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The quest for superheavy elements and the limit of the periodic table

Nature Reviews Physics volume 6, pages 86–98 (2024)Cite this article

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Abstract

The borders of the periodic table of the elements and of the chart of nuclides are not set in stone. The desire to explore the properties of atoms and their nuclei in a regime of very large numbers of electrons, protons and neutrons has motivated new experimental facilities to create new elements and nuclides at the limits of atomic number and mass. But the small production rates and short lifetimes of superheavy nuclei and their atoms mean that ‘atom-at-a-time’ studies are the only experimental way to probe them. The physical and chemical data obtained so far, augmented by theoretical calculations, indicate significant deviations from extrapolations from lighter elements and isotopes. This situation raises the following question: how much further can one push the limits of the periodic table? In this Review, we describe the major challenges in the field of the superheavy elements and speculate about future directions.

Key points

  • Experiments to synthesize new superheavy nuclei and elements beyond the heaviest currently known element oganesson are underway. These systems will be crucial for benchmarking and testing many-body atomic and nuclear theory.

  • Rapid and efficient chemistry experiments with single atoms and molecules elucidate the influence of the high atomic charge on chemical properties, thus probing the fundamental architecture of the periodic table.

  • The field of superheavy element research puts atomic and nuclear theory to the test. For many superheavy systems, all available information must come from theoretical extrapolations based on models aided by high-performance computing and machine learning.

  • The presence of large electrostatic forces gives rise to pronounced relativistic effects in the atomic system and strong Coulomb frustration effects in the nuclear system. There are theoretical suggestions indicating that superheavy atoms should differ fundamentally from lighter species, leading to deviations from the current patterns of the periodic table.

  • Fundamental difficulties are encountered when dealing with the many-particle Dirac equation, as beyond a certain nuclear charge, levels such as the 1s are predicted to merge with the negative-energy continuum, eventually leading to a potentially unstable atomic structure and real electron–positron pair creation.

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Fig. 1: The nuclear landscape.
Fig. 2: The main contribution to the ground-state configurations of the superheavy elements by means of the DCBQ-CI2 method93.
Fig. 3: An attempt to place the superheavy elements into the PTE according to Fig. 2.

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References

  1. Mendelejew, D. Über die Beziehungen der Eigenschaften zu den Atomgewichten der Elemente. Z. Chem. 12, 173 (1869).

    Google Scholar 

  2. Boeck, G. Das Periodensystem der Elemente und Lothar Meyer. Chem. Unserer Zeit 53, 372–382 (2019).

    Article  CAS  Google Scholar 

  3. Schwerdtfeger, P., Smits, O. R. & Pyykkö, P. The periodic table and the physics that drives it. Nat. Rev. Chem. 4, 359–380 (2020). This paper reviews the PTE with a focus on the fundamental physical principles that influence its structure and the anomalies in chemical and physical properties observed among elements within specific groups.

    Article  CAS  PubMed  Google Scholar 

  4. Seaborg, G. T. The transuranium elements. Science 104, 379–386 (1946).

    Article  ADS  CAS  PubMed  Google Scholar 

  5. Karol, P. J., Barber, R. C., Sherrill, B. M., Vardaci, E. & Yamazaki, T. Discovery of the element with atomic number Z = 118 completing the 7th row of the periodic table (IUPAC Technical Report). Pure Appl. Chem. 88, 155–160 (2016).

    Article  CAS  Google Scholar 

  6. Seaborg, G. T. & Loveland, W. D. The Elements Beyond Uranium (Wiley-Interscience, 1990).

  7. Oganessian, Y. T. & Utyonkov, V. K. Super-heavy element research. Rep. Prog. Phys. 78, 036301 (2015). This paper reviews the discovery of the heaviest known elements 114Fl to 118Og.

    Article  ADS  PubMed  Google Scholar 

  8. Dechargé, J., Berger, J.-F., Dietrich, K. & Weiss, M. Superheavy and hyperheavy nuclei in the form of bubbles or semi-bubbles. Phys. Lett. B 451, 275–282 (1999).

    Article  Google Scholar 

  9. Smits, O. R., Indelicato, P., Nazarewicz, W., Piibeleht, M. & Schwerdtfeger, P. Pushing the limits of the periodic table — a review on atomic relativistic electronic structure theory and calculations for the superheavy elements. Phys. Rep. 1035, 1–57 (2023); https://doi.org/10.1016/j.physrep.2023.09.004. This paper reviews relativistic electronic structure methods for the superheavy elements, addressing the scenario in which an electron level is embedded within the Dirac negative-energy continuum.

  10. Giuliani, S. A., Martínez-Pinedo, G., Wu, M.-R. & Robledo, L. M. Fission and the r-process nucleosynthesis of translead nuclei in neutron star mergers. Phys. Rev. C 102, 045804 (2020).

    Article  ADS  CAS  Google Scholar 

  11. Holmbeck, E. M., Sprouse, T. M. & Mumpower, M. R. Nucleosynthesis and observation of the heaviest elements. Eur. Phys. J. A 59, 28 (2023). This paper reviews the astrophysical synthesis of the heaviest elements.

    Article  ADS  CAS  Google Scholar 

  12. Türler, A. & Pershina, V. Advances in the production and chemistry of the heaviest elements. Chem. Rev. 113, 1237–1312 (2013). This paper reviews superheavy element chemistry.

    Article  PubMed  Google Scholar 

  13. Düllmann, Ch. E., Herzberg, R.-D., Nazarewicz, W. & Oganessian, Y. (eds) Nuclear Physics A: Special Issue on Superheavy Elements Vol. 944 (Elsevier, 2015). This special issue contains articles covering all aspects of superheavy element research, some of which are listed among further references of the present review.

  14. Nazarewicz, W. The limits of nuclear mass and charge. Nat. Phys. 14, 537–541 (2018). This perspective offers a high-level view of the field of nuclear structure theory and outlines future challenges for superheavy systems.

    Article  CAS  Google Scholar 

  15. Giuliani, S. A. et al. Colloquium: superheavy elements: oganesson and beyond. Rev. Mod. Phys. 91, 011001 (2019). This review offers a broad perspective on the field of superheavy element research.

    Article  ADS  CAS  Google Scholar 

  16. Roberto, J. B. et al. Actinide targets for the synthesis of super-heavy elements. Nucl. Phys. A 944, 99–116 (2015).

    Article  Google Scholar 

  17. Hofmann, S. et al. Review of even element super-heavy nuclei and search for element 120. Eur. Phys. J. A 52, 180 (2016).

    Article  ADS  Google Scholar 

  18. Düllmann, Ch. E. On the search for elements beyond Z = 118. An outlook based on lessons from the heaviest known elements. EPJ Web Conf. 131, 08004 (2016).

    Article  Google Scholar 

  19. Tanaka, M. et al. Probing optimal reaction energy for synthesis of element 119 from 51V+248Cm reaction with quasielastic barrier distribution measurement. J. Phys. Soc. Jpn 91, 084201 (2022).

    Article  ADS  Google Scholar 

  20. Sakai, H., Haba, H., Morimoto, K. & Sakamoto, N. Facility upgrade for superheavy-element research at RIKEN. Eur. Phys. J. A 58, 238 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Oganessian, Y. T. et al. First experiment at the super heavy element factory: high cross section of 288Mc in the 243Am + 48Ca reaction and identification of the new isotope 264Lr. Phys. Rev. C 106, L031301 (2022).

    Article  ADS  CAS  Google Scholar 

  22. Gan, Z. G., Huang, W. X., Zhang, Z. Y., Zhou, X. H. & Xu, H. S. Results and perspectives for study of heavy and super-heavy nuclei and elements at IMP/CAS. Eur. Phys. J. A 58, 158 (2022).

    Article  ADS  CAS  Google Scholar 

  23. Rykaczewski, K. P., Roberto, J. B., Brewer, N. T. & Utyonkov, V. K. ORNL actinide materials and a new detection system for superheavy nuclei. EPJ Web Conf. 131, 05005 (2016).

    Article  Google Scholar 

  24. Kratz, J., Schädel, M. & Gäggeler, H. Reexamining the heavy-ion reactions 238U+238U and 238U+248Cm and actinide production close to the barrier. Phys. Rev. C 88, 054615 (2013).

    Article  ADS  Google Scholar 

  25. Zagrebaev, V. & Greiner, W. Production of heavy trans-target nuclei in multinucleon transfer reactions. Phys. Rev. C 87, 034608 (2013).

    Article  ADS  Google Scholar 

  26. Welsh, T. et al. Modeling multi-nucleon transfer in symmetric collisions of massive nuclei. Phys. Lett. B 771, 119–124 (2017).

    Article  ADS  CAS  Google Scholar 

  27. Loveland, W. Synthesis of transactinide nuclei using radioactive beams. Phys. Rev. C 76, 014612 (2007).

    Article  ADS  Google Scholar 

  28. Zagrebaev, V., Karpov, A. & Greiner, W. Possibilities for synthesis of new isotopes of superheavy elements in fusion reactions. Phys. Rev. C 85, 014608 (2012).

    Article  ADS  Google Scholar 

  29. Lohse, S. et al. Quartz resonators for penning traps toward mass spectrometry on the heaviest ions. Rev. Sci. Instrum. 91, 093203 (2020); https://doi.org/10.1063/5.0015011.

  30. Gregorich, K. How good are superheavy element Z and A assignments? EPJ Web Conf. 131, 06002 (2016).

    Article  Google Scholar 

  31. Rudolph, D. Results and plans for nuclear spectroscopy of superheavy nuclei: the Lund perspective. Eur. Phys. J. A 58, 242 (2022).

    Article  ADS  CAS  Google Scholar 

  32. Oganessian, Y. T. et al. New isotope 276Ds and its decay products 272Hs and 268Sg from the 232Th + 48Ca reaction. Phys. Rev. C 108, 024611 (2023).

    Article  ADS  CAS  Google Scholar 

  33. Düllmann, Ch. E. et al. Advancements in the fabrication and characterization of actinide targets for superheavy element production. J. Radioanal. Nucl. Chem. 332, 1505–1514 (2023).

    Article  Google Scholar 

  34. Lauber, S. et al. An alternating phase focusing injector for heavy ion acceleration. Nucl. Instrum. Methods Phys. Res. A 1040, 167099 (2022).

    Article  CAS  Google Scholar 

  35. Morita, K. et al. New result in the production and decay of an isotope, 278113, of the 113th element. J. Phys. Soc. Jpn 81, 103201 (2012).

    Article  ADS  Google Scholar 

  36. Ackermann, D. & Theisen, C. Nuclear structure features of very heavy and superheavy nuclei-tracing quantum mechanics towards the ‘island of stability’. Phys. Scr. 92, 083002 (2017).

    Article  ADS  Google Scholar 

  37. Minaya Ramirez, E. et al. Direct mapping of nuclear shell effects in the heaviest elements. Science 337, 1207–1210 (2012). The paper provides a direct high-precision mass measurement in the SHE realm.

    Article  ADS  CAS  PubMed  Google Scholar 

  38. Block, M., Laatiaoui, M. & Raeder, S. Recent progress in laser spectroscopy of the actinides. Prog. Part. Nucl. Phys. 116, 103834 (2021). The paper provides a summary of recent progress in the field of laser spectroscopy of the heaviest elements.

    Article  CAS  Google Scholar 

  39. Heenen, P.-H., Skalski, J., Staszczak, A. & Vretenar, D. Shapes and α- and β-decays of superheavy nuclei. Nucl. Phys. A 944, 415–441 (2015).

    Article  Google Scholar 

  40. Singh, U. et al. Study of decay modes in transfermium isotopes. Nucl. Phys. A 1004, 122035 (2020).

    Article  CAS  Google Scholar 

  41. Sarriguren, P. Electron-capture decay in isotopic transfermium chains from self-consistent calculations. J. Phys. G 47, 125107 (2020).

    Article  ADS  CAS  Google Scholar 

  42. Sarriguren, P. Competition between weak and α-decay modes in superheavy nuclei. Phys. Rev. C 105, 014312 (2022).

    Article  ADS  CAS  Google Scholar 

  43. Khuyagbaatar, J. et al. Search for electron-capture delayed fission in the new isotope 244Md. Phys. Rev. Lett. 125, 142504 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  44. Ney, E. M., Engel, J., Li, T. & Schunck, N. Global description of β− decay with the axially deformed Skyrme finite-amplitude method: extension to odd-mass and odd-odd nuclei. Phys. Rev. C 102, 034326 (2020).

    Article  ADS  CAS  Google Scholar 

  45. Neufcourt, L., Cao, Y., Nazarewicz, W. & Viens, F. Bayesian approach to model-based extrapolation of nuclear observables. Phys. Rev. C 98, 034318 (2018).

    Article  ADS  CAS  Google Scholar 

  46. Stetzler, S., Grosskopf, M. & Lawrence, E. in Applications of Machine Learning 2022 Vol. 12227 (eds Zelinski, M. E. et al.) (SPIE, 2022).

  47. Phillips, D. R. et al. Get on the BAND wagon: a Bayesian framework for quantifying model uncertainties in nuclear dynamics. J. Phys. G 48, 072001 (2021).

    Article  ADS  CAS  Google Scholar 

  48. Neufcourt, L. et al. Quantified limits of the nuclear landscape. Phys. Rev. C 101, 044307 (2020).

    Article  ADS  CAS  Google Scholar 

  49. Boehnlein, A. et al. Colloquium: machine learning in nuclear physics. Rev. Mod. Phys. 94, 031003 (2022).

    Article  ADS  CAS  Google Scholar 

  50. Agbemava, S. E. & Afanasjev, A. V. Hyperheavy spherical and toroidal nuclei: the role of shell structure. Phys. Rev. C 103, 034323 (2021).

    Article  ADS  CAS  Google Scholar 

  51. Perera, U. C. & Afanasjev, A. V. Bubble nuclei: single-particle versus Coulomb interaction effects. Phys. Rev. C 106, 024321 (2022).

    Article  ADS  CAS  Google Scholar 

  52. Cao, Y., Agbemava, S. E., Afanasjev, A. V., Nazarewicz, W. & Olsen, E. Landscape of pear-shaped even-even nuclei. Phys. Rev. C 102, 024311 (2020).

    Article  ADS  CAS  Google Scholar 

  53. Rodríguez-Guzmán, R., Humadi, Y. M. & Robledo, L. M. Microscopic description of fission in superheavy nuclei with the parametrization D1M* of the Gogny energy density functional. Eur. Phys. J. A 56, 43 (2020).

    Article  ADS  Google Scholar 

  54. Sadhukhan, J., Giuliani, S. A. & Nazarewicz, W. Theoretical description of fission yields: toward a fast and efficient global model. Phys. Rev. C 105, 014619 (2022).

    Article  ADS  CAS  Google Scholar 

  55. Mumpower, M. R., Jaffke, P., Verriere, M. & Randrup, J. Primary fission fragment mass yields across the chart of nuclides. Phys. Rev. C 101, 054607 (2020).

    Article  ADS  CAS  Google Scholar 

  56. Lemaître, J.-F., Goriely, S., Bauswein, A. & Janka, H.-T. Fission fragment distributions and their impact on the r-process nucleosynthesis in neutron star mergers. Phys. Rev. C 103, 025806 (2021).

    Article  ADS  Google Scholar 

  57. Vassh, N. et al. Using excitation-energy dependent fission yields to identify key fissioning nuclei in r-process nucleosynthesis. J. Phys. G 46, 065202 (2019).

    Article  ADS  CAS  Google Scholar 

  58. Holmbeck, E. M. et al. Actinide production in the neutron-rich ejecta of a neutron star merger. Astrophys. J. 870, 23 (2018).

    Article  ADS  Google Scholar 

  59. Laatiaoui, M. et al. Atom-at-a-time laser resonance ionization spectroscopy of nobelium. Nature 538, 495–498 (2016).

    Article  ADS  PubMed  Google Scholar 

  60. Warbinek, J. et al. Advancing radiation-detected resonance ionization towards heavier elements and more exotic nuclides. Atoms 10, 41 (2022).

    Article  ADS  CAS  Google Scholar 

  61. Allehabi, S. O., Dzuba, V. A. & Flambaum, V. V. Calculation of the hyperfine structure of Dy, Ho, Cf, and Es. Phys. Rev. A 107, 032805 (2023).

    Article  ADS  CAS  Google Scholar 

  62. Dzuba, V. A. & Flambaum, V. V. Calculation of the hyperfine structure of Er and Fm. Phys. Rev. A 108, 012823 (2023).

    Article  ADS  CAS  Google Scholar 

  63. Porsev, S. G., Safronova, M. S., Safronova, U. I., Dzuba, V. A. & Flambaum, V. V. Nobelium energy levels and hyperfine-structure constants. Phys. Rev. A 98, 052512 (2018).

    Article  ADS  Google Scholar 

  64. Dzuba, V. A., Flambaum, V. V. & Webb, J. K. Isotope shift and search for metastable superheavy elements in astrophysical data. Phys. Rev. A 95, 062515 (2017).

    Article  ADS  Google Scholar 

  65. Letokhov, V. Laser Photoionization Spectroscopy (Academic, 1987).

  66. Hurst, G. S. & Payne, M. G. Principles and Applications of Resonance Ionisation Spectroscopy (CRC, 1988).

  67. Raeder, S. et al. Probing sizes and shapes of nobelium isotopes by laser spectroscopy. Phys. Rev. Lett. 120, 232503 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  68. Chhetri, P. et al. Precision measurement of the first ionization potential of nobelium. Phys. Rev. Lett. 120, 263003 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  69. Ferrer, R. et al. Towards high-resolution laser ionization spectroscopy of the heaviest elements in supersonic gas jet expansion. Nat. Commun. 8, 14520 (2017). The paper researches on-line applications of advanced atomic laser ionization spectroscopy for high-precision studies of the ground-state and isomeric-state properties of the heaviest elements.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  70. Münzberg, D. et al. Resolution characterizations of JetRIS in Mainz using 164Dy. Atoms 10, 57 (2022).

    Article  ADS  Google Scholar 

  71. Raeder, S. et al. Opportunities and limitations of in-gas-cell laser spectroscopy of the heaviest elements with RADRIS. Nucl. Instr. Methods B 541, 370–374 (2023).

    Article  ADS  CAS  Google Scholar 

  72. Laatiaoui, M. et al. On laser spectroscopy of the element nobelium (Z = 102). Eur. Phys. J. D 68, 71 (2014).

    Article  ADS  Google Scholar 

  73. Fritzsche, S. On the accuracy of valence-shell computations for heavy and super-heavy elements. Eur. Phys. J. D 33, 15–21 (2005).

    Article  ADS  CAS  Google Scholar 

  74. Indelicato, P., Santos, J., Boucard, S. & Desclaux, J.-P. QED and relativistic corrections in superheavy elements. Eur. Phys. J. D 45, 155–170 (2007).

    Article  ADS  CAS  Google Scholar 

  75. Liu, Y., Hutton, R. & Zou, Y. Atomic structure of the super-heavy element No I (Z = 102). Phys. Rev. A 76, 062503 (2007).

    Article  ADS  Google Scholar 

  76. Borschevsky, A., Eliav, E., Vilkas, M. J., Ishikawa, Y. & Kaldor, U. Predicted spectrum of atomic nobelium. Phys. Rev. A 75, 042514 (2007).

    Article  ADS  Google Scholar 

  77. Borschevsky, A., Eliav, E., Vilkas, M., Ishikawa, Y. & Kaldor, U. Transition energies of atomic lawrencium. Eur. Phys. J. D 45, 115–119 (2007).

    Article  ADS  CAS  Google Scholar 

  78. Eliav, E., Kaldor, U., Schwerdtfeger, P., Hess, B. A. & Ishikawa, Y. Ground state electron configuration of element 111. Phys. Rev. Lett. 73, 3203–3206 (1994).

    Article  ADS  CAS  PubMed  Google Scholar 

  79. Mohr, P. J., Plunien, G. & Soff, G. QED corrections in heavy atoms. Phys. Rep. 293, 227–369 (1998).

    Article  ADS  CAS  Google Scholar 

  80. Autschbach, J., Siekierski, S., Seth, M., Schwerdtfeger, P. & Schwarz, W. H. E. Dependence of relativistic effects on electronic configuration in the neutral atoms of d- and f-block elements. J. Comput. Chem. 23, 804–813 (2002).

    Article  CAS  PubMed  Google Scholar 

  81. Pyykkö, P. & Desclaux, J. P. Relativity and the periodic system of elements. Acc. Chem. Res. 12, 276–281 (1979).

    Article  Google Scholar 

  82. Pyykkö, P. Relativistic effects in structural chemistry. Chem. Rev. 88, 563–594 (1988).

    Article  Google Scholar 

  83. Grant, I. P. Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation Vol. 40 (Springer Science & Business Media, 2007).

  84. Mohr, P., Plunien, G. & Soff, G. QED corrections in heavy atoms. Phys. Rep. 293, 227 (1998). The paper reviews atomic structure theory within bound-state quantum electrodynamics.

    Article  ADS  CAS  Google Scholar 

  85. Indelicato, P. & Mohr, P. J. in Handbook of Relativistic Quantum Chemistry (eds Liu, W. et al.) Part II, Ch. 5,131 (Springer, 2017).

  86. Indelicato, P. & Mohr, P. J. Coordinate-space approach to the bound-electron self-energy: self-energy screening calculation. Phys. Rev. A 63, 052507 (2001).

    Article  ADS  Google Scholar 

  87. Flambaum, V. V. & Ginges, J. S. M. Radiative potential and calculations of QED radiative corrections to energy levels and electromagnetic amplitudes in many-electron atoms. Phys. Rev. A 72, 052115 (2005).

    Article  ADS  Google Scholar 

  88. Shabaev, V. M., Tupitsyn, I. I. & Yerokhin, V. A. Model operator approach to the Lamb shift calculations in relativistic many-electron atoms. Phys. Rev. A 88, 012513 (2013).

    Article  ADS  Google Scholar 

  89. Ginges, J. S. M. & Berengut, J. C. Atomic many-body effects and lamb shifts in alkali metals. Phys. Rev. A 93, 052509 (2016).

    Article  ADS  Google Scholar 

  90. Malyshev, A. V. et al. Model-QED operator for superheavy elements. Phys. Rev. A 106, 012806 (2022).

    Article  ADS  CAS  Google Scholar 

  91. Indelicato, P., Lindroth, E. & Desclaux, J. Nonrelativistic limit of Dirac-Fock codes: the role of Brillouin configurations. Phys. Rev. Lett. 94, 013002 (2005).

    Article  ADS  CAS  PubMed  Google Scholar 

  92. Grant, I. P. & Pyper, N. C. Breit interaction in multi-configuration relativistic atomic calculations. J. Phys. B 9, 761–774 (1976).

    Article  ADS  Google Scholar 

  93. Savelyev, I. M. et al. Ground state of superheavy elements with 120 ≤ Z ≤ 170: systematic study of the electron-correlation, Breit, and QED effects. Phys. Rev. A 107, 042803 (2023). The paper is a comprehensive study on possible electronic ground-state configurations for the superheavy elements.

    Article  ADS  CAS  Google Scholar 

  94. Pyykkö, P. A suggested periodic table up to Z ≤ 172, based on Dirac-Fock calculations on atoms and ions. Phys. Chem. Chem. Phys. 13, 161–168 (2011).

    Article  PubMed  Google Scholar 

  95. Indelicato, P. MDFGME, a Multiconfiguration Dirac Fock and General Matrix Elements Program (release 2022v3); http://www.lkb.upmc.fr/metrologysimplesystems/mdfgme-a-general-purpose-multiconfiguration-dirac-foc-program/ (2022).

  96. Müller, B., Peitz, H., Rafelski, J. & Greiner, W. Solution of the Dirac equation for strong external fields. Phys. Rev. Lett. 28, 1235–1238 (1972).

    Article  ADS  Google Scholar 

  97. Wondrak, M. F., van Suijlekom, W. D. & Falcke, H. Gravitational pair production and black hole evaporation. Phys. Rev. Lett. 130, 221502 (2023).

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  98. Rafelski, J., Kirsch, J., Müller, B., Reinhardt, J. & Greiner, W. in New Horizons in Fundamental Physics (eds Schramm, S. & Schäfer, M.) 211–251 (Springer, 2017).

  99. Müller-Nehler, U. & Soff, G. Electron excitations in superheavy quasimolecules. Phys. Rep. 246, 101–250 (1994).

    Article  Google Scholar 

  100. Maltsev, I. A. et al. Electron-positron pair creation in low-energy collisions of heavy bare nuclei. Phys. Rev. A 91, 032708 (2015).

    Article  ADS  Google Scholar 

  101. Popov, R. V. et al. How to access QED at a supercritical Coulomb field. Phys. Rev. D 102, 076005 (2020).

    Article  ADS  CAS  Google Scholar 

  102. Pershina, V. in The Chemistry of Superheavy Elements (eds Schädel, M. & Shaughnessy, D.) 135–239 (Springer, 2014).

  103. Schwerdtfeger, P., Pašteka, L. F., Punnett, A. & Bowman, P. O. Relativistic and quantum electrodynamic effects in superheavy elements. Nucl. Phys. A 944, 551–577 (2015).

    Article  ADS  CAS  Google Scholar 

  104. Pershina, V. Relativity in the electronic structure of the heaviest elements and its influence on periodicities in properties. Radiochim. Acta 107, 833–863 (2019). This paper is a recent overview of theoretical studies of atomic and chemical properties of SHEs, with comparison to the experimental status.

    Article  CAS  Google Scholar 

  105. Hoffman, D. C. & Lee, D. M. Chemistry of the heaviest elements — one atom at a time. J. Chem. Ed. 76, 331-347 (1999).

    Article  Google Scholar 

  106. Nagame, Y., Kratz, J. V. & Schädel, M. Chemical studies of elements with Z ≥ 104 in liquid phase. Nucl. Phys. A 944, 614–639 (2015).

    Article  ADS  CAS  Google Scholar 

  107. Krupp, D. & Scherer, U. W. Prototype development of ion exchanging alpha detectors. Nucl. Instrum. 897, 120–128 (2018).

    Article  CAS  Google Scholar 

  108. Toyoshima, A. et al. Chemical studies of Mo and W in preparation of a seaborgium (Sg) reduction experiment using MDG, FEC, and SISAK. J. Radioanal. Nucl. Chem. 303, 1169–1172 (2015).

    Article  CAS  Google Scholar 

  109. Schädel, M. Chemistry of superheavy elements. Angew. Chem. Int. Ed. Engl. 45, 368–401 (2006).

    Article  PubMed  Google Scholar 

  110. Even, J. et al. Synthesis and detection of a seaborgium carbonyl complex. Science 345, 1491–1493 (2014). The paper studies a carbonyl compound of a superheavy element, representing a new compound class for atom-at-a-time chemistry and extending the area into the direction of organometallic chemistry of the superheavy elements.

    Article  ADS  CAS  PubMed  Google Scholar 

  111. Iliaš, M. & Pershina, V. Hexacarbonyls of Mo, W, and Sg: metal–CO bonding revisited. Inorg. Chem. 56, 1638–1645 (2017).

    Article  PubMed  Google Scholar 

  112. Eichler, R. et al. Complex chemistry with complex compounds. EPJ Web Conf. 131, 07005 (2016).

    Article  Google Scholar 

  113. Iliaš, M. & Pershina, V. Carbonyl compounds of Rh, Ir, and Mt: electronic structure, bonding and volatility. Phys. Chem. Chem. Phys. 22, 18681–18694 (2020).

    Article  Google Scholar 

  114. Hasnip, P. J. et al. Density functional theory in the solid state. Phil. Trans. R. Soc. A 372, 20130270 (2014).

    Article  ADS  MathSciNet  PubMed  PubMed Central  Google Scholar 

  115. Teale, A. M. et al. DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science. Phys. Chem. Chem. Phys. 24, 28700–28781 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  116. Goerigk, L. & Mehta, N. A trip to the density functional theory zoo: warnings and recommendations for the user. Aust. J. Chem. 72, 563–573 (2019).

    Article  CAS  Google Scholar 

  117. Jerabek, P., Smits, O. R., Mewes, J.-M., Peterson, K. A. & Schwerdtfeger, P. Solid oganesson via a many-body interaction expansion based on relativistic coupled-cluster theory and from plane-wave relativistic density functional theory. J. Phys. Chem. A 123, 4201–4211 (2019).

    Article  CAS  PubMed  Google Scholar 

  118. Mewes, J.-M., Smits, O. R., Kresse, G. & Schwerdtfeger, P. Copernicium: a relativistic noble liquid. Angew. Chem. Int. Ed. 58, 17964–17968 (2019).

    Article  CAS  Google Scholar 

  119. Smits, O. R., Mewes, J.-M., Jerabek, P. & Schwerdtfeger, P. Oganesson: a noble gas element that is neither noble nor a gas. Angew. Chem. Int. Ed. 59, 23636–23640 (2020). The paper shows that the heaviest group 18 element oganesson is not quite behaving like a rare gas element owing to strong relativistic effects.

    Article  CAS  Google Scholar 

  120. Florez, E., Smits, O. R., Mewes, J.-M., Jerabek, P. & Schwerdtfeger, P. From the gas phase to the solid state: the chemical bonding in the superheavy element flerovium. J. Chem. Phys. 157, 064304 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  121. Trombach, L., Ehlert, S., Grimme, S., Schwerdtfeger, P. & Mewes, J.-M. Exploring the chemical nature of super-heavy main-group elements by means of efficient plane-wave density-functional theory. Phys. Chem. Chem. Phys. 21, 18048–18058 (2019).

    Article  CAS  PubMed  Google Scholar 

  122. Grimme, S., Hansen, A., Brandenburg, J. G. & Bannwarth, C. Dispersion-corrected mean-field electronic structure methods. Chem. Rev. 116, 5105–5154 (2016).

    Article  CAS  PubMed  Google Scholar 

  123. Pershina, V. & Iliaš, M. Reactivity of superheavy elements Cn and Fl and of their oxides in comparison with homologous species of Hg and Pb, respectively, towards gold and hydroxylated quartz surfaces. Dalton Trans. 51, 7321–7332 (2022).

    Article  CAS  PubMed  Google Scholar 

  124. Pershina, V. & Iliaš, M. Theoretical predictions of properties and adsorption behavior of group 1 and 2 elements, including elements 119 and 120, on the surface of gold from periodic DFT calculations. Mol. Phys. https://doi.org/10.1080/00268976.2023.2237614 (2023).

  125. Yakushev, A. et al. On the adsorption and reactivity of element 114, flerovium. Front. Chem. 10, 976635 (2022). The paper discusses the current experimental status on 114Fl, the heaviest element that was studied experimentally.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  126. Düllmann, Ch. E. et al. Heavy-ion-induced production and physical preseparation of short-lived isotopes for chemistry experiments. Nucl. Instr. Methods A 551, 528–539 (2005).

    Article  ADS  Google Scholar 

  127. Lens, L. et al. Online chemical adsorption studies of Hg, Tl, and Pb on SiO2 and Au surfaces in preparation for chemical investigations on Cn, Nh, and Fl at TASCA. Radiochim. Acta 106, 949–962 (2018).

    Article  CAS  Google Scholar 

  128. Chiera, N. et al. Interaction of elemental mercury with selenium surfaces: model experiments for investigations of superheavy elements copernicium and flerovium. J. Radioanal. Nucl. Chem. 311, 99–108 (2017).

    Article  CAS  Google Scholar 

  129. Eichler, R. et al. Indication for a volatile element 114. Radiochim. Acta 98, 133–139 (2010).

    Article  CAS  Google Scholar 

  130. Yakushev, A. et al. Superheavy element flerovium (element 114) is a volatile metal. Inorg. Chem. 53, 1624–1629 (2014).

    Article  MathSciNet  CAS  PubMed  Google Scholar 

  131. Pitzer, K. S. Are elements 112, 114 and 118 relatively inert gases? J. Chem. Phys. 63, 1032–1033 (1975).

    Article  ADS  CAS  Google Scholar 

  132. Pershina, V. Reactivity of superheavy elements Cn, Nh, and Fl and their lighter homologues Hg, Tl, and Pb, respectively, with a gold surface from periodic DFT calculations. Inorg. Chem. 57, 3948–3955 (2018).

    Article  CAS  PubMed  Google Scholar 

  133. Busani, R., Folkers, M. & Cheshnovsky, O. Direct observation of band-gap closure in mercury clusters. Phys. Rev. Lett. 81, 3836–3839 (1998).

    Article  ADS  CAS  Google Scholar 

  134. Götz, S. et al. Rapid extraction of short-lived isotopes from a buffer gas cell for use in gas-phase chemistry experiments, part II: on-line studies with short-lived accelerator-produced radionuclides. Nucl. Instrum. Methods Phys. Res. B 507, 27–35 (2021).

    Article  ADS  Google Scholar 

  135. Götz, S. et al. Rapid extraction of short-lived isotopes from a buffer gas cell for use in gas-phase chemistry experiments. Part I: off-line studies with 219Rn and 221Fr. Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 995, 165090 (2021).

    Article  Google Scholar 

  136. Varentsov, V. & Yakushev, A. Concept of a new universal high-density gas stopping cell setup for study of gas-phase chemistry and nuclear properties of super heavy elements (UniCell). Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 940, 206–214 (2019).

    Article  ADS  CAS  Google Scholar 

  137. Steinegger, P. et al. Vacuum chromatography of Tl on SiO2 at the single-atom level. J. Phys. Chem. C 120, 7122–7132 (2016).

    Article  CAS  Google Scholar 

  138. Oganessian, Y. T. et al. Measurements of cross sections and decay properties of the isotopes of elements 112, 114, and 116 produced in the fusion reactions 233,238U, 242Pu, and 248Cm + 48Ca. Phys. Rev. C 70, 064609 (2004).

    Article  ADS  Google Scholar 

  139. Hofmann, S. et al. The reaction 48Ca + 248Cm → 296116* studied at the GSI-SHIP. Eur. Phys. J. A 48, 62 (2012).

    Article  ADS  Google Scholar 

  140. Kaji, D. et al. Study of the reaction 48Ca + 248Cm →  296Lv* at RIKEN-GARIS. J. Phys. Soc. Jpn 86, 034201 (2017).

    Article  ADS  Google Scholar 

  141. Oganessian, Y. T. et al. Synthesis of a new element with atomic number Z = 117. Phys. Rev. Lett. 104, 142502 (2010).

    Article  ADS  PubMed  Google Scholar 

  142. Khuyagbaatar, J. et al. 48Ca + 249Bk fusion reaction leading to element Z = 117: long-lived α-decaying 270Db and discovery of 266Lr. Phys. Rev. Lett. 112, 172501 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  143. Steinegger, P. et al. Diamond detectors for high-temperature transactinide chemistry experiments. Nucl. Instr. Methods Phys. Res. A 850, 61–67 (2017).

    Article  ADS  CAS  Google Scholar 

  144. Eichler, R. et al. Thermochemical and physical properties of element 112. Angew. Chem. Int. Ed. Engl. 47, 3262–3266 (2008).

    Article  CAS  PubMed  Google Scholar 

  145. Dmitriev, S. N. et al. Pioneering experiments on the chemical properties of element 113. Mendeleev Commun. 24, 253–256 (2014).

    Article  CAS  Google Scholar 

  146. Aksenov, N. V. et al. On the volatility of nihonium (Nh, Z = 113). Eur. Phys. J. A 53, 158 (2017).

    Article  ADS  Google Scholar 

  147. Pershina, V. & Iliaš, M. Properties and reactivity of hydroxides of group 13 elements In, Tl, and Nh from molecular and periodic DFT calculations. Inorg. Chem. 58, 9866–9873 (2019).

    Article  CAS  PubMed  Google Scholar 

  148. Yakushev, A. et al. First study on nihonium (Nh, element 113) chemistry at TASCA. Front. Chem. 9, 753738 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  149. Ryzhkov, A., Pershina, V., Iliaš, M. & Shabaev, V. A theoretical study of the adsorption behavior of superheavy 7p-elements and their compounds on a surface of gold in comparison with their lighter homologs. Phys. Chem. Chem. Phys. 25, 15362–15370 (2023).

    Article  CAS  PubMed  Google Scholar 

  150. Jerabek, P., Schuetrumpf, B., Schwerdtfeger, P. & Nazarewicz, W. Electron and nucleon localization functions of oganesson: approaching the Thomas-Fermi limit. Phys. Rev. Lett. 120, 053001 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  151. Knecht, S. Trendbericht theoretische chemie: relativistische quantenchemie. Nachr. Chem. 67, 57–61 (2019).

    Article  CAS  Google Scholar 

  152. Kaygorodov, M. Y. et al. Electron affinity of oganesson. Phys. Rev. A 104, 012819 (2021).

    Article  ADS  CAS  Google Scholar 

  153. Eliav, E., Kaldor, U., Ishikawa, Y. & Pyykkö, P. Element 118: the first rare gas with an electron affinity. Phys. Rev. Lett. 77, 5350–5352 (1996).

    Article  ADS  CAS  PubMed  Google Scholar 

  154. Kaygorodov, M. et al. Ionization potentials and electron affinities of Rg, Cn, Nh and Fl superheavy elements. Phys. Rev. A 105, 062805 (2022).

    Article  ADS  CAS  Google Scholar 

  155. Pershina, V., Borschevsky, A., Anton, J. & Jacob, T. Theoretical predictions of trends in spectroscopic properties of homonuclear dimers and volatility of the 7p elements. J. Chem. Phys. 132, 194314 (2010).

    Article  ADS  CAS  PubMed  Google Scholar 

  156. Oganessian, Y. T. et al. Production and decay of the heaviest nuclei 293,294117 and 294118. Phys. Rev. Lett. 109, 162501 (2012).

    Article  ADS  PubMed  Google Scholar 

  157. Oganessian, Y. & Utyonkov, V. Superheavy nuclei from 48Ca-induced reactions. Nucl. Phys. A 944, 62–98 (2015).

    Article  Google Scholar 

  158. Brewer, N. T. et al. Search for the heaviest atomic nuclei among the products from reactions of mixed-Cf with a 48Ca beam. Phys. Rev. C 98, 024317 (2018).

    Article  ADS  CAS  Google Scholar 

  159. Oganessian, Y. T. et al. Investigation of 48Ca-induced reactions with 242Pu and 238U targets at the JINR superheavy element factory. Phys. Rev. C 106, 024612 (2022).

    Article  ADS  CAS  Google Scholar 

  160. Dognon, J.-P. & Pyykkö, P. Chemistry of the 5g elements: relativistic calculations on hexafluorides. Angew. Chem. Int. Ed. 56, 10132–10134 (2017).

    Article  CAS  Google Scholar 

  161. Mayer, M. G. On closed shells in nuclei. Phys. Rev. 74, 235–239 (1948).

    Article  ADS  Google Scholar 

  162. Mayer, M. G. On closed shells in nuclei. II. Phys. Rev. 75, 1969–1970 (1949).

    Article  ADS  Google Scholar 

  163. Haxel, O., Jensen, J. H. D. & Suess, H. E. On the “magic numbers” in nuclear structure. Phys. Rev. 75, 1766–1766 (1949).

    Article  ADS  CAS  Google Scholar 

  164. Myers, W. D. & Swiatecki, W. J. Nuclear masses and deformations. Nucl. Phys. 81, 1–60 (1966).

    Article  Google Scholar 

  165. Sobiczewski, A., Gareev, F. A. & Kalinkin, B. N. Closed shells for Z > 82 and N > 126 in a diffuse potential well. Phys. Lett. 22, 500–502 (1966).

    Article  ADS  Google Scholar 

  166. Nilsson, S. et al. On the nuclear structure and stability of heavy and superheavy elements. Nucl. Phys. A 131, 1–66 (1969).

    Article  Google Scholar 

  167. Viola, V. E. & Seaborg, G. T. Nuclear systematics of the heavy elements — II. Lifetimes for alpha, beta and spontaneous fission decay. J. Inorg. Nucl. Chem. 28, 741–761 (1966).

    Article  Google Scholar 

  168. Meldner, H. & Herrmann, G. Superheavy elements in nature? Z. Naturforsch. A 24, 1429–1430 (1969).

    Article  ADS  CAS  Google Scholar 

  169. Ter-Akopian, G. & Dmitriev, S. Searches for superheavy elements in nature: cosmic-ray nuclei; spontaneous fission. Nucl. Phys. A 944, 177–189 (2015).

    Article  ADS  CAS  Google Scholar 

  170. Korschinek, G. & Kutschera, W. Mass spectrometric searches for superheavy elements in terrestrial matter. Nucl. Phys. A 944, 190–203 (2015).

    Article  Google Scholar 

  171. Ćwiok, S., Dobaczewski, J., Heenen, P. H., Magierski, P. & Nazarewicz, W. Shell structure of the superheavy elements. Nucl. Phys. A 611, 211–246 (1996).

    Article  ADS  Google Scholar 

  172. Bender, M., Nazarewicz, W. & Reinhard, P.-G. Shell stabilization of super- and hyperheavy nuclei without magic gaps. Phys. Lett. B 515, 42–48 (2001).

    Article  Google Scholar 

  173. Agbemava, S. E., Afanasjev, A. V., Nakatsukasa, T. & Ring, P. Covariant density functional theory: reexamining the structure of superheavy nuclei. Phys. Rev. C 92, 054310 (2015).

    Article  ADS  Google Scholar 

  174. Såmark-Roth, A. et al. Spectroscopy along flerovium decay chains: discovery of 280Ds and an excited state in 282Cn. Phys. Rev. Lett. 126, 032503 (2021).

    Article  ADS  PubMed  Google Scholar 

  175. Utyonkov, V. K. et al. Experiments on the synthesis of superheavy nuclei 284Fl and 285Fl in the 239,240Pu + 48Ca reactions. Phys. Rev. C 92, 034609 (2015).

    Article  ADS  Google Scholar 

  176. Smolańczuk, R. Properties of the hypothetical spherical superheavy nuclei. Phys. Rev. C 56, 812–824 (1997).

    Article  ADS  Google Scholar 

  177. Warda, M. & Egido, J. L. Fission half-lives of superheavy nuclei in a microscopic approach. Phys. Rev. C 86, 014322 (2012).

    Article  ADS  Google Scholar 

  178. Karpov, A. V., Zagrebaev, V. I., Martinez Palenzuela, Y., Felipe Ruiz, L. & Greiner, W. Decay properties and stability of heaviest elements. Int. J. Mod. Phys. E 21, 1250013 (2012).

    Article  ADS  Google Scholar 

  179. Staszczak, A., Baran, A. & Nazarewicz, W. Spontaneous fission modes and lifetimes of superheavy elements in the nuclear density functional theory. Phys. Rev. C 87, 024320 (2013).

    Article  ADS  Google Scholar 

  180. Bao, X. J. et al. Competition between α-decay and spontaneous fission for superheavy nuclei. J. Phys. G Nucl. Part. Phys. 42, 085101 (2015).

    Article  ADS  Google Scholar 

  181. Giuliani, S. A., Martínez-Pinedo, G. & Robledo, L. M. Fission properties of superheavy nuclei for r-process calculations. Phys. Rev. C 97, 034323 (2018).

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

We thank V. Pershina, M. Block, J. Khuyagbaatar and W. Loveland for discussions. We acknowledge financial support by the Program Hubert Curien Dumont d’Urville New Zealand - France Science & Technology Support Program number 43245QC, and the Marsden Fund of the Royal Society of New Zealand. This work was also supported by the US Department of Energy under Award Numbers DOE-DE-NA0004074 (NNSA, the Stewardship Science Academic Alliances program) and DE-SC0013365 and DE-SC0023175 (Office of Science, Office of Nuclear Physics).

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Authors and Affiliations

  1. Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Auckland, New Zealand

    Odile R. Smits & Peter Schwerdtfeger

  2. Department of Chemistry – TRIGA Site, Johannes Gutenberg University Mainz, Mainz, Germany

    Christoph E. Düllmann

  3. GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

    Christoph E. Düllmann

  4. Helmholtz Institute Mainz, Mainz, Germany

    Christoph E. Düllmann

  5. Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, Paris, France

    Paul Indelicato

  6. Facility for Rare Isotope Beams and Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA

    Witold Nazarewicz

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Glossary

Atom-at-a-time chemistry

Chemistry studies in which only single atoms of the element of interest are present owing to small production rates and short half-lives.

Bayesian machine learning

Machine learning methods based on or applying Bayesian statistics.

Coulomb frustration

The competition between the short-range attractive nuclear interaction and the long-range Coulomb repulsion leading to exotic topologies of nucleonic densities.

Density functional theory

Density functional theory is an alternative to wave function-based methods using approximate functionals of the one-particle densities and currents.

Electron correlation

The difference between an atomic or molecular property evaluated with a single determinant at the Dirac–Hartree–Fock level and the same evaluated using either a sum of determinants or many-body perturbation theory.

Heavy ion-induced fusion reactions

Nuclear reactions induced by ions with Z > 2, with superheavy elements typically being produced in cold fusion reactions based on targets near 208Pb that form a compound nucleus that is excited typically in the range of ECN < 20 MeV and favourable for the production of the elements with Z < 113, or in hot fusion reactions using 48Ca beams leading to more highly excited (hotter) compound nuclei which evaporate more neutrons to de-excite, favourable for the production of the elements with Z > 112.

Multinucleon transfer reactions

Nuclear reactions in which beam nuclei and target nuclei exchange nucleons (in contrast to fusion reactions in which they fuse, forming a compound nucleus comprising all nucleons of beam nucleus and target nucleus).

Negative-energy continuum

The continuum spectrum with energy below −mc2 that are a solution to the Dirac equation.

Nucleon dripline

The boundary beyond which atomic nuclei are unbound with respect to the emission of a nucleon.

Quantum electrodynamics

Relativistic quantum field theory of the interactions of charged particles with the quantized electromagnetic field (that is, photons) containing in particular contributions of particle vacuum fluctuations (virtual electron–positron pairs) leading to the vacuum polarization and the electromagnetic field fluctuations leading to the self-energy.

Radioactive-ion beams

Ion beams consisting of radioactive ions.

Rapid neutron-capture process (r-process)

A network of nuclear reactions taking place in high-neutron density environments that is responsible for the creation of approximately half of the atomic nuclei heavier than iron.

Recoil separators

Electromagnetic separators isolating single superheavy nuclei from the intense primary ion beam and from unwanted byproducts of the nuclear formation reaction to allow their detailed study.

Relativistic effects

The difference between solutions of the nonrelativistic Schrödinger and the relativistic Dirac equation for a specific property.

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Smits, O.R., Düllmann, C.E., Indelicato, P. et al. The quest for superheavy elements and the limit of the periodic table. Nat Rev Phys 6, 86–98 (2024). https://doi.org/10.1038/s42254-023-00668-y

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