1. The i 13/2 Proton and j 15/2 Neutron Orbital and the SD Band in A~190 Region Xiao-tao He En-guang Zhao En-guang Zhao Institute of Theoretical Physics, CAS, Beijing, China Summer school Peking University 2004

2. Outline Introduction Particle-number conserving method Numerical result Summary

3. Introduction In experiment, more than 80 SD bands have been observed in A~190 mass region. For even-even nuclei, the dynamical moment of inertia (J (2) ) exhibits a gradual increase with the increasing rotational frequency ћω. A. V. Afanasjev, P. Ring, J. König, Nucl. Phys A 676 (2000) 196.. Y. Sun, J. Y. Zhang, and M. Guidry, Phys. Rev. Lett. 78 (1997) 2321; Phys. Rev. C 63 (2001) 047306. For the odd-odd nuclei, quite a part of the moments of inertia for SD bands keep constant. X. T. He, S. X. Liu, S. Y. Yu, E. G. Zhao HEP & NP 27 (2003) 124 X. T. He, S. Y. Yu, S. X. Liu, Y. X. liu, E. G. Zhao Chin. Phys. Lett. 21 (2004) 813 X. T. He, S. X. Liu, S. Y. Yu, J. Y. Zeng, E. G. Zhao J. Phys. G: Nucl. Part. Phys. (submited)

4. Some different methods: HF method B. -Q. Chen, et al., Phys. Rev. C 46 (1992) R1582. J. Terasaki, et al,. Phys. Rev. C 55 (1997) 1231. RMF J. D. Walecka, Ann. Phys. 83 491 (1974) PRM X.Q.Chen and Z Xing J.Phys.G:Nucl.Part.Phys.19(1993)1869 PSM Y. Sun, J. Y. Zhang, and M. Guidry, Phys. Rev. Lett. 78 (1997) 2321 IBM (IBFM) Y. X. Liu, et al., Phys. Rev. C 63, (2001) 054314 Phys. Rev. C 59 (1999) 2511 CSM D. R. Inglis, Phys. Rev. 95, (1954) 1059

5. Particle-number conserving (PNC) method advantage ： Particle number is conserved A cranked many-particles configuration (CMPC) truncation is adopted instead of the single-particle level (SPL) truncation. The blocking effects is taken into account strictly and consistently. disadvantage ： Angular momentum is not conserved

6. Formula CSM Hamiltonian ： H 0 ： single particle part H p ： pairing interaction part

7. 1. Nilsson level single-particle Nilsson hamiltonian ： good quantum number ：  (parity),  [N,n z,L]   : is the good quantum number of H 0,H z,l z and j z under the extreme large deformation degeneracy: （ ±  ）。

8. 2. Cranked Nilsson level Cranked Nilsson hamiltonian  : signature The eignstate of R x (  ) and j 2 z ： diagonalize h 0 (  ) in space| , we get |  ：

9. 3. Many-body system n particles system ， the configuration |i  ： According to configuration |i , the system possess certain energy E i 、 parity P i 、 signature  i and particle number N:

10. ４.paring interaction In Nilsson single particle space ： In |  space ： In |  space ： Similar to H P (0), we can get H P (2)

11. In |  space ： Diagonalize H CSM in the CMPC space, we get the solution of CSM Hamiltonian ： D i ： interger

12. ５. moment of inertia The angular momentum alignment in |  ： Dynamic ： Kinematic ：

13. Result The cranked Nilsson orbital in A~190 mass region

14. Parameters The Nilsson parameters (  ) are taken from Lund systematics. T.Bengtsson and I. Ragnarsson, Nucl. Phys. A436, 14 (1985) The deformation parameters  2 =0.46,  4 =0.03. M. A. Riley et al., Nucl. Phys. A512 178 (1990) The effective pairing interaction strengths ( G 0 for monopole pairing and G 2 for quadrupole pairing ) in unite of MeV are given as follow: G 0p =0.3, G 2p =0.01, G 0n =0.2, G 2n =0.013

15. Experimental and calculated J (1) and J (2) of the yrast SD band in even-even nuclei 192 Hg

16. Experimental and calculated J (1) and J (2) of the SD bands in odd-A nuclei 193 Tl and 195 Tl

17. Occupation probability of each proton cranked orbital near the Fermi surface in 193 Tl

18. The separate contributions to J(2) from each cranked proton orbitals near the Fermi surface

19. Experimental and calculated J (1) and J (2) of the six SD bands in odd-odd nuclei 194 Tl

20. Occupation probability of each neutron cranked orbital near the Fermi surface in 194 Tl

21. Experimental and calculated J (1) and J (2) of the four SD bands in odd-odd nuclei 192 Tl

22. Occupation probability of each neutron cranked orbital near the Fermi surface in 192 Tl

23. Summary The PNC method in the frame of CSM is one of the useful method to deal with the SD nuclei. The i 13/2 Proton and j 15/2 Neutron intruder Orbital plays a very important role in the variation in both kinematic and dynamical moments of inertia (MOI) with rotational frequency in A~190 Region.

24. Thank you !