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Isovector pairing in nuclei near the N=Z line

Isovector pairing in nuclei near the N=Z line. Anatoli Afanasjev S. Frauendorf Kai Neergard J. Sheikh. Mean-field theory of isovector pairing. Frauendorf SG , Sheikh JA Cranked shell model and isospin symmetry near N=Z NUCLEAR PHYSICS A 645 (4): 509-535 JAN 25 1999.

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Isovector pairing in nuclei near the N=Z line

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  1. Isovector pairing in nuclei near the N=Z line Anatoli Afanasjev S. Frauendorf Kai Neergard J. Sheikh

  2. Mean-field theory of isovector pairing Frauendorf SG, Sheikh JACranked shell model and isospin symmetry near N=ZNUCLEAR PHYSICS A 645 (4): 509-535 JAN 25 1999

  3. Simple model: deformed potential+monopole isovector pairing

  4. Mean-field approximation

  5. Spontaneous breaking of isospin symmetry Mean field does not have these symmetries. Degenerate mf-solutions: gauge angle

  6. Parities of proton and neutron numbers are good. Intrinsic excitation spectrum Symmetries

  7. Symmetry restoration –Isorotations (strong symmetry breaking) Bayman, Bes, Broglia PRL 23 (1969) 1299 ( 2 particle transfer) Organize into bands with even or odd N

  8. The relative strengths of pp, nn, and pn pairing are determined by the isospin symmetry

  9. Comparison with shell model calculation SM calculation: J. Engel et al. PLB 389, 211 (96) Shell model Strong symmetry breaking

  10. Isorotation bands with even or odd N

  11. N odd N even bands with even or odd N Remove Coulomb energy!

  12. Very regular Band!

  13. Wigner Energy: Manifestation of spontaneous isospin symmetry breaking Odd A

  14. T=0 and ½ states

  15. States with good N, Z –parity are in general no eigenstates of If they are (T=0) the symmetry restricts the possible configurations, if not (T=1/2) the symmetry does not lead to anything new. Restrictions due to the

  16. Excitation energy of first T=1 state 10 20 30 40 50 60 A

  17. Ordinary nn pair field Adding nn pairs to the condensate does not change the structure. Pair rotational bands are an evidence for the presence of a pair field.

  18. total angular momentum • A. L. GoodmanPhys. Rev. C 63, 044325 (2001) Predicted by Isoscalar pairing at high spin? Isoscalar pairs carry finite angular momentum Which evidence?

  19. Symmetries of the isoscalar pair field Frauendorf S, Sheikh JASymmetry breaking by proton-neutron pairingPHYSICA SCRIPTA T88: 162-169 2000

  20. which symmetries leave invariant? total angular momentum If the isoscalar pair field is present, Either even or odd A belong to the band. Even and odd N belong to the band. Both signatures belong to the band.

  21. Pair rotational bands for an isoscalar neutron-proton pair field Even-even, even I Odd-odd, odd I

  22. Only quenching of isovector pairing or evidence for isoscalar pairfield?

  23. Conclusions • Ground state energies explained by strong isovector pair field • Very regular isorotational bands • Wigner energy: T(T+1) dependence • Excitation spectra explained by isovector pair field that is quenched at high spin. • Maybe isoscalar correlations enhanced at highspin.

  24. Too small symmetry energy With realistic level spacing h Ensures the right symmetry Energy by choice of k Symmetry restoration by RPA Kai Neergard, PLB 537 (2002) 287, ArXiv nucl-th Mean-field approximation

  25. T T+1/2 RPA correlation energy RPA roots 2qp energies

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