- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Ab initio calculations of the electronic structure of Ac+

Genevieve Geehan1, Marten Luit Reitsma1, Johan David Polet1, Mustapha Laatiaoui2, Julian Berengut3, and Anastasia Borschevsky1

PDF

Phys. Rev. A 114, 012801 – Published 6 July, 2026

DOI: https://doi.org/10.1103/bqfj-4pxz

Abstract

Accurate spectroscopic investigations of the heaviest elements are inherently challenging, due to their short lifetimes and low production yields. Success of such measurements requires both dedicated experimental techniques and strong theoretical support. Laser resonance chromatography (LRC) is a promising approach for heavy-ion spectroscopy, in particularly for metals with low vapor pressure, such as actinium. We have employed the state-of-the-art relativistic Fock space coupled-cluster approach as well as the configuration interaction with the many-body perturbation theory method to calculate the energy levels, the transition amplitudes, the branching ratios, and the hyperfine structure parameters of the lowest excited states in Ac+. Knowledge of these properties is required for the design of experiments. Our calculations are in close agreement with experimental transition energies, leading us to expect a similar level of accuracy for the calculated hyperfine structure parameters. Based on these predictions, two possible experimental schemes are proposed for the planned LRC measurements.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (46)

  1. P. Campbell, I. Moore, and M. Pearson, Laser spectroscopy for nuclear structure physics, Prog. Part. Nucl. Phys. 86, 127 (2016).
  2. M. Block, M. Laatiaoui, and S. Raeder, Recent progress in laser spectroscopy of the actinides, Prog. Part. Nucl. Phys. 116, 103834 (2021).
  3. X. Yang, S. Wang, S. Wilkins, and R. G. Ruiz, Laser spectroscopy for the study of exotic nuclei, Prog. Part. Nucl. Phys. 129, 104005 (2023).
  4. D. Trubert and C. Le Naour, Fundamental aspects of single atom chemistry, in The Chemistry of Superheavy Elements, edited by M. Schädel (Springer, Boston, 2003), pp. 95–116.
  5. M. Laatiaoui, W. Lauth, H. Backe, M. Block, D. Ackermann, B. Cheal, P. Chhetri, C. E. Düllmann, P. van Duppen, J. Even, R. Ferrer, F. Giacoppo, S. Götz, F. P. Heßberger, M. Huyse, O. Kaleja, J. Khuyagbaatar, P. Kunz, F. Lautenschläger, A. K. Mistry, et al., Atom-at-a-time laser resonance ionization spectroscopy of nobelium, Nature (London) 538, 495 (2016).
  6. P. Chhetri, D. Ackermann, H. Backe, M. Block, B. Cheal, C. Droese, C. E. Düllmann, J. Even, R. Ferrer, F. Giacoppo, S. Götz, F. P. Heßberger, M. Huyse, O. Kaleja, J. Khuyagbaatar, P. Kunz, M. Laatiaoui, F. Lautenschläger, W. Lauth, N. Lecesne, et al., Precision measurement of the first ionization potential of nobelium, Phys. Rev. Lett. 120, 263003 (2018).
  7. S. Raeder, D. Ackermann, H. Backe, R. Beerwerth, J. C. Berengut, M. Block, A. Borschevsky, B. Cheal, P. Chhetri, C. E. Düllmann, V. A. Dzuba, E. Eliav, J. Even, R. Ferrer, V. V. Flambaum, S. Fritzsche, F. Giacoppo, S. Götz, F. P. Heßberger, M. Huyse, et al., Probing sizes and shapes of nobelium isotopes by laser spectroscopy, Phys. Rev. Lett. 120, 232503 (2018).
  8. T. Murböck, S. Raeder, P. Chhetri, K. Diaz, M. Laatiaoui, F. Giacoppo, and M. Block, Filament studies for laser spectroscopy on lawrencium, Hyperfine Interact. 241, 35 (2020).
  9. E. V. Kahl, S. Raeder, E. Eliav, A. Borschevsky, and J. C. Berengut, Ab initio calculations of the spectrum of lawrencium, Phys. Rev. A 104, 052810 (2021).
  10. J. S. Andrews, A. I. Bondarev, P. Jönsson, J. Grumer, S. Raeder, S. Fritzsche, and J. Bieroń, Ab initio multiconfigurational calculations of experimentally significant energy levels and transition rates in Lr i (Z=103), Phys. Rev. A 112, 062802 (2025).
  11. M. Laatiaoui, A. A. Buchachenko, and L. A. Viehland, Laser resonance chromatography of superheavy elements, Phys. Rev. Lett. 125, 023002 (2020).
  12. E. Kim, B. Jana, A. Arya, M. Block, S. Raeder, H. Ramanantoanina, E. Rickert, E. R. Romero, and M. Laatiaoui, Laser resonance chromatography: First commissioning results and future prospects, Nucl. Instrum. Methods Phys. Res. Sect. B 555, 165461 (2024).
  13. E. Jajčišinová, K. Dockx, M. Au, S. Bara, T. E. Cocolios, K. Chrysalidis, G. Farooq-Smith, D. Fedorov, V. Fedosseev, K. Flanagan, et al., Production study of Fr, Ra and Ac radioactive ion beams at ISOLDE, CERN, Sci. Rep. 14, 11033 (2024).
  14. S. Raeder, B. Anđelić, J. Auler, M. Block, P. Chauveau, P. Chhetri, A. Claessens, A. de Roubin, C. E. Düllmann, R. Ferrer, F. Giacoppo, M. J. Gutiérrez, F.-P. Heßberger, F. Ivandikov, M. Kaja, O. Kaleja, T. Kieck, E. Kim, S. Kraemer, M. Laatiaoui, et al., Opportunities and limitations of in-gas-cell laser spectroscopy of the heaviest elements with RADRIS, Nucl. Instrum. Methods Phys. Res. Sect. B 541, 370 (2023).
  15. A. Kramida, Y. Ralchenko, J. Reader, and NIST ASD Team, NIST Atomic Spectra Database, National Institute of Standards and Technology, Gaithersburg, MD, 2026 (version 5.12), available at https://doi.org/10.18434/T4W30F.
  16. W. F. Meggers, M. Fred, and F. S. Tomkins, Emission spectra of actinium, J. Res. Natl. Inst. Stand. 58, 297 (1957).
  17. L. Visscher, E. Eliav, and U. Kaldor, Formulation and implementation of the relativistic Fock-space coupled cluster method for molecules, J. Chem. Phys. 115, 9720 (2001).
  18. L. F. Pašteka, E. Eliav, M. L. Reitsma, and A. Borschevsky, Relativistic atomic structure calculations in support of spectroscopy, Prog. Part. Nucl. Phys. 146, 104200 (2026).
  19. V. A. Dzuba, V. V. Flambaum, and M. G. Kozlov, Combination of the many-body perturbation theory with the configuration-interaction method, Phys. Rev. A 54, 3948 (1996).
  20. E. V. Kahl and J. C. Berengut, ambit: A program for high-precision relativistic atomic structure calculations, Comput. Phys. Commun. 238, 232 (2019).
  21. E. V. Kahl, J. C. Berengut, M. Laatiaoui, E. Eliav, and A. Borschevsky, High-precision ab initio calculations of the spectrum of Lr+, Phys. Rev. A 100, 062505 (2019).
  22. H. Bekker, A. Borschevsky, Z. Harman, C. Keitel, T. Pfeifer, P. Schmidt, J. C. López-Urrutia, and J. Berengut, Detection of the 5p–4f orbital crossing and its optical clock transition in Pr9+, Nat. Commun. 10, 5651 (2019).
  23. F. P. Gustafsson, C. M. Ricketts, M. L. Reitsma, R. F. G. Ruiz, S. W. Bai, J. C. Berengut, J. Billowes, C. L. Binnersley, A. Borschevsky, T. E. Cocolios, B. S. Cooper, R. P. de Groote, K. T. Flanagan, A. Koszorús, G. Neyens, H. A. Perrett, A. R. Vernon, Q. Wang, S. G. Wilkins, and X. F. Yang, Tin resonance-ionization schemes for atomic- and nuclear-structure studies, Phys. Rev. A 102, 052812 (2020).
  24. R. Li, A. Teigelhöfer, J. Li, J. Bieroń, A. Gácsbaranyi, J. Johnson, P. Jönsson, V. Karner, M. Ma, M. Radulov, M. Roman, M. Stachura, and J. Lassen, Collinear laser spectroscopy on neutron-rich actinium isotopes, Phys. Rev. C 111, 054320 (2025).
  25. E. Verstraelen, A. Teigelhöfer, W. Ryssens, F. Ames, A. Barzakh, M. Bender, R. Ferrer, S. Goriely, P.-H. Heenen, M. Huyse, P. Kunz, J. Lassen, V. Manea, S. Raeder, and P. Van Duppen, Search for octupole-deformed actinium isotopes using resonance ionization spectroscopy, Phys. Rev. C 100, 044321 (2019).
  26. L. Visscher, H. J. A. Jensen, R. Bast, A. S. P. Gomes, T. Saue, I. A. Aucar, V. Bakken, J. Brandejs, C. Chibueze, J. Creutzberg, K. G. Dyall, S. Dubillard, U. Ekström, E. Eliav, T. Enevoldsen, E. Faßhauer, T. Fleig, O. Fossgaard, L. Halbert, E. D. Hedegård, et al., DIRAC24, a relativistic ab initio electronic structure program, DIRAC24 (v24.0), Zenodo, 2024, doi: 10.5281/zenodo.10680561, see also https://www.diracprogram.org.
  27. J. Sucher, Foundations of the relativistic theory of many-electron atoms, Phys. Rev. A 22, 348 (1980).
  28. L. Visscher and K. G. Dyall, Dirac–Fock atomic electronic structure calculations using different nuclear charge distributions, At. Data Nucl. Data Tables 67, 207 (1997).
  29. E. Eliav, M. J. Vilkas, Y. Ishikawa, and U. Kaldor, Extrapolated intermediate Hamiltonian coupled-cluster approach: Theory and pilot application to electron affinities of alkali atoms, J. Chem. Phys. 122, 224113 (2005).
  30. K. G. Dyall, Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the actinides Ac-Lr, Theor. Chem. Acc. 117, 491 (2007).
  31. J. M. Martin, Ab initio total atomization energies of small molecules — towards the basis set limit, Chem. Phys. Lett. 259, 669 (1996).
  32. A. Kanellakopoulos, X. F. Yang, M. L. Bissell, M. L. Reitsma, S. W. Bai, J. Billowes, K. Blaum, A. Borschevsky, B. Cheal, C. S. Devlin, R. F. G. Ruiz, H. Heylen, S. Kaufmann, K. König, Á. Koszorús, S. Lechner, S. Malbrunot-Ettenauer, R. Neugart, G. Neyens, W. Nörtershäuser, et al., Nuclear moments of germanium isotopes near N=40, Phys. Rev. C 102, 054331 (2020).
  33. P. A. B. Haase, E. Eliav, M. Iliaš, and A. Borschevsky, Hyperfine structure constants on the relativistic coupled cluster level with associated uncertainties, J. Phys. Chem. A 124, 39 (2020).
  34. H. D. Cohen and C. C. J. Roothaan, Electric dipole polarizability of atoms by the Hartree—Fock method. I. Theory for closed-shell systems, J. Chem. Phys. 43, S34 (1965).
  35. J. A. Pople, J. W. McIver, and N. S. Ostlund, Self-consistent perturbation theory. I. Finite perturbation methods, J. Chem. Phys. 49, 2960 (1968).
  36. H. J. Monkhorst, Calculation of properties with the coupled-cluster method, Int. J. Quantum Chem. 12, 421 (2009).
  37. V. V. Flambaum and J. S. M. Ginges, Radiative potential and calculations of QED radiative corrections to energy levels and electromagnetic amplitudes in many-electron atoms, Phys. Rev. A 72, 052115 (2005).
  38. J. S. M. Ginges and J. C. Berengut, Atomic many-body effects and Lamb shifts in alkali metals, Phys. Rev. A 93, 052509 (2016).
  39. V. A. Dzuba, V. V. Flambaum, P. G. Silvestrov, and O. P. Sushkov, Relativistic many-body calculations in atoms and parity violation in caesium, J. Phys. B: At. Mol. Phys. 18, 597 (1985).
  40. V. A. Dzuba, V. V. Flambaum, P. G. Silvestrov, and O. Sushkov, Correlation potential method for the calculation of energy levels, hyperfine structure and E1 transition amplitudes in atoms with one unpaired electron, J. Phys. B: At. Mol. Phys. 20, 1399 (1987).
  41. J. S. M. Ginges, A. V. Volotka, and S. Fritzsche, Ground-state hyperfine splitting for Rb, Cs, Fr, Ba+, and Ra+, Phys. Rev. A 96, 062502 (2017).
  42. B. M. Roberts and J. S. M. Ginges, Nuclear magnetic moments of francium-207–213 from precision hyperfine comparisons, Phys. Rev. Lett. 125, 063002 (2020).
  43. J. E. Sansonetti, W. C. Martin, and S. L. Young, Handbook of Basic Atomic Spectroscopic Data, National Institute of Standards and Technology, Gaithersburg, MD, 2023 (version 1.1.3), available at http://physics.nist.gov/Handbook.
  44. A. Kramida, Update of atomic data for the first three spectra of actinium, Atoms 10, 42 (2022).
  45. B. M. Roberts, V. A. Dzuba, and V. V. Flambaum, Strongly enhanced atomic parity violation due to close levels of opposite parity, Phys. Rev. A 89, 042509 (2014).
  46. G. Visentin, H. Ramanantoanina, A. Borschevsky, L. Viehland, B. Jana, A. Arya, S. Fritzsche, and M. Laatiaoui, Transport-property predictions for laser resonance chromatography on Rf+(Z=104), Phys. Rev. A 110, 012805 (2024).

Outline

Information

Phys. Rev. A 114, 012801– Published 6 July, 2026
  • Received 6 February 2026
  • Accepted 16 June 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation