rotation and alignment of high-j orbitls in transfermium nuclei Dr. Xiao-tao He College of Material Science and Technology, Nanjing University of Aeronautics and Astronautics Chifeng China ， 2010,07,25-31

2 Motivation ！ Exploration of the island of stability with high mass and charge, i.e. the region of superheavy elements (SHE) has been one of the fundamental questions in nature science ！ ?How to get structure information about superheavy elements (SHE) ?

3 αdecays spins and parities: Spectroscopy of collective rotation Difficulty: The extremely low production cross- sections. It can rarely reveal the detailed spectroscopic information of SHE in the experiments. Tansfermium nuclei (Z = 102, N = 152) are the heaviest system accessible in present in-beam experimentMotivation

4 ε 2 = Motivation the study of these deformed transfermium nuclei may provide an indirect way to access the single particle states of the next closed spherical shells.

5 P. Reiter, et al., PRL82 (1999) No β 2 =0.27±2 Some experimental results Even-even nuclei: Rotational Band

6 R.-D. Herzberg, et al., PRC, 65 (2001) No β 2 =0.28±2 Even-even nuclei: Rotational Band

7 250 Fm β 2 =0.28±2 J. E. Bastin, et al., PRC 73 (2006) Even-even nuclei: Rotational Band

8 P. Reiter, et al., PRL 95, (2005). 253 No Odd-neutron nuclei: R.-D. Herzberg, et al., Eur. Phys. J. A (2009) Rotational Band

9 251 Md A. Chatillon, et al., PRL 98, (2007). Odd-proton nuclei: This band: 1/2[521] Ground state band: 7/2[514] Rotational Band

Lr S. Ketelhut, et al., PRL 102, (2007). Odd-proton nuclei: The structures are tentatively assigned to be based on the 1/2[521] and 7/2[514] Nilsson states, respectively. Rotational Band

11 R.D. Herzberg et al., Nature 442 (2006) 896 High-K structure

Fm High-K structure B. Sulignano, et al., EPJA 33 (2007) 327.

Fm P. T. Greenlees, et al., PRC 78 (2008) High-K structure

14 A. P. Robinson, et al., PRC 78 (2008)

15 High-K structure H. B. Jeppesen,et al., PRC 79, (R) (2009).

16 High-K structure J. Qian, et.al., PRC 79, (2009). 257 Rf 1/2+[620]. the ground-state configuration in 257 Rf is 1/2+[620]. 11/2−[725]

17 H. B. Jeppesen, et al., PRC 80, (2009). Odd-proton nuclei: β 2 = 0.3 Assuming the quadrupole deformation of the band to be β 2 = 0.3 (typical for nuclei in this region). [624]9/2+ the lowest observed sequence is built upon the [624]9/2+ Nilsson state. 255 Lr High-K structure

18 with Particle number conserving method treatment for the pairing correlation: H p Cranked Shell Model single particle part : H 0 Theoretical study

19 In rotating frame ： H CSM is diagonalized in the Cranked Many-Particle Configuration (CMPC) space, we get the solution of CSM Hamiltonian ： D i ： Real Theoretical study

20 The angular momentum alignment in ： Kinematic MoI ： Dynamic MoI ： Theoretical study

21 Parameters The Nilsson parameters (κ,μ) are taken from: S.G. Nilsson, et al., Nucl. Phys. A131 (1969) 1. * The deformation parameters ε 2 =0.29, ε 4 =0.02 for 252,253,254 No and 250 Fm, ε 2 =0.30, ε 4 =0.02 for 251 Md. * 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 =0.45, G 0n =0.35, G 2p =0.02, G 2n =0.02 ~ 1000 * Proton: E cut : 0.60  ω 0 CMCP space ~ 1000 ~ 1000 Neutron: E cut : 0.50  ω 0 CMCP space ~ 1000 Theoretical study

22 Theoretical results Even-even nuclei: Experimental and theoretical J (1) of the bands in 250 Fm, 252 No and 254 No.

23 Odd-neutron nuclei: Experimental and theoretical J (1) of the band in 253 No. Theoretical results

24 Odd-proton nuclei: Experimental and theoretical J (1) of the band in 251 Md. Theoretical results

25 The cranked Nilsson orbitals near the Fermi surface in 251 Md Theoretical results

26 Occupation probabilities of each cranked orbital near the Fermi surface (include both α =±1/2) in 251 Md. Theoretical results

27 The total angular momentum alignment, and the separate contributions to from neutron and proton in 251 Md. Theoretical results

28 The contribution to from each neutron (N=5,6,7) and proton (N=4,5,6,7) major shells for the 1/2−[521] band in 251 Md. Theoretical results

29 The contributions to from the particle in each proton cranked orbitalμ, j x (μ) and the interference term j x (μ ν ) between cranked orbitals μ and ν for the 1/2−[521] band in 251 Md, which are simply denoted by μ and μ ν, respectively. Theoretical results

30 Theoretical results The contributions to from the particle in each proton cranked orbitalμ, j x (μ) and the interference term j x (μ ν ) between cranked orbitals μ and ν for the 7/2+[624] band in 253 No, which are simply denoted by μ and μ ν, respectively.

31 * The observed bands are reproduced very well by the theoretical results. * Exploration of behaviors of these bands at high spin shows that there is backbending taking place at hω ≈ MeV in bands of 252,253,254 No. * α = −1/2 band in 251 Md is predicted. It is very encouraged to find that there is a backbending occurring at very low frequency, hω ≈ 0.15 MeV,which might be during the possible observed frequency. * The neutron 2h 11/2 (1/2[761]) and proton 1j 15/2 (1/2[770]) orbitals play a very important role in the rotational properties of transfermium nuclei. Summary

32 Thank you !

33 Thank you !

34 Welcome to Nanjing !

35 Theoretical results Nilsson S G et al., NPA, 131 (1969) 1.

36 Theoretical results Nilsson S G et al., NPA, 131 (1969) 1.

37 Theoretical results Nilsson S G et al., NPA, 131 (1969) 1.

38 Theoretical results Nilsson S G et al., NPA, 131 (1969) 1.

39 Theoretical results Nilsson S G et al., NPA, 131 (1969) 1.

40 Theoretical results Nilsson S G et al., NPA, 131 (1969) 1.

41 Theoretical results

42 Theoretical results T. Bengtsson, I. Ragnarsson, NPA436 (1985) 14-82

43 Theoretical results T. Bengtsson, I. Ragnarsson, NPA436 (1985) 14-82

rotation and alignment of high-j orbitls in transfermium nuclei Dr. Xiao-tao He College of Material Science and Technology, Nanjing University of Aeronautics and Astronautics Prof. Zhong-zhou Ren Department of Physics, Nanjing University Prof. En-guang Zhao Institute of Theoretical Physics, Chinese of Academy of Sciences. Prof. Shu-xin Liu & Jin-yan Zeng School of Physics, Peking University Chifeng China ， 2010,07,25-31

45 Odd-mass transfermium nuclei are seldom studied; Cranked shell model are seldom used. We used the cranked shell model to calculate the collective rotation of SHE. Collective rotational bands provide important testing ground to check the extrapolations of current models to SHE region! Theoretical study