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

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 ！

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.

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

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

252No β2=0.28±2 Even-even nuclei: Rotational Band R.-D. Herzberg, et al., PRC, 65 (2001) 014303

250Fm β2=0.28±2 Even-even nuclei: Rotational Band J. E. Bastin, et al., PRC 73 (2006) 024308.

253No Odd-neutron nuclei: Rotational Band R.-D. Herzberg, et al., Eur. Phys. J. A 15, 205 (2002) P. Reiter, et al., PRL 95, 032501 (2005). R.-D. Herzberg, et al., Eur. Phys. J. A 42, 333 (2009).

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, 132503 (2007).

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, 212501 (2007).

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

250Fm High-K structure B. Sulignano, et al., EPJA 33 (2007) 327. P. T. Greenlees, et al., PRC 78 (2008) 021303

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, 031303(R) (2009). J. Qian, et.al., PRC 79, 064319 (2009).

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, 034324 (2009).

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

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

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

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=0.02 for 252,253,254No and 250Fm, ε2 =0.30 , ε4=0.02 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=240-255)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).

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

Odd-proton nuclei 251Md Theoretical results ε2=0.30

Theoretical results

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

Odd-neutron nuclei 253No: Theoretical results

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 ≈ 0.275 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.

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

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.

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

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

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

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

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

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

Theoretical results

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

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

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!