Skip to main content
SpringerLink
Log in

The Unitarity Expansion for Light Nuclei

  • Conference paper
  • First Online:
Recent Progress in Few-Body Physics (FB22 2018)

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 238))

Included in the following conference series:

Abstract

It is argued here that (at least light) nuclei may reside in a sweet spot: bound weakly enough to be insensitive to the details of the interaction, but dense enough to be insensitive to the exact values of the large two-body scattering lengths as well. In this scenario a systematic expansion of nuclear observables around the unitarity limit converges. In particular, the nuclear force in this scheme is constructed such that the gross features of states in the nuclear chart are determined by a very simple leading-order interaction, whereas—much like the fine structure of atomic spectra—observables are moved to their physical values by small perturbative corrections. Explicit evidence in favor of this conjecture is shown for the binding energies of three and four nucleons.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Schwinger, J.: hectographed Notes on Nuclear Physics. Harvard University (1947)

    Google Scholar 

  2. Barker, F.C., Peierls, R.E.: Phys. Rev. 75, 312 (1949)

    Article  ADS  Google Scholar 

  3. Chew, G.F., Goldberger, M.L.: Phys. Rev. 75, 1637 (1949)

    Article  ADS  Google Scholar 

  4. Bethe, H.A.: Phys. Rev. 76, 38 (1949)

    Article  ADS  Google Scholar 

  5. Beane, S.R., Bedaque, P.F., Savage, M.J., van Kolck, U.: Nucl. Phys. A 700, 377 (2002)

    Google Scholar 

  6. Beane, S.R., Savage, M.J.: Nucl. Phys. A 713, 148 (2003)

    Google Scholar 

  7. Epelbaum, E., Meißner, U.-G., Glöckle, W.: Nucl. Phys. A 714, 535 (2003)

    Google Scholar 

  8. Beane, S.R., Savage, M.J.: Nucl. Phys. A 717, 91 (2003)

    Google Scholar 

  9. Braaten, E., Hammer, H.W.: Phys. Rev. Lett. 91, 102002 (2003)

    Google Scholar 

  10. Chin, C., Grimm, R., Julienne, P., Tiesinga, E.: Rev. Mod. Phys. 82, 1225 (2010)

    Article  ADS  Google Scholar 

  11. Braaten, E., Kusunoki, M.: Phys. Rev. D 69, 074005 (2004)

    Google Scholar 

  12. Efimov, V.: Phys. Lett. B 33, 563 (1970)

    Google Scholar 

  13. Bedaque, P.F., Hammer, H.-W., van Kolck, U.: Phys. Rev. Lett. 82, 463 (1999)

    Article  ADS  Google Scholar 

  14. Bedaque, P.F., Hammer, H.-W., van Kolck, U.: Nucl. Phys. A 646, 444 (1999)

    Google Scholar 

  15. Bedaque, P.F., Hammer, H.-W., van Kolck, U.: Nucl. Phys. A 676, 35 (2000)

    Google Scholar 

  16. van Oers, W.T.H., Seagrave, J.D.: Phys. Lett. 24B, 562 (1967)

    Google Scholar 

  17. Girard, B.A., Fuda, M.G.: Phys. Rev. C 19, 579 (1979)

    Article  ADS  Google Scholar 

  18. Rupak, G., Vaghani, A., Higa, R., van Kolck, U.: Phys. Lett. B 791, 414 (2019)

    Google Scholar 

  19. Adhikari, S.K., Fonseca, A.C., Tomio, L.: Phys. Rev. C 26, 77 (1982)

    Article  ADS  Google Scholar 

  20. König, S., Grießhammer, H.W., Hammer, H.-W., van Kolck, U.: Phys. Rev. Lett. 118, 202501 (2017)

    Google Scholar 

  21. Hammer, H.-W., König, S., van Kolck, U.: (submitted manuscript). arXiv:1906.12122 [nucl-th]

  22. König, S., Grießhammer, H.W., Hammer, H.-W., van Kolck, U.: J. Phys. G 43, 055106 (2016)

    Google Scholar 

  23. König, S.: J. Phys. G 44, 064007 (2017)

    Google Scholar 

  24. Vanasse, J.: Phys. Rev. C 88, 044001 (2013)

    Google Scholar 

  25. Platter, L., Hammer, H.-W., Meißner, U.-G.: Phys. Rev. A 70, 052101 (2004)

    Google Scholar 

  26. Platter, L., Hammer, H.-W., Meißner, U.-G.: Phys. Lett. B 607, 254 (2005)

    Google Scholar 

  27. Platter, L.: From Cold Atoms to Light Nuclei: The Four-Body Problem in an Effective Theory with Contact Interactions, Doctoral thesis (Dissertation), University of Bonn (2005)

    Google Scholar 

  28. Platter, L., Hammer, H.-W.: Nucl. Phys. A 766, 132 (2006)

    Google Scholar 

  29. Kamada, H., Glöckle, W.: Nucl. Phys. A 548, 205 (1992)

    Google Scholar 

  30. Glöckle, W.: The Quantum Mechanical Few-Body Problem. Springer, Berlin (1983)

    Book  Google Scholar 

  31. Stadler, A., Glöckle, W., Sauer, P.U.: Phys. Rev. C 44, 2319 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  32. Platter, L., Hammer, H.-W.: Eur. Phys. J. A 32, 113 (2007)

    Article  ADS  Google Scholar 

  33. Deltuva, A.: Phys. Rev. A 82, 040701 (2010)

    Google Scholar 

  34. Bazak, B., Kirscher, J., König, S., Pavón Valderrama, M., Barnea, N., van Kolck, U.: Phys. Rev. Lett. 122, 143001 (2019)

    Google Scholar 

  35. van Kolck, U.: Few Body Syst. 58, 112 (2017)

    Google Scholar 

  36. Fossez, K., Rotureau, J., Nazarewicz, W.: Phys. Rev. C 98, 061302 (2018)

    Google Scholar 

  37. Lei, J., Hlophe, L., Elster, C., Nogga, A., Nunes, F.M., Phillips, D.R.: Phys. Rev. C 98, 051001 (2018)

    Google Scholar 

  38. Carlson, J., Gandolfi, S., van Kolck, U., Vitiello, S.A.: Phys. Rev. Lett. 119, 223002 (2017)

    Google Scholar 

  39. Kievsky, A., Viviani, M., Logoteta, D., Bombaci, I., Girlanda, L.: Phys. Rev. Lett. 121, 072701 (2018)

    Google Scholar 

Download references

Acknowledgements

I would like to thank Harald Grießhammer, Hans-Werner Hammer, and Bira van Kolck for their collaboration as well as for many insightful discussions and comments on this manuscript. This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Projektnummer 279384907 – SFB 1245 and by the ERC Grant No. 307986 STRONGINT.

Author information

Authors and Affiliations

  1. Institut für Kernphysik, Technische Universität Darmstadt, 64289, Darmstadt, Germany

    Sebastian König

  2. ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291, Darmstadt, Germany

    Sebastian König

Authors
  1. Sebastian König
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sebastian König .

Editor information

Editors and Affiliations

  1. LPC-Caen, ENSICAEN, IN2P3/CNRS, Université de Caen Normandie, Caen, France

    N. A. Orr

  2. GANIL, CEA/DRF-IN2P3/CNRS, Caen, France

    M. Ploszajczak

  3. LPC-Caen, ENSICAEN, IN2P3/CNRS, Université de Caen Normandie, Caen, France

    F. M. Marqués

  4. IPN-Orsay, IN2P3/CNRS, Université Paris-Sud, Université Paris-Saclay, Orsay, France

    J. Carbonell

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

König, S. (2020). The Unitarity Expansion for Light Nuclei. In: Orr, N., Ploszajczak, M., Marqués, F., Carbonell, J. (eds) Recent Progress in Few-Body Physics. FB22 2018. Springer Proceedings in Physics, vol 238. Springer, Cham. https://doi.org/10.1007/978-3-030-32357-8_54

Download citation

Publish with us

Policies and ethics

Search

Navigation