How atomic nuclei cluster

Abstract

Nucleonic matter displays a quantum-liquid structure, but in some cases finite nuclei behave like molecules composed of clusters of protons and neutrons. Clustering is a recurrent feature in light nuclei, from beryllium to nickel1,2,3. Cluster structures are typically observed as excited states close to the corresponding decay threshold; the origin of this phenomenon lies in the effective nuclear interaction, but the detailed mechanism of clustering in nuclei has not yet been fully understood. Here we use the theoretical framework of energy-density functionals4,5, encompassing both cluster and quantum liquid-drop aspects of nuclei, to show that conditions for cluster formation can in part be traced back to the depth of the confining nuclear potential. For the illustrative example of neon-20, we show that the depth of the potential determines the energy spacings between single-nucleon orbitals in deformed nuclei, the localization of the corresponding wavefunctions and, therefore, the degree of nucleonic density clustering. Relativistic functionals, in particular, are characterized by deep single-nucleon potentials. When compared to non-relativistic functionals that yield similar ground-state properties (binding energy, deformation, radii), they predict the occurrence of much more pronounced cluster structures. More generally, clustering is considered as a transitional phenomenon between crystalline and quantum-liquid phases of fermionic systems.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Self-consistent ground-state densities of 20 Ne.
Figure 2: Partial nucleon density distributions.
Figure 3: Harmonic oscillators of different depths.
Figure 4: Schematic illustration of the transition from a crystalline to a quantum liquid phase, including the cluster phase.

References

  1. 1

    Weizsäcker, C. F. V. Neuere Modellvorstellungen über den Bau der Atomkerne. Naturwissenschaften 26, 209–217 (1938)

    ADS  Article  Google Scholar 

  2. 2

    Wheeler, J. A. On the mathematical description of light nuclei by the method of resonating group structure. Phys. Rev. 52, 1107–1122 (1937)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Von Oertzen, W. V., Freer, M. & Kanada-En’yo, Y. Nuclear clusters and nuclear molecules. Phys. Rep. 432, 43–113 (2006)

    ADS  CAS  Article  Google Scholar 

  4. 4

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

    ADS  CAS  Article  Google Scholar 

  5. 5

    Vretenar, D., Afanasjev, A. V., Lalazissis, G. A. & Ring, P. Relativistic Hartree−Bogoliubov theory: static and dynamic aspects of exotic nuclear structure. Phys. Rep. 409, 101–259 (2005)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Kanada-En’yo, Y. & Horiuchi, H. Structure of light unstable nuclei studied with antisymmetrized molecular dynamics. Prog. Theor. Phys. 142 (Suppl.). 205–263 (2001)

    Article  Google Scholar 

  7. 7

    Feldmeier, H., Bieler, K. & Schnack, J. Fermionic molecular dynamics for ground states and collision of nuclei. Nucl. Phys. A 586, 493–532 (1995)

    ADS  Article  Google Scholar 

  8. 8

    Neff, T. & Feldmeier, H. Tensor correlations in the unitary correlation operator method. Nucl. Phys. A 713, 311–371 (2003)

    ADS  Article  Google Scholar 

  9. 9

    Tohsaki, A., Horiuchi, H., Schuck, P. & Röpke, G. Alpha cluster condensation in 12C and 16O. Phys. Rev. Lett. 87, 192501 (2001)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Fynbo, H. O. U. et al. Revised rates for the stellar triple-α process from measurement of 12C nuclear resonances. Nature 433, 136–139 (2005)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Rose, H. J. & Jones, G. A. A new kind of natural radioactivity. Nature 307, 245–247 (1984)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Greiner, W., Park, J. Y. & Scheid, W. Nuclear Molecules (World Scientific, 1995)

    Google Scholar 

  13. 13

    Ikeda K, Tagikawa N & Horiuchi H The systematic structure-change into the molecule-like structures in the self-conjugate 4n nuclei. Prog. Theor. Phys. 464 (Suppl.). 464–475 (1968)

    Article  Google Scholar 

  14. 14

    Arumugam, P., Sharma, B. K. & Patra, S. K. Relativistic mean field study of clustering in light nuclei. Phys. Rev. C 71, 064308 (2005)

    ADS  Article  Google Scholar 

  15. 15

    Maruhn, J. A. et al. α-Cluster structure and exotic states in a self-consistent model for light nuclei. Phys. Rev. C 74, 044311 (2006)

    ADS  Article  Google Scholar 

  16. 16

    Reinhard, P.-G., Maruhn, J. A., Umar, A. S. & Oberacker, V. E. Localization in light nuclei. Phys. Rev. C 83, 034312 (2011)

    ADS  Article  Google Scholar 

  17. 17

    Okolowicz, J., Ploszajczak, M. & Nazarewicz, W. On the origin of nuclear clustering. Preprint at 〈http://arxiv.org/abs/1202.6290〉 (2012)

  18. 18

    Girod, M. & Grammaticos, B. Triaxial Hartree−Fock−Bogolyubov calculations with D1 effective interaction. Phys. Rev. C 27, 2317–2339 (1983)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Ichikawa, T., Marhun, J. A., Itagaki, N. & Ohkubo, S. Linear chain structure of four-α clusters in 16O. Phys. Rev. Lett. 107, 112501 (2011)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Robledo, L. M. & Bertsch, G. F. Global systematics of octupole excitations in even−even nuclei. Phys. Rev. C 84, 054302 (2011)

    ADS  Article  Google Scholar 

  21. 21

    Chabanat, E., Bonche, P., Haensel, P., Meyer, J. & Schaeffer, R. A Skyrme parametrization from subnuclear to neutron star densities part II. Nuclei far from stabilities. Nucl. Phys. A 635, 231–256 (1998)

    ADS  Article  Google Scholar 

  22. 22

    Lalazissis, G. A., Nikšić, T., Vretenar, D. & Ring, P. New relativistic mean-field interaction with density-dependent meson-nucleons couplings. Phys. Rev. C 71, 024312 (2005)

    ADS  Article  Google Scholar 

  23. 23

    Fricke, G. et al. Behavior of the nuclear charge radii systematics in the s-d shell from muonic atom measurement. Phys. Rev. C 45, 80–89 (1992)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Chulkov, L. et al. Interaction cross sections and matter radii of A = 20 isobars. Nucl. Phys. A 603, 219–237 (1996)

    ADS  Article  Google Scholar 

  25. 25

    Nilsson, S. G. Binding states of individual nucleons in strongly deformed nuclei Mat. Fys. Medd. Dan. Vid. Selsk. 29, 1–69 (1955)

    MATH  Google Scholar 

  26. 26

    Cohen-Tannoudji, C., Diu, B. & Laloë, F. Mécanique Quantique (Hermann Ed., 1973)

    Google Scholar 

  27. 27

    Walecka, J. D. Theoretical Nuclear and Subnuclear Physics (Imperial College Press and World Scientific, 2004)

    Google Scholar 

  28. 28

    Mottelson, B. Elementary features of nuclear structure. In Les Houches Session LXVI, Trends in Nuclear Physics, 100 Years Later (eds Nifenecker, H., Blaizot, J.-P., Bertsch, G. F., Weise, W. & David, F. ). 25–121 (North-Holland Elsevier, 1996)

  29. 29

    Pines, D. & Nozières, P. The theory of quantum liquids (Benjamin, 1966)

    Google Scholar 

  30. 30

    Stoitsov, M. V., Dobaczewski, J., Nazarewicz, W. & Ring, P. Axially deformed solution of the Skyrme−Hartree−Fock−Bogolyubov equations using the transformed harmonic oscillator basis. The program HFBTHO (v1.66p). Comput. Phys. Commun. 167, 43–63 (2005)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Institut Universitaire de France and by the Croatian Ministry of Science, Education and Sport—project 1191005-1010. The authors thank J. Margueron, M. Milin, T. Neff, N. Van Giai and P. Schuck for comments and suggestions.

Author information

Affiliations

Authors

Contributions

Model calculations were done by J.-P.E., E.K., T.N. and D.V. The manuscript text was prepared by E.K. and D.V. with contributions from J.-P.E. and T.N. J.-P.E. and E.K. prepared the figures.

Corresponding author

Correspondence to E. Khan.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ebran, J., Khan, E., Nikšić, T. et al. How atomic nuclei cluster. Nature 487, 341–344 (2012). https://doi.org/10.1038/nature11246

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.