Advertisement

Relativistic Pseudospin Symmetry in Nuclei

  • J. N. Ginocchio
  • A. Leviatan
Part of the NATO Science Series book series (NAII, volume 53)

Abstract

Peter Ring was one of the first to really grasp the significance of pseudospin symmetry as a relativistic symmetry [1, 2, 3, 4]. Originally, pseudospin doublets were introduced into nuclear physics to accommodate an observed near degeneracy of certain normal-parity shell-model orbitals with non-relativistic quantum numbers (n r , , j = + 1/2) and (n r − 1, + 2, j = + 3/2) where n r , , and j are the single-nucleon radial, orbital, and total angular momentum quantum numbers, respectively [5, 6]. The doublet structure, is expressed in terms of a “pseudo” orbital angular momentum ~ = + 1 coupled to a “pseudo” spin, ~s = 1/2. For example, (n r s 1/2, (n r − 1)d 3/2) will have ~ = 1, (n r p 3/2, (n r − 1)f 5/2) will have ~ℓ = 2, etc. Since j = ~ ± ~s, the energy of the two states in the doublet is then approximately independent of the orientation of the pseudospin. Some examples are given in Table 1. In the presence of deformation the doublets persist with asymptotic (Nilsson) quantum numbers [N, n 3, Λ, Ω = Λ +1/2] and [N, n 3, Λ + 2, Ω = Λ + 3/2], and can be expressed in terms of pseudoorbital and total angular momentum projections ~Λ = Λ + 1, Ω = ~Λ ± 1/2. This pseudospin “symmetry” has been used to explain features of deformed nuclei [7], including superdeformation [8] and identical bands [9, 10, 11]. While pseudospin symmetry is experimentally well corroborated in nuclei, its foundations remained a mystery and “no deeper understanding of the origin of these (approximate) degeneracies” existed [12].

Keywords

Orbital Angular Momentum Chiral Symmetry Breaking Lower Component Pseudospin Symmetry Gamow Teller 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.N. Ginocchio, Phys. Rev. Lett. 78 (1997) 436.ADSCrossRefGoogle Scholar
  2. 2.
    J.N. Ginocchio and A. Leviatan, Phys. Lett. B 425 (1998) 1.ADSGoogle Scholar
  3. 3.
    J.N. Ginocchio and D. G. Madland, Phys. Rev. C 57 (1998) 1167.ADSGoogle Scholar
  4. 4.
    G.A. Lalazissis, Y.K. Gambhir, J.P. Maharana, C.S. Warke and P. Ring, Phys. Rev. C 58 (1998) R45.ADSGoogle Scholar
  5. 5.
    A. Arima, M. Harvey and K. Shimizu, Phys. Lett. B 30 (1969) 517.ADSGoogle Scholar
  6. 6.
    K.T. Hecht and A. Adler, Nucl. Phys. A 137 (1969) 129.ADSGoogle Scholar
  7. 7.
    A. Bohr, I. Hamamoto and B.R. Mottelson, Phys. Scr. 26 (1982) 267.ADSCrossRefGoogle Scholar
  8. 8.
    J. Dudek et al., Phys. Rev. Lett. 59 (1987) 1405.ADSCrossRefGoogle Scholar
  9. 9.
    W. Nazarewicz et al., Phys. Rev. Lett. 64 (1990) 1654.ADSCrossRefGoogle Scholar
  10. 10.
    F.S. Stephens et al., Phys. Rev. Lett. 65 (1990) 301ADSCrossRefGoogle Scholar
  11. 10a.
    F.S. Stephens et al.,Phys. Rev. C 57 (1998) R1565.ADSGoogle Scholar
  12. 11.
    A.M. Bruce et. al., Phys. Rev. C 56 (1997) 1438.ADSGoogle Scholar
  13. 12.
    B. Mottelson, Nucl. Phys. A 522 (1991) 1.ADSGoogle Scholar
  14. 13.
    A. L. Blokhin, C. Bahri, and J.P. Draayer, Phys. Rev. Lett. 74 (1995) 4149.ADSCrossRefGoogle Scholar
  15. 14.
    A. Leviatan and J.N. Ginocchio, Phys. Lett. B in press, nucl-th/0108016.Google Scholar
  16. 15.
    A. Leviatan and J.N. Ginocchio, contribution to these proceedings.Google Scholar
  17. 16.
    J. Meng et al., Phys. Rev. C 58 (1998) R628.ADSGoogle Scholar
  18. 17.
    J.N. Ginocchio and A. Leviatan, Phys. Rev. Lett. 87 (2001) 072502.ADSCrossRefGoogle Scholar
  19. 18.
    J.N. Ginocchio, Phys. Rev. C 59 (1999) 2487.ADSCrossRefGoogle Scholar
  20. 19.
    P. von Neumann Cosel and J.N. Ginocchio, Phys. Rev. C 62 (2000) 014308.ADSCrossRefGoogle Scholar
  21. 20.
    T.D. Cohen et al., Prog, in Part, and Nucl. Phys. 35 (1995) 221.ADSCrossRefGoogle Scholar
  22. 21.
    J. N. Ginocchio, Phys. Rev. Lett. 82 (1999) 4599.ADSCrossRefGoogle Scholar
  23. 22.
    H. Leeb and S. Wilmsen, Phys. Rev. C 62 (2000) 024602.ADSCrossRefGoogle Scholar
  24. 23.
    J. B. Bowlin, A. S. Goldhaber and C. Wilkin, Z. Phys. A 331 (1988) 83.ADSGoogle Scholar
  25. 24.
    P. Alberto et al. Phys. Rev. Lett. 86 (2001) 5015.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • J. N. Ginocchio
    • 1
  • A. Leviatan
    • 2
  1. 1.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Racah Institute of PhysicsThe Hebrew UniversityJerusalemIsrael

Personalised recommendations