bar-Shalom, M. Klapisch, and J. Oreg, hullac, An integrated computer package for atomic processes in plasmas, J. Quant. Spectrosc. Radiat. Transfer 71, 169 (2001).
- R. D. Cowan, The Theory of Atomic Structure and Spectra, Los Alamos Series in Basic and Applied Sciences (University of California Press, Ltd., Berkeley, 1981).
- C. J. Fontes, H. L. Zhang, J. Abdallah, Jr., R. E. H. Clark, D. P. Kilcrease, J. Colgan, R. T. Cunningham, P. Hakel, N. H. Magee, and M. E. Sherrill, The Los Alamos suite of relativistic atomic physics codes, J. Phys. B 48, 144014 (2015).
- J. P. Desclaux, A multiconfiguration relativistic DIRAC-FOCK program, Comput. Phys. Commun. 9, 31 (1975).
- N. Domoto, M. Tanaka, D. Kato, K. Kawaguchi, K. Hotokezaka, and S. Wanajo, Lanthanide features in near-infrared spectra of kilonovae, Astrophys. J. 939, 8 (2022).
- Q. Lu, C. L. Yan, J. Meng, G. Q. Xu, Y. Yang, C. Y. Chen, J. Xiao, J. G. Li, J. G. Wang, and Y. Zou, Visible spectra of in an electron-beam ion trap, Phys. Rev. A 103, 022808 (2021).
- M. McCann, S. Bromley, S. D. Loch, and C. P. Ballance, Atomic data calculations for Au I-Au III and exploration in the application of collisional-radiative theory to laboratory and neutron star merger plasmas, Mon. Not. R. Astron. Soc. 509, 4723 (2022).
- R. Ferreira da Silva, A. Flörs, L. Leitão, J. P. Marques, G. Martínez-Pinedo, and J. M. Sampaio, Systematic bayesian optimization for atomic structure calculations of heavy elements, Phys. Rev. A 112, 012802 (2025).
- M. Hoffman, E. Brochu, and N. de Freitas, Portfolio allocation for bayesian optimization, in Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, UAI’11 (AUAI Press, Arlington, Virginia, 2011), pp. 327–336.
- A. Kramida, Yu. Ralchenko, and J. Reader (NIST ASD Team), NIST Atomic Spectra Database (ver. 5.9) (2021), national Institute of Standards and Technology, Gaithersburg, MD.
- P. Quinet and P. Palmeri, Current status and developments of the atomic Database on Rare-Earths at Mons University (DREAM), Atoms 8, 18 (2020).
- M. Ding, A. N. Ryabtsev, E. Y. Kononov, T. Ryabchikova, C. P. Clear, F. Concepcion, and J. C. Pickering, Spectrum and energy levels of the low-lying configurations of Nd III, Astron. Astrophys. 684, A149 (2024).
- N. Spector, J. Sugar, and J.-F. Wyart, Analysis of the third spectrum of dysprosium (Dy III), J. Opt. Soc. Am. B 14, 511 (1997).
- G. Gaigalas, C. Fischer, P. Rynkun, and P. Jönsson, jj2lsj transformation and unique labeling for energy levels, Atoms 5, 6 (2017).
- C. Ferrara, M. Giarrusso, and F. Leone, Experimental atomic data of spectral lines—I. Cs, Ba, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Re, and Os in the 370–1000 nm interval, Mon. Not. R. Astron. Soc. 527, 4440 (2024).
- E. A. Den Hartog, G. T. Voith, and I. U. Roederer, Atomic transition probabilities for ultraviolet and optical lines of Tm II, Astrophys. J. Suppl. Ser. 274, 9 (2024).
- G. T. Voith, E. A. Den Hartog, and I. U. Roederer, Atomic transition probabilities for UV and optical lines of Gd II, Astrophys. J. Suppl. Ser. 278, 7 (2025).
- W. F. Meggers, Regularities in the arc spectrum of lanthanum, J. Wash. Acad. Sci. 17, 25 (1927), https://www.jstor.org/stable/24522554?seq=11.
- H. N. Russell and W. F. Meggers, An analysis of lanthanum spectra (La I, La II, La III), Bur Stand J Res 9, 625 (1932).
- G. R. Harrison, N. Rosen, and J. Rand McNally, Zeeman effect data for the spectra of Lanthanum—La I and La II, J. Opt. Soc. Am. 35, 658 (1945).
- F. Güzelçimen, M. Tonka, Z. Uddin, N. A. Bhatti, L. Windholz, S. Kröger, and G. Başar, Revised energy levels of singly ionized lanthanum, J. Quant. Spectrosc. Radiat. Transfer 211, 188 (2018).
- R. C. Gibbs and H. E. White, Rubidium and caesium-like doublets of stripped atoms, Proc. Natl. Acad. Sci. U.S.A. 12, 551 (1926).
- J. S. Badami, The spectrum of trebly-ionized cerium (Ce IV), Proc. Phys. Soc. 43, 53 (1931).
- R. J. Lang, The spectrum of trebly ionized cerium, Can. J. Res. 13, 1 (1935).
- J. Sugar, Analyses of lanthanide and actinide spectra, J. Opt. Soc. Am. 55, 1283 (1965).
- H. Odabasi, Spectrum of doubly ionized Lanthanum (La iii)*, J. Opt. Soc. Am. 57, 1459 (1967).
- W. C. Martin, R. Zalubas, and L. Hagan, Atomic Energy Levels: The Rare Earth Elements (The Spectra of Lanthanum, Cerium, Praseodymium, Neodymium, Promethium, Samarium, Europium, Gadolinium, Terbium, Dysprosium, Holmium, Ebrium, Thulium, Ytterbium, and Lutetium), National Standard Reference Data Series Vol. NSRDS-NBS 60 (National Bureau of Standards, Washington, DC, 1978), 10.6028/NBS.NSRDS.60.
- W. E. Albertson and G. R. Harrison, Preliminary analysis of the first spark spectrum of Cerium-Ce II, Phys. Rev. 52, 1209 (1937).
- G. R. Harrison, W. E. Albertson, and N. F. Hosford, Zeeman effect data and further classification of the first spark spectrum of Cerium—Ce II, J. Opt. Soc. Am. 31, 439 (1941).
- C. H. Corliss, Wavelengths and energy levels of the second spectrum of Cerium (Ce II), J. Res. Natl. Bur. Stand. 77A, 419 (1973).
- T. L. Bruin, J. N. Lier, and H. J. va de Vliet, The Zeeman-effect of doubly ionized cerium, Proc. R. Acad. Amsterdam 40, 334 (1937), https://nvlpubs.nist.gov/nistpubs/Legacy/NSRDS/nbsnsrds60.pdf.
- H. N. Russell, R. B. King, and R. J. Lang, The third spectrum of cerium (Ce III), Phys. Rev. 52, 456 (1937).
- S. Johansson and U. Litzén, The -4f5d lines of Ce III, Phys. Scr. 6, 139 (1972).
- N. Rosen, G. R. Harrison, and J. R. McNally, Zeeman effect data and preliminary classification of the spark spectrum of Praseodymium-Pr II, Phys. Rev. 60, 722 (1941).
- A. Ginibre, Fine and hyperfine structures of singly ionized praseodymium: I. Energy levels, hyperfine structures and Zeeman effect, classified lines, Phys. Scr. 39, 694 (1989).
- A. Ginibre, Fine and hyperfine structures of singly ionised praseodymium: II. Parametric interpretation of fine and hyperfine structures for the even levels of singly ionised praseodymium, Phys. Scr. 39, 710 (1989).
- S. Ivarsson, U. Litzén, and G. M. Wahlgren, Accurate wavelengths, oscillator strengths and hyperfine structure in selected praseodymium lines of astrophysical interest, Phys. Scr. 64, 455 (2001).
- B. Furmann, D. Stefańska, E. Stachowska, J. Ruczkowski, and J. Dembczyński, Hyperfine-structure measurements and new levels evaluation in singly ionized praseodymium, Eur. Phys. J. D 17, 275 (2001).
- B. Furmann, D. Stefańska, J. Dembczyński, and E. Stachowska, New levels and hyperfine structure evaluation in singly ionized praseodymium, Phys. Scr. 72, 300 (2005).
- B. Furmann, D. Stefańska, J. Dembczyński, and E. Stachowska, New electron levels and classified lines in Pr II from hyperfine structure measurements, At. Data Nucl. Data Tables 93, 127 (2007).
- J. Sugar, Analysis of the third spectrum of praseodymium*, J. Opt. Soc. Am. 53, 831 (1963).
- J. Sugar, The third spectrum of Praseodymium (Pr (III) in the vacuum ultraviolet, J. Res. Natl. Bur. Stand., Sect. A 73A, 333 (1969).
- H. Crosswhite, H. M. Crosswhite, and B. R. Judd, Magnetic parameters for the configuration , Phys. Rev. 174, 89 (1968).
- J. Sugar, Spectrum of doubly ionized praseodymium from 2107 Å to 10716 Å, J. Res. Natl. Bur. Stand., Sect. A 78A, 555 (1974).
- J. F. Wyart, J. Blaise, and P. Camus, Progrès Récents dans l’Interprétation des configurations des Lanthanides II. Etude Paramétrique des configurations, Phys. Scr. 9, 325 (1974).
- W. E. Albertson, G. R. Harrison, and J. R. McNally, First spark spectrum of neodymium-preliminary classification and Zeeman effect data, Phys. Rev. 61, 167 (1942).
- J. F. Wyart, Ph.D. thesis, University of Paris, Orsay, 1968.
- R. Kielkopf, Ph.D. thesis, University of Amsterdam, 1969.
- J. Blaise, J. Chevillard, J. Vergès, and J. F. Wyart, Etude des spectres d’émission dans l’infrarouge par l’emploi d’un SISAM—IV. spectre d’émission du néodyme, Spectrochim. Acta B Atom. Spectros. 25, 333 (1970).
- J. Blaise, J. F. Wyart, R. Hoekstra, and P. J. G. Kruiver, Present state of the analysis of Nd I and Nd II, J. Opt. Soc. Am. 61, 1335 (1971).
- J. Blaise (unpublished analysis, 2002).
- H. Crosswhite (unpublished analysis, 1976).
- G. H. Dieke, H. M. Crosswhite, and B. Dunn, Emission spectra of the doubly and triply ionized rare earths*, J. Opt. Soc. Am. 51, 820 (1961).
- G. H. Dieke and H. M. Crosswhite, The spectra of the doubly and triply ionized rare earths, Appl. Opt. 2, 675 (1963).
- M. Aldenius, Ph.D. thesis, University of Lund, 2001.
- T. Ryabchikova, A. Ryabtsev, O. Kochukhov, and S. Bagnulo, Rare-earth elements in the atmosphere of the magnetic chemically peculiar star HD 144897. New classification of the Nd III spectrum, Astron. Astrophys. 456, 329 (2006).
- J. A. Weinman, Promethium spectra: Pm II and Pm III, Phys. Rev. 78, 628 (1950).
- R. G. Gutmacher, J. G. Conway, and C. E. Moore, The second spectrum of promethium, J. Opt. Soc. Am. 48, 389 (1958).
- R. Otto, H. Huhnermann, J. Reader, and J. F. Wyart, Hyperfine structure investigations and identification of new energy levels in the ionic spectrum of , J. Phys. B 28, 3615 (1995).
- W. C. Martin, Energy levels and classified lines in the second spectrum of thorium (Th II), J. Opt. Soc. Am. 61, 1682 (1971).
- W. Albertson, Analysis of the spectrum of singly ionized samarium, Astrophys. J. 84, 26 (1936).
- J. Blaise, C. Morillon, M.-G. Schweighofer, and J. Verges, Etude des spectres d’émission dans l’infrarouge par l’emploi d’un SISAM—III. Spectre d’émission du samarium, Spectrochim. Acta B Atom. Spectros. 24, 405 (1969).
- A. Dupont, Spectrum of Sm III*, J. Opt. Soc. Am. 57, 867 (1967).
- W. Albertson, The spectrum of singly ionized europium, Phys. Rev. 45, 499 (1934).
- H. N. Russell, W. Albertson, and D. N. Davis, The spark spectrum of europium, Eu II, Phys. Rev. 60, 641 (1941).
- B. Furmann and D. Stefańska, Experimental determination of core relaxation and screening effects on the wavefunction at a nucleus for stable isotopes of— II, Eur. Phys. J. Special Topics 222, 2279 (2013).
- J. Sugar and N. Spector, Spectrum and energy levels of doubly ionized europium (Eu III), J. Opt. Soc. Am. 64, 1484 (1974).
- J. F. Wyart, W. Ü. L. Tchang-Brillet, S. S. Churilov, and A. N. Ryabtsev, Extended analysis of the Eu III spectrum, Astron. Astrophys. 483, 339 (2008).
- W. E. Albertson, H. Bruynes, and R. Hanau, The normal electron configuration of singly ionized gadolinium, Phys. Rev. 57, 292 (1940).
- H. N. Russell, The arc and spark spectra of gadolinium, J. Opt. Soc. Am. 40, 550 (1950).
- J. Blaise, J. Chevillard, J. Verges, J. F. Wyart, and T. A. M. van Kleef, Etude des spectres d’émission dans l’infrarouge par l’emploi d’un SISAM—V. Spectre d’émission du gadolinium, Spectrochim. Acta B Atom. Spectros. 26, 1 (1971).
- A. Venugopalan, S. M. Afzal, and S. A. Ahmad, Isotope shift studies in the UV spectrum of singly ionised gadolinium, Spectrochim. Acta B Atom. Spectros. 53, 633 (1998).
- N. Spector, Analysis of even configurations in the second spectrum of gadolinium (Gd II), J. Opt. Soc. Am. 60, 763 (1970).
- W. R. Callahan, The spectrum of doubly ionized gadolinium, Ph.D. thesis, Johns Hopkins University, Maryland, 1962.
- W. R. Callahan, Spectrum of doubly ionized gadolinium*, J. Opt. Soc. Am. 53, 695 (1963).
- J. F. J. Kielkopf, Ph.D. thesis, Johns Hopkins University, 1969.
- E. Meinders, Classification of Tb II-lines in connection with hyperfine structure, Physica (Utrecht) 42, 427 (1969).
- P. F. A. Klinkenberg, Interpretation of Zeeman patterns of Tb II-lines, Opt. Pura Apl. 10 (1977), https://sedoptica.es/Menu_Volumenes/Pdfs/OPA_10_3_10.pdf.
- J. Blaise, P. Camus, and J. Wyart, Gmelin Handbuch der Anorganischen Chemie, Vol. 39 (Springer-Verlag, Berlin, 1976).
- E. Meinders, T. A. M. Van Kleef, and J. F. Wyart, The analysis of doubly ionized terbium (Tb III), Physica (Utrecht) 61, 443 (1972).
- E. Paulson, Wave-lengths of elements at high temperatures, Astrophys. J. 40, 298 (1914).
- W. F. Meggers, Series regularities in the spectra of the lanthanide rare earths, Rev. Mod. Phys. 14, 96 (1942).
- J. M. Blank, Zeeman effect of Dy II, J. Opt. Soc. Am. 42, 117 (1952).
- V. G. Mossotti and V. A. Fassel, Emission flame spectrometry of the rare earths, Spectrochim. Acta 20, 1117 (1964).
- K. L. Vander Sluis and J. R. McNally, Zeeman effect in Dy II, J. Opt. Soc. Am. 60, 1209 (1970).
- J. G. Conway and E. F. Worden, Preliminary level analysis of the first and second spectra of dysprosium, Dy I and Dy II*, J. Opt. Soc. Am. 61, 704 (1971).
- J.-F. Wyart, Dysprosium levels II: Odd configurations, Spectrochim. Acta B Atom. Spectros. 27, 443 (1972).
- J.-F. Wyart, Dysprosium levels III: Even configurations, Spectrochim. Acta B Atom. Spectros. 27, 616 (1972).
- J.-F. Wyart, Analyse paramétrique de la configuration de Dy II, Physica (Utrecht) 89, 361 (1976).
- G. Nave and U. Griesmann, New energy levels and classifications of spectral lines from neutral and singly-ionized dysprosium (Dy I and Dy II), Phys. Scr. 62, 463 (2000).
- H. M. Crosswhite, Spectra of quadruply ionized praseodymium (Pr V), doubly and triply ionized neodymium (Nd III and Nd IV), and doubly ionized dysprosium (Dy III), J. Opt. Soc. Am. 53, 202 (1963).
- J. Sugar, Energy levels of neutral and singly ionized holmium (Ho I and Ho II), J. Opt Soc. Am. 58, 1519 (1968).
- A. E. J. Livingston and E. H. Pinnington, Spectrum of singly-ionized holmium (Ho II), J. Opt. Soc. Am. 61, 1429 (1971).
- J.-F. Wyart, J. Blaise, and T. A. M. Van Kleef, A parametric study of the configuration of Ho II, J. Phys. B 7, 1111 (1974).
- J. Gurell, G. M. Wahlgren, G. Nave, and J.-F. Wyart, The spectrum of singly ionized holmium (Ho II), Phys. Scr. 79, 035306 (2009).
- J. H. McElaney, The spectrum of doubly ionized homium, Ph.D. thesis, Johns Hopkins University, Maryland, 1966.
- J. H. McElaney, Spectrum of Ho III*, J. Opt. Soc. Am. 57, 870 (1967).
- J. Becher, Theoretical Investigation of Doubly-Ionized and Triply-Ionized Lanthanides, and the Empirical Analysis of Erbium, Ph.D. thesis, Johns Hopkins University, Maryland, 1965.
- R. Hussain, The Spectra of Dysprosium-Iv and Holmium-Iii, Ph.D. thesis, Johns Hopkins University, Maryland, 1973.
- J. F. Wyart, H. M. Crosswhite, and R. Hussain, Energy levels of Ho III, Physica (Amsterdam) 85B+C, 386 (1976).
- J. R. McNally and K. L. V. Sluis, Low levels of the arc spectrum of erbium (Er II), J. Opt. Soc. Am. 49, 200 (1959).
- J. W. Lindner and S. P. Davis, Zeeman effect in the arc spectrum of erbium, J. Opt. Soc. Am. 48, 542 (1958).
- A. Gatterer and J. Junkes, Spektren der Seltenen Erden (Specola Vaticana, Vatican City, 1945).
- B. R. Judd and L. C. Marquet, A pair coupling scheme for , J. Opt. Soc. Am. 52, 504 (1962).
- C. H. Corliss, Electrostatic parameters for erbium in the spectra Er II and Er III, Astrophys. J. 138, 272 (1963).
- L. C. Marquet and S. P. Davis, Atomic energy levels of neutral erbium*, J. Opt. Soc. Am. 55, 471 (1965).
- K. L. V. Sluis and J. R. McNally, Zeeman effect of Er II, J. Opt. Soc. Am. 60, 94 (1970).
- N. Spector, New low even levels of singly ionized Erbium (Er II), Astrophys. J. 167, 205 (1971).
- N. Spector, A study of infrared spectra of lanthanide and actinide free ions in yttrium and lanthanum trichloride matrices, J. Opt. Soc. Am. 61, 1495 (1971).
- J.-F. Wyart and J. E. Lawler, Assessment and optimization of the Er II spectroscopic data, Phys. Scr. 79, 035301 (2009).
- G. H. Dieke, H. M. Crosswhite, and B. Dunn, Interpretations of the spectra of the third spectra of the rare earths, J. Opt. Soc. Am. 51, 337 (1961).
- N. Spector, Level structure of doubly ionized erbium (Er III), J. Opt. Soc. Am. 63, 358 (1973).
- J. F. Wyart, J. J. A. Koot, and T. A. M. Van Kleef, The configuration in the lanthanide spectra, Physica (Utrecht) 77, 159 (1974).
- J. F. Wyart and C. Bauche-Arnoult, Interprétation des configurations et par la Méthode paramétrique généralisée, Phys. Scr. 22, 583 (1980).
- J. F. Wyart, J. Blaise, W. P. Bidelman, and C. R. Cowley, Energy levels and transition probabilities in doubly-ionized erbium (Er III), Phys. Scr. 56, 446 (1997).
- J. Blaise and P. Camus, Spectre d’arc du thulium, J. Phys. (Paris) 26, 605 (1965).
- P. Camus, A. Gatterer, and J. Junkes, The spectrum of the singly ionized thulium atom (Tm II), Spectrochim. Acta B Atom. Spectros. 24, 367 (1969).
- N. Spector, Spectrum of singly ionized thulium (Tm II), J. Opt. Soc. Am. 57, 1358 (1967).
- P. Camus and J. Sugar, Analysis of the even-parity configurations in the second spectrum of thulium, Phys. Scr. 3, 231 (1971).
- J.-F. Wyart, J. Blaise, and P. Camus, A parametric study of the configuration of Tm II, J. Phys. B 7, 1112 (1974).
- J.-F. Wyart, Analysis of the low-lying levels of doubly ionized thulium (Tm III), Can. J. Phys. 89, 451 (2011).
- J.-G. Li and V. A. Dzuba, Testing Bohr–Weisskopf effect and accuracy of electronic structure calculations with hyperfine structure of Tm II, J. Phys. B 53, 035004 (2020).
- J. Sugar, Energy levels of doubly ionized thulium (Tm III), J. Opt. Soc. Am. 59, 1383 (1969).
- J. Sugar, Spectrum of doubly ionized thulium (Tm III)*, J. Opt. Soc. Am. 60, 454 (1970).
- J.-F. Wyart, Analysis of the third spectrum of thulium (Tm III), Phys. Scr. 4, 53 (1971).
- W. F. Meggers, Spectra of the singly ionized rare earths, J. Opt. Soc. Am. 57, 396 (1967).
- N. Spector, The spectrum of singly ionized ytterbium (Yb II), J. Opt. Soc. Am. 58, 837 (1968).
- J.-F. Wyart and P. Camus, Interpretation of , , and configurations of Yb II, J. Quant. Spectrosc. Radiat. Transfer 21, 115 (1979).
- B. W. Bryant, The spectra of doubly and triply ionized ytterbium, Johns Hopkins Spectroscopic Report No. 21 (1961).
- B. W. Bryant, Spectra of doubly and triply ionized ytterbium, Yb III and Yb IV†, J. Opt. Soc. Am. 55, 771 (1965).
- J. Sugar, Configuration of doubly ionized Ytterbium, J. Opt. Soc. Am. 60, 571 (1970).
- G. Gaigalas, D. Kato, P. Rynkun, L. Radžiūtė, and M. Tanaka, Extended calculations of energy levels and transition rates of Nd II-IV ions for application to neutron star mergers, Astrophys. J. Suppl. Ser. 240, 29 (2019).
- R. G. Eastman and P. A. Pinto, Spectrum formation in supernovae: Numerical techniques, Astrophys. J. 412, 731 (1993).
- V. V. Sobolev, Moving Envelopes of Stars (Harvard University Press, Cambridge, MA; London, England, 1960).
- H. J. G. L. M. Lamers and J. P. Cassinelli, Introduction to Stellar Winds (Cambridge University Press, Cambridge, England, 1999), 10.1017/CBO9781139175012.
- Q. Pognan, A. Jerkstrand, and J. Grumer, NLTE effects on kilonova expansion opacities, Mon. Not. R. Astron. Soc. 513, 5174 (2022).
- K. Hotokezaka, M. Tanaka, D. Kato, and G. Gaigalas, Nebular emission from lanthanide-rich ejecta of neutron star merger, Mon. Not. R. Astron. Soc. 506, 5863 (2021).
- J. H. Gillanders, S. J. Smartt, S. A. Sim, A. Bauswein, and S. Goriely, Modelling the spectra of the kilonova AT2017gfo—I. The photospheric epochs, Mon. Not. R. Astron. Soc. 515, 631 (2022).
- E. Pian, Binary neutron star mergers: A multi-messenger revolution, Front. Astron. Space Sci. 7, 108 (2021).
- D. Watson, C. J. Hansen, J. Selsing, A. Koch, D. B. Malesani, A. C. Andersen, J. P. U. Fynbo, A. Arcones, A. Bauswein, S. Covino, A. Grado, K. E. Heintz, L. Hunt, C. Kouveliotou, G. Leloudas, A. J. Levan, P. Mazzali, and E. Pian, Identification of strontium in the merger of two neutron stars, Nature (London) 574, 497 (2019).
- C. E. Collins, A. Bauswein, S. A. Sim, V. Vijayan, G. Martínez-Pinedo, O. Just, L. J. Shingles, and M. Kromer, 3D radiative transfer kilonova modelling for binary neutron star merger simulations, Mon. Not. R. Astron. Soc. 521, 1858 (2023).
- Spectral analysis and radiative data for elemental kilonovae identification (sparkle), 10.54499/2023.14470.PEX (2025), this project has received funding from Fundação para a Ciência e a Tecnologia (FCT).
- Astropy Collaboration, T. P. Robitaille, E. J. Tollerud, P. Greenfield, M. Droettboom, E. Bray, T. Aldcroft, M. Davis, A. Ginsburg, and A. M. Price-Whelan, astropy: A community python package for astronomy, Astron. Astrophys. 558, A33 (2013).
- Astropy Collaboration, A. M. Price-Whelan, B. M. Sipőcz, H. M. Günther, P. L. Lim, S. M. Crawford, S. Conseil, D. L. Shupe, M. W. Craig, and N. Dencheva, The astropy Project: Building an open-science project and status of the v2.0 core package, Astron. J. 156, 123 (2018).
- S. van der Walt, S. C. Colbert, and G. Varoquaux, The numpy array: A structure for efficient numerical computation, Comput. Sci. Eng. 13, 22 (2011).
- E. Jones, T. Oliphant, P. Peterson et al., scipy: Open source scientific tools for python http://www.scipy.org/ (2001).
- W. McKinney, Data structures for statistical computing in python, in Proceedings of the 9th python in Science Conference, edited by S. van der Walt and J. Millman (2010), pp. 51–56, 10.25080/Majora-92bf1922-00a.
- J. D. Hunter, matplotlib: A 2D graphics environment, Comput. Sci. Eng. 9, 90 (2007).
- A. Flörs, GSI database for kilonova radiative transfer, 10.5281/zenodo.15835361 (2025).