rotation and alignment of high-j orbitls in transfermium nuclei dr. xiao-tao he college of material...

rotation and alignment of high-j rotation and alignment of high-j orbitls in transfermium nucleiorbitls in transfermium nuclei


Dr. Xiao-tao HeDr. Xiao-tao He College of Material Science and Technology, College of Material Science and Technology,

Nanjing University of Aeronautics and AstronauticsNanjing University of Aeronautics and Astronautics

Chifeng • China ， 2010,07,25-31

2

MotivationMotivation

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 experiment


4

εε22=0.25=0.25

100100

102102


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

5P. Reiter, et al., PRL82 (1999) 509.

254254NoNo

β2=0.27±2

Some experimental resultsSome experimental results

Even-even nuclei:Even-even nuclei:

Rotational BandRotational Band

6

R.-D. Herzberg, et al., PRC, 65 (2001) 014303

252252NoNo

β2=0.28±2



7

250250FmFm

β2=0.28±2

J. E. Bastin, et al., PRC 73 (2006) 024308.



8

P. Reiter, et al., PRL 95, 032501 (2005).

253253NoNoOdd-neutron Odd-neutron nuclei:nuclei:

R.-D. Herzberg, et al., Eur. Phys. J. A (2009)


9

251251MdMd

A. Chatillon, et al., PRL 98, 132503 (2007).

Odd-proton nuclei:Odd-proton nuclei:

This band: 1/2[521]Ground state band: 7/2[514]


10

255255LrLr

S. Ketelhut, et al., PRL 102, 212501 (2007).


The structures are tentatively assigned to be based on the 1/2[521] and 7/2[514] Nilsson states, respectively.


11

R.D. Herzberg et al., Nature 442 (2006) 896

High-High-K K structurestructure

12

250250FmFm


B. Sulignano, et al., EPJA 33 (2007) 327.

13

250250FmFm

P. T. Greenlees, et al., PRC 78 (2008) 021303


14A. P. Robinson, et al., PRC 78 (2008) 034308

15


H. B. Jeppesen,et al., PRC 79, 031303(R) (2009).

16


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

257257RfRf

the ground-state configuration in 257Rf is 11//2+[620].2+[620].

11/2−[725]

17

H. B. Jeppesen, et al., PRC 80, 034324 (2009).


Assuming the quadrupole deformation of the band to be ββ22 = =

00..33 (typical for nuclei in this region).

the lowest observed sequence is built upon the [624]9[624]9//2+2+ Nilsson state.

255255LrLr


18

with Particle number conserving method treatment for the pairing correlation: Hp

pxSPpCSM HJHHHH 0

ii hH ))(( 00 xNil jhh )(0

)2()0( ppp HHH

Cranked Shell Model

single particle part : H0

Theoretical studyTheoretical study

19

In rotating frame ：

HCSM is diagonalized in the Cranked Many-Particle Configuration (CMPC) space, we get the solution of CSM Hamiltonian ：

Di ： Real

pCSM HHH 0

i

i iD


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The angular momentum alignment in ：

Kinematic MoI ：

Dynamic MoI ：

ji

xjii

xix jJiDDiJiDJ 22

xJ

J )1(

d

JdJ x)2(


21

ParameterParameterss

• 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 ( G0 for monopole pairing and G2 for quadrupole pairing ) in unite of MeV are given as follow,

G0p=0.45, G0n=0.35, G2p=0.02, G2n=0.02

* Proton: Ecut : 0.60 ω0 CMCP space ~ 1000~ 1000 Neutron: Ecut : 0.50 ω0 CMCP space ~ 1000 ~ 1000


22

0.0 0.1 0.2 0.3

60

80

100

120

140

0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3

60

80

100

120

140

Experiment - symbolTheoretical - line

250Fm


252No

Kin

emat

ical

mom

ent o

f in

ertia

J(1

) (2 M

eV-1)

(MeV)


254No

Theoretical resultsTheoretical resultsEven-even nuclei:Even-even nuclei:

Experimental and theoretical J(1) of the bands in 250Fm, 252No and 254No.

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Odd-neutron Odd-neutron nuclei:nuclei:

Experimental and theoretical J(1) of the band in 253No.

Theoretical resultsTheoretical results

24


Experimental and theoretical J(1) of the band in 251Md.


25

The cranked Nilsson orbitals near the Fermi surface in 251Md

-0.1 0.0 0.1 0.2 0.3 0.47.3

7.4

7.5

7.6

7.7

7.8

7.9

8.0

8.1

-0.1 0.0 0.1 0.2 0.3 0.4

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

7.0

148

(MeV)

Cra

nke

d p

roto

n N

ilsso

n le

vels

(

0)

168

166

154

152[734] 9/2

[741] 3/2

[604] 9/2

[750] 1/2

[716]13/2

[611] 3/2[743] 5/2

[615] 9/2

[752] 3/2

[761] 1/2

[725]11/2

[622] 3/2[613] 7/2[620] 1/2

[606]13/2

[624] 7/2

[501] 1/2

[503] 5/2[622] 5/2

[631] 1/2[743] 7/2

(MeV)

Cra

nke

d n

eu

tro

n N

ilsso

n le

vels

(

0)

[521] 1/2

[521] 1/2

[615]11/2

86

[660] 1/2[651] 3/2[530] 1/2

[642] 5/2

[523] 5/2[402] 3/2

[400] 1/2[505]11/2[521] 3/2

[752] 5/2

[642] 3/2[761] 3/2[651] 1/2[770] 1/2[512] 5/2

[624] 9/2[521] 1/2[514] 7/2

[633] 7/2

106

100


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0.0 0.1 0.2 0.30

1

2

1

2

1

2

0.0 0.1 0.2 0.30

1

2

1

2

1

2

[521] 1/2 (=-1/2)[514] 7/2 (=-1/2)

[624] 9/2

[633] 7/2

251Md (=-1/2)

[770] 1/2 =-1/2

(MeV)

Pro

ton

occu

patio

n pr

obab

ilitie

s n

[514] 7/2

[521] 1/2 (=+1/2)

[521] 3/2

[624] 9/2

[633] 7/2

251Md (=+1/2)

[770

] 1/2

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


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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0

10

20

30

40

50

60

tot

(=-1/2)

(=+1/2)

Ang

ular

mom

entu

m a

lignm

ent

<J x>

()

(MeV)

101251Md

=+1/2 =-1/2

Experiment - solid circleTheoretical - lines

1/2-[521]

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


28

0.0 0.1 0.2 0.3-2

0

2

4

6

8

10

12

14

16

18

20

0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3-2

0

2

4

6

8

10

12

14

16

18

20

Ang

ular

mom

entu

m o

f alig

nmen

t ()

251Md Neutron

N=7

N=6

N=5

[521]1/2 =+1/2

251Md Proton

N=4

N=7

N=6

N=5

(MeV)

N=4

N=7

N=6

N=5

[521]1/2 =-1/2

251Md Proton

0.0 0.1 0.2 0.3-2

0

2

4

6

8

10

12

14

16

18

20

0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3-2

0

2

4

6

8

10

12

14

16

18

20

Ang

ular

mom

entu

m o

f alig

nmen

t ()

251Md Neutron

N=7

N=6

N=5

[521]1/2 =+1/2

251Md Proton

N=4

N=7

N=6

N=5

(MeV)

N=4

N=7

N=6

N=5

[521]1/2 =-1/2

251Md Proton

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


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0.0 0.1 0.2 0.3-5

0

5

10

0

5

10

15

0

5

10

15

0.0 0.1 0.2 0.3-5

0

5

10

[523] 7/2

[514] 7/2 [523] 5/2[521] 1/2

[532] 3/2

[541] 1/2

[532] 5/2

[541] 3/2

[550] 1/2

(MeV)

251Md Proton (=-1/2)

[770] 1/2

251Md Proton (=+1/2)

Ang

ular

mom

entu

m a

lignm

ent

()

[770

] 1/2

[523] 7/2

[541] 3/2

[532] 5/2

[541] 1/2

[550] 1/2

[532] 3/2

[521] 1/2

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 1/2−[521] band in 251Md, which are simply denoted by μ and μν, respectively.


30

0.0 0.1 0.2 0.3-5

0

5

10-10

-5

0

5

10

15

0.0 0.1 0.2 0.3-5

0

5

10 -10

-5

0

5

10

15

[521] 1/2[532] 3/2

[541] 3/2[523] 7/2[532] 5/2

[541] 1/2

[550] 1/2

[725]11/2 [734] 9/2

[734] 9/2 [743] 7/2

[750] 1/2 [761] 1/2

[761] 1/2

(MeV)

[734] 9/2

[752] 5/2[761] 3/2

[770] 1/2

[624] 7/2

[642] 5/2

[640] 1/2

[743] 7/2

[651] 1/2

[633] 7/2

[651] 3/2

[660]

1/2

253No NeutronA

ngul

ar m

omen

tum

alig

nmen

t (

)

[770

] 1/2

253No Proton


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.

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* 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.

Summary

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Thank you !Thank you !Thank you !Thank you !

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Thank you Thank you !!

Thank you Thank you !!

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Welcome to Welcome to Nanjing !Nanjing !

Welcome to Welcome to Nanjing !Nanjing !

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

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42


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

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



Dr. Xiao-tao HeDr. Xiao-tao He College of Material Science and Technology, College of Material Science and Technology,

Nanjing University of Aeronautics and AstronauticsNanjing University of Aeronautics and Astronautics

Prof. Zhong-zhou RenProf. Zhong-zhou RenDepartment of Physics, Nanjing UniversityDepartment of Physics, Nanjing University

Prof. En-guang ZhaoProf. En-guang ZhaoInstitute of Theoretical Physics, Chinese of Academy of Sciences.

Prof. Shu-xin Liu Prof. Shu-xin Liu & Jin-yan Zeng& Jin-yan ZengSchool 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!


rotation and alignment of high-j orbitls in transfermium nuclei dr. xiao-tao he college of material...

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