1. 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
Huzhou • China，2012,04,12-16

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 ！

3. α-decays: life time, spin, parity … …
Motivation
How to get structure information about superheavy elements (SHE) ?
α-decays: life time, spin, parity … …
Spectroscopy of collective rotation: spin, parity, configurations, deformations, single-particle orbiting … …
! Difficulty: The extremely low production cross-sections. It can rarely reveal the detailed spectroscopic information of SHE in the experiments.
Tansfermium nuclei (Z > 100) are the heaviest system accessible in present in-beam experiment.

4. 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.
ε2=0.30
100
102
ε2=0.25

5. Some experimental results
Even-even nuclei:
254No
β2=0.27±2
P. Reiter, et al., PRL82 (1999) 509.

6. 252No β2=0.28±2 Even-even nuclei: Rotational Band
R.-D. Herzberg, et al.,
PRC, 65 (2001)

7. 250Fm β2=0.28±2 Even-even nuclei: Rotational Band
J. E. Bastin, et al.,
PRC 73 (2006)

8. 253No Odd-neutron nuclei: Rotational Band R.-D. Herzberg, et al.,
Eur. Phys. J. A 15, 205 (2002)
P. Reiter, et al., PRL 95, (2005).
R.-D. Herzberg, et al., Eur. Phys. J. A 42, 333 (2009).

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

10. Rotational Band
Odd-proton nuclei:
255Lr
The structures are tentatively assigned to be based on the 1/2[521] and 7/2[514] Nilsson states, respectively.
S. Ketelhut, et al., PRL 102, (2007).

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

12. 250Fm High-K structure B. Sulignano, et al., EPJA 33 (2007) 327.
P. T. Greenlees, et al., PRC 78 (2008)

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

14. High-K structure
Odd-proton nuclei:
255Lr
Assuming the quadrupole deformation of the band to be β2 = 0.3 (typical for nuclei in this region).
the lowest observed sequence is built upon the [624]9/2+ Nilsson state.
H. B. Jeppesen, et al., PRC 80, (2009).

15. Theoretical study Cranked Shell Model single particle part : H0
with Particle number conserving method treatment for
the pairing correlation: Hp

16. Theoretical study
In rotating frame：
HCSM is diagonalized in the Cranked Many-Particle Configuration (CMPC) space, we get the solution of CSM Hamiltonian：
Di：Real

17. The angular momentum alignment in ：
Theoretical study
The angular momentum alignment in ：
Kinematic MoI：
Dynamic MoI：

18. Parameters The Nilsson parameters (κ,μ) are taken from:
Theoretical study
Parameters
The Nilsson parameters (κ,μ) are taken from:
S.G. Nilsson, et al., Nucl. Phys. A131 (1969) 1.
* The deformation parameters
ε2 =0.29 , ε4= for 252,253,254No and 250Fm,
ε2 =0.30 , ε4= for 251Md.
The effective pairing interaction strengths (in unite of MeV),
G0p=0.45, G0n=0.35, G2p=0.02, G2n=0.02
* Proton: Ecut : 0.60 ω0 CMCP space ~ 1000
Neutron: Ecut : 0.50 ω0 CMCP space ~ 1000
通过拟合Z=96-103(A= )的30多个原子核的带头能量以及转动惯量，确定了一组主量子数，轨道角动量量子数依赖的(κ,μ)
Zhen-Hua Zhang et al., Phys. Rev. C 85, 014324 (2012);
83, 011304 (2011).

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

20. Odd-proton nuclei 251Md
Theoretical results
ε2=0.30

21. Theoretical results

22. The cranked proton Nilsson orbitals near the Fermi surface in 251Md
Theoretical results
The cranked proton Nilsson orbitals near the Fermi surface in 251Md

23. Odd-neutron nuclei 253No:
Theoretical results

24. Summary
* 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 252,253,254No.
* α = −1/2 band in 251Md 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 2h11/2 (1/2[761]) and proton 1j15/2 (1/2[770]) orbitals play a very important role in the rotational properties of transfermium nuclei.

25. Thank you !
Thank you !

26. Welcome to Nanjing !

27. Thank you !

28. Thank you !

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

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

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

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

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

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

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

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

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

40. 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

41. Theoretical study 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!