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Superheavy elements and ultradense matter


In order to characterize the mass density of superheavy elements, we solve numerically the relativistic Thomas–Fermi model of an atom. To obtain a range of mass densities for superheavy matter, this model is supplemented with an estimation of the number of electrons shared between individual atoms. Based on our computation, we expect that elements in the island of nuclear stability around \(Z = 164\) will populate a mass density range of 36.0–68.4 g/cm\(^{3}\). We then extend our method to the study of macroscopic alpha particle nuclear matter condensate drops.

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  1. B. Fricke, W. Greiner, J. Waber, The continuation of the periodic table up to \(Z = 172\). The chemistry of superheavy elements. Theor. Chim. Acta 21, 235–260 (1971)

    Article  Google Scholar 

  2. B. Müller, J. Rafelski, Stabilization of the charged vacuum created by very strong electrical fields in nuclear matter. Phys. Rev. Lett. 34, 349 (1975)

    Article  ADS  Google Scholar 

  3. J. Rafelski, L. Labun, J. Birrell, Compact ultradense matter impactors. Phys. Rev. Lett. 110, 111102 (2013)

    Article  ADS  Google Scholar 

  4. C. Dietl, L. Labun, J. Rafelski, Properties of gravitationally bound compact ultra dense objects. Phys. Lett. B 709(3), 123–127 (2012)

    Article  ADS  Google Scholar 

  5. D.R. Lide (ed.), Physical Constants of Organic Compounds. CRC Handbook of Chemistry and Physics, Internet Version 2005 (CRC Press, Boca Raton, 2005).

  6. B. Carry, Density of asteroids. Planet. Space Sci. 73, 98–118 (2012)

    Article  ADS  Google Scholar 

  7. J. Grumann, U. Mosel, B. Fink, W. Greiner, Investigation of the stability of superheavy nuclei around \(Z=114\) and \(Z=164\). Z. Phys. 228, 371–386 (1969)

    Article  ADS  Google Scholar 

  8. M. Bender, P.H. Heenen, P.G. Reinhard, Self-consistent mean-field models for nuclear structure. Rev. Mod. Phys. 75, 121–180 (2003)

    Article  ADS  Google Scholar 

  9. A. Sobiczewski, K. Pomorski, Description of structure and properties of superheavy nuclei. Prog. Part. Nucl. Phys. 58, 292–349 (2007)

    Article  ADS  Google Scholar 

  10. W. Nazarewicz, M. Bender, S. Ćwiok, P.H. Heenen, A.T. Kruppa, P.G. Reinhard, T. Vertse, Theoretical description of superheavy nuclei. Nucl. Phys. A 701, 165–171 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. J. Dechargé, J.F. Berger, M. Girod, K. Dietrich, Bubbles and semi-bubbles as a new kind of superheavy nuclei. Nucl. Phys. A 716, 55–86 (2003)

    Article  ADS  Google Scholar 

  13. A.V. Afanasjev, S.E. Agbemava, A. Gyawali, Hyperheavy nuclei: existence and stability. Phys. Lett. B 782, 533–540 (2018). arXiv:1804.06395 [nucl-th]

    Article  ADS  Google Scholar 

  14. S.E. Agbemava, A.V. Afanasjev, A. Taninah, A. Gyawali, Extension of the nuclear landscape to hyperheavy nuclei. Phys. Rev. C 99(3), 034316 (2019)

    Article  ADS  Google Scholar 

  15. S.E. Agbemava, A.V. Afanasjev, Hyperheavy spherical and toroidal nuclei: the role of shell structure. Phys. Rev. C 103(3), 034323 (2021)

    Article  ADS  Google Scholar 

  16. M. Veselský, V. Petousis, Ch.C. Moustakidis, G.A. Souliotis, A. Bonasera, Investigating the possible existence of hyper-heavy nuclei in a neutron-star environment. Phys. Rev. C 106, L012802 (2022)

    Article  ADS  Google Scholar 

  17. J.W. Clark, E. Krotscheck, Alpha matter revisited. arXiv:2304.08543 [nucl-th]

  18. L.D. Landau, E.M. Lifshitz, Statistical Physics, Part 1, 3rd edn. (Elsevier, Amsterdam, 1980)

    Google Scholar 

  19. J. Rafelski, L.P. Fulcher, A. Klein, Fermions and bosons interacting with arbitrarily strong external fields. Phys. Rep. 38, 227–361 (1978)

    Article  ADS  Google Scholar 

  20. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes; The Art of Scientific Computing, 3rd edn. (Cambridge University Press, New York, 2007)

    MATH  Google Scholar 

  21. A. Kramida, Y. Ralchenko, J. Reader, NIST ASD Team, NIST Atomic Spectra Database (ver. 5.10) (National Institute of Standards and Technology, Gaithersburg, 2022). [2023, May 23]

  22. J. Gyanchandani, S.K. Sikka, Physical properties of the 6d-series elements from density functional theory: close similarity to lighter transition metals. Phys. Rev. B 83, 172101 (2011)

    Article  ADS  Google Scholar 

  23. J.D. Walecka, A theory of highly condensed matter. Ann. Phys. 83, 491–529 (1974)

    Article  ADS  Google Scholar 

  24. K. Sun, K. Padavić, F. Yang, S. Vishveshwara, C. Lannert, Static and dynamic properties of shell-shaped condensates. Phys. Rev. A 98, 013609 (2018)

    Article  ADS  Google Scholar 

  25. R.A. Carollo, D.C. Aveline, B. Rhyno, S. Vishveshwara, C. Lannert, J.D. Murphree, E.R. Elliott, J.R. Williams, R.J. Thompson, N. Lundblad, Observation of ultracold atomic bubbles in orbital microgravity. Nature 606, 281–286 (2022)

    Article  ADS  Google Scholar 

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Correspondence to Johann Rafelski.

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LaForge, E., Price, W. & Rafelski, J. Superheavy elements and ultradense matter. Eur. Phys. J. Plus 138, 812 (2023).

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