Skip to main content

An Introduction to Nuclear Supersymmetry: A Unification Scheme for Nuclei

  • Chapter
  • First Online:
The Hispalensis Lectures on Nuclear Physics Vol. 2

Part of the book series: Lecture Notes in Physics ((LNP,volume 652))

Abstract

The main ideas behind nuclear supersymmetry are presented, starting from the basic concepts of symmetry and the methods of group theory in physics. We propose new, more stringent experimental tests that probe the supersymmetry classification in nuclei and point out that specific correlations should exist for particle transfer intensities among supersymmetric partners. We also discuss possible ways to generalize these ideas to cases where no dynamical symmetries are present. The combination of these theoretical and experimental studies may play a unifying role in nuclear phenomena.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • 1. A. Arima and F. Iachello: Phys. Rev. Lett. 35, 1069 (1975); F. Iachello and A. Arima: The Interacting Boson Model, (Cambridge University Press, Cambridge, 1987)

    Article  Google Scholar 

  • 2. F. Iachello and O. Scholten: Phys. Rev. Lett. 43, 679 (1979); F. Iachello and P. Van Isacker: The Interacting Boson-Fermion Model (Cambridge University Press, Cambridge, 1991)

    Google Scholar 

  • 3. F. Iachello: Phys. Rev. Lett. 44, 772 (1980)

    Google Scholar 

  • 4. A.B. Balantekin, I. Bars and F. Iachello: Phys. Rev. Lett. 47, 19 (1981); A.B. Balantekin, I. Bars and F. Iachello: Nucl. Phys. A 370, 284 (1981)

    Google Scholar 

  • 5. A.B. Balantekin, I. Bars, R. Bijker and F. Iachello: Phys. Rev. C 27, 1761 (1983)

    Google Scholar 

  • 6. A. Mauthofer, K. Stelzer, J. Gerl, Th.W. Elze, Th. Happ, G. Eckert, T. Faestermann, A. Frank and P. Van Isacker: Phys. Rev. C 34, 1958 (1986)

    Google Scholar 

  • 7. R. Bijker: Ph.D. Thesis, University of Groningen (1984)

    Google Scholar 

  • 8. D.D. Warner, R.F. Casten and A. Frank: Phys. Lett. B 180, 207 (1986)

    Google Scholar 

  • 9. P. Van Isacker, J. Jolie, K. Heyde and A. Frank: Phys. Rev. Lett. 54, 653 (1985)

    Google Scholar 

  • 10. A. Frank and P. Van Isacker: Algebraic Methods in Molecular and Nuclear Structure Physics, (Wiley, New York, 1994)

    Google Scholar 

  • 11. R. Gilmore: Lie Groups, Lie Algebras, and Some of Their Applications, (Wiley-Interscience, New York, 1974)

    Google Scholar 

  • 12. M.E. Rose: Elementary Theory of Angular Momentum, Wiley, New York, 1957

    Google Scholar 

  • 13. B.G. Wybourne: Classical Groups for Physicists, (Wiley-Interscience, New York, 1974)

    Google Scholar 

  • 14. H.J. Lipkin: Lie Groups for Pedestrians, (North-Holland, Amsterdam, 1966)

    Google Scholar 

  • 15. V.I. Man’ko: in Symmetries in Science V, ed. by B. Gruber, L.C. Biedenharn, and H.D. Doebner, (Plenum, New York, 1991), pp. 453

    Google Scholar 

  • 16. A. Messiah: Quantum Mechanics, (Wiley, New York, 1968)

    Google Scholar 

  • 17. O. Castaños, A. Frank, and R. Lopez–Peña: J. Phys. A 23, 5141 (1990)

    Google Scholar 

  • 18. W. Heisenberg: Z. Phys. 77, 1 (1932)

    Google Scholar 

  • 19. J.P. Elliott and P.G. Dawber: Symmetry in Physics. I. Principles and Simple Applications (Oxford University Press, New York, 1979)

    Google Scholar 

  • 20. A. Bohr and B.R. Mottelson: Nuclear Structure. II. Nuclear Deformations (Benjamin, New York, 1975)

    Google Scholar 

  • 21. M. Gell-Mann: Phys. Rev. 125, 1067 (1962)

    Google Scholar 

  • 22. S. Okubo: Progr. Theor. Phys. 27, 949 (1962)

    Google Scholar 

  • 23. M. Gell-Mann and Y. Ne’eman: The Eightfold Way, (Benjamin, New York, 1964)

    Google Scholar 

  • 24. J. Wess and B. Zumino: Nucl. Phys. B 70, 39 (1974)

    Google Scholar 

  • 25. P. Fayet and S. Ferrara: Phys. Rep. 32, 249 (1977)

    Google Scholar 

  • 26. P. van Nieuwenhuizen: Phys. Rep. 68, 189 (1981)

    Google Scholar 

  • 27. S. Weinberg: The quantum theory of fields: Supersymmetry (Cambridge University Press, Cambridge, 2000)

    Google Scholar 

  • 28. I. Bars: in Introduction to Supersymmetry in Particle and Nuclear Physics, ed. by O. Castaños, A. Frank, and L. Urrutia, (Plenum, New York, 1983), pp 107

    Google Scholar 

  • 29. A. Metz, J. Jolie, G. Graw, R. Hertenberger, J. Gröger, C. Günther, N. Warr and Y. Eisermann: Phys. Rev. Lett. 83, 1542 (1999)

    Google Scholar 

  • 30. A. Kostelecky and D.K. Campbell, Eds.: Supersymmetry in Physics (North Holland, Amsterdam, 1984)

    Google Scholar 

  • 31. A. Metz, Y. Eisermann, A. Gollwitzer, R. Hertenberger, B.D. Valnion, G. Graw and J. Jolie: Phys. Rev. C 61, 064313 (2000)

    Google Scholar 

  • 32. J. Gröger, J. Jolie, R. Krücken, C.W. Beausang, M. Caprio, R.F. Casten, J. Cederkall, J.R. Cooper, F. Corminboeuf, L. Genilloud, G. Graw, C. Günther, M. de Huu, A.I. Levon, A. Metz, J.R. Novak, N. Warr and T. Wendel: Phys. Rev. C 62, 064304 (2000)

    Google Scholar 

  • 33. R. Bijker, J. Barea and A. Frank: preprint (2004), submitted to J. Phys. A

    Google Scholar 

  • 34. A. Frank, P. Van Isacker and D.D. Warner: Phys. Lett. B 197, 474 (1987)

    Google Scholar 

  • 35. J. Barea: Ph.D. Thesis, Universidad de Sevilla (2002)

    Google Scholar 

  • 36. H.-F. Wirth and G. Graw: private communication

    Google Scholar 

  • 37. J.P. Elliott: Proc. Roy. Soc. A 245, 128 (1958); Proc. Roy. Soc. A 245, 562 (1958)

    Google Scholar 

  • 38. F. Iachello and S. Kuyucak: Ann. Phys. (N.Y.) 136, 19 (1981)

    Google Scholar 

  • 39. J.A. Cizewski, R.F. Casten, G.J. Smith, M.L. Stelts, W.R. Kane, H.G. Börner and W.F. Davidson: Phys. Rev. Lett. 40, 167 (1978); A. Arima and F. Iachello: Phys. Rev. Lett. 40, 385 (1978)

    Google Scholar 

  • 40. H.Z. Sun, A. Frank and P. Van Isacker: Phys. Rev. C 27, 2430 (1983); H.Z. Sun, A. Frank and P. Van Isacker: Ann. Phys. (N.Y.) 157, 183 (1984)

    Google Scholar 

  • 41. A. Mauthofer, K. Stelzer, Th.W. Elze, Th. Happ, J. Gerl, A. Frank and P. Van Isacker: Phys. Rev. C 39, 1111 (1989)

    Google Scholar 

  • 42. J. Jolie, U. Mayerhofer, T. von Egidy, H. Hiller, J. Klora, H. Lindner and H. Trieb: Phys. Rev. C 43, R16 (1991)

    Google Scholar 

  • 43. G. Rotbard, G. Berrier, M. Vergnes, S. Fortier, J. Kalifa, J.M. Maison, L. Rosier, J. Vernotte, P. Van Isacker and J. Jolie: Phys. Rev. C 47, 1921 (1993)

    Google Scholar 

  • 44. O. Scholten: Prog. Part. Nucl. Phys. 14, 189 (1985)

    Google Scholar 

  • 45. R. Bijker and F. Iachello: Ann. Phys. (N.Y.) 161, 360 (1985)

    Google Scholar 

  • 46. J. Barea, R. Bijker, A. Frank and G. Loyola: Phys. Rev. C 64, 064313 (2001)

    Google Scholar 

  • 47. M.L. Munger and R.J. Peterson: Nucl. Phys. A 303, 199 (1978)

    Google Scholar 

  • 48. Y. Yamazaki and R.K. Sheline: Phys. Rev. C 14, 531 (1976)

    Google Scholar 

  • 49. H.-F. Wirth, S. Christen, Y. Eisermann, A. Gollwitzer, G. Graw, R. Hertenberger, J. Jolie, A. Metz, O. Möller, D. Tonev and B.D. Valnion: preprint (2004)

    Google Scholar 

  • 50. J. Barea, C.E. Alonso and J.M. Arias: Phys. Rev. C 65, 034328 (2002)

    Google Scholar 

  • 51. I. Talmi: Simple Models for Complex Nuclei, (Harwood, 1993)

    Google Scholar 

  • 52. P. Navrátil alnd J. Dobes: Phys. Rev. C 37, 2126 (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

José Miguel Arias Manuel Lozano

Rights and permissions

Reprints and permissions

About this chapter

Cite this chapter

Frank, A., Barea, J., Bijker, R. An Introduction to Nuclear Supersymmetry: A Unification Scheme for Nuclei. In: Arias, J.M., Lozano, M. (eds) The Hispalensis Lectures on Nuclear Physics Vol. 2. Lecture Notes in Physics, vol 652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44504-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-44504-3_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22512-6

  • Online ISBN: 978-3-540-44504-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics