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

3. Mean-field theory of isovector pairing Mean-field calculations in the A=74 region Isocranking and RPA

4. Mean-field theory of isovector pairing S. F., J Sheikh, NPA 645 (1999) 509

5. Simple model: deformed potential+monopole isovector pairing

6. Mean-field approximation

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

10. Symmetry restoration –Isorotations (strong symmetry breaking) Bayman, Bes, Broglia PRL 23 (1969) 1299 ( 2 particle transfer)

12. The relative strengths of pp, nn, and pn pairing are determined by the isospin symmetry Moment of inertia for isorotation

13. Ground states 10 20 30 40 50 60 A

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

15. T=0 and ½ states

16. Restrictions due to the 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.

17. Model study: half-filled deformed j-shell Full shell model diagonalization HFB solution: no isoscalar pair field, only isovector

18. Quasiparticle routhians Mean-field kept at its value at

21. Mean-field calculations in the A=74 region D. Jenkins, et al. PRC 65 (2002) 064307 C.D. O’Leary et al. PRC 67 (2003) 021301 (R) N. S. Kelsall et al. PRC65 (2002) 044331 N. S. Kelsall et al. Proc. Berkeley 2002, AIP Conf. Proc. 656 (2002) 269

22. Realistic calculations Cranked Relativistic Mean-Field Pairing: Gogny force, HFB, Lipkin-Nogami Isocranking: experimental symmetry energy

23. Quasiparticles around N=Z=36

25. Calculation TRS, R. Wyss

27. full: experiment dashed: CRMF

28. full: experiment dashed: CRMF

29. no pairing

31. Isocranking and RPA

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

33. RPA correlation energy RPA roots 2qp energies TT+1/2