Post on 14-Aug-2020
Hidden symmetries in atomic nuclei: a brief introduction
Jie Meng 孟 杰
北京大学物理学院
School of Physics, Peking Universitymengj@pku.edu.cn
iTHES workshop on "Exploration of hidden symmetries in atomic nuclei“Saturday, 27 July 2013 from 9:00 to 18:00at RIKEN Wako Campus
two-nucleon separation energy
ΔS2p
much smaller after 8, 20, 28, 50, 82, 126
ΔS2n
Nuclear magic number
Nuclear properties change periodicallywith proton or neutron number原子核性质随中子数或质子数周期性地变化
ARn + A-4Po TSudden rise at N = 126
Neutron capture cross section
Very small at N = 28, 50, 82, 126
Abrupt change in nuclear radius at N = 20, 28, 50, 82, 126R
Ravg
RRavg
Nuclear magic number
Only smallest magic numbers are reproduced. Why ?
Spin-orbit term is necessary
Mayer and Jensen et al., 1949
srrV
rVV sso .)(1
M. G. Mayer, Phys. Rev. 75(1949)1969; 78(1950).O. Haxel, J. H. D. Jensen, and H. E. Suess, Phys. Rev. 75(1949)1766;Z. Phys. 128(1950)295;
原子核壳结构 Nuclear Shell Model
Great for:magic numbersground state propertiessome low lying excited states
强自旋-轨道壳模型是原子核结构的所有微观理论的出发点
S. G. Nilsson的轴对称变形核的强自旋-轨道壳模型能级系
S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No.16(1955).S. G. Nilssion, et al., Nucl. Phys. A131(1969) 1.
原子核壳结构 Nuclear Shell Model
2013-07-27 6
s1
p1
d1s2
f1p2g1
s3
h1
2/1
2/3
2/12/5
2/32/72/32/1
2/1
2/52/9
2/72/52/32/12/11
2/9
2
6
1614
20283240
8
3850
5864687082
92
d2
3/21/2,p~
5/23/2,d~
3/21/2,p~
7/25/2,f~
2
321
,2,,,1
ljlnljln
0
1
2
3
4
1/2s~
2/1~:spinpseudo1~:orbitpseudo
sll
Hecht & AdlerNPA137(1969)129
sl
Arima, Harvey & ShimizuPLB30(1969)517
Spin and pseudospin symmetry in atomic nuclei
Woods-Saxon
2013-07-27 7A. Bohr, I. Hamamoto, and B. R. Mottelson, Phys. Scr. 26,267 1982
Earlier attempt to understand PSS
Earlier attempt to understand PSS
Since PSS was suggested, lots of nuclearphenomena have been interpreted inconnection with the PSS, for example …
Nuclear superdeformed configurations
Interpretation of the identical bands
Observation of the PSS partner bands…Meng and Zhang, JPG37, 064025 (2010)
Even for Magnetic moments, transitions and γ-vibrational states
On the validity of the pseudo-spin concept for axially symmetric deformed nucleiD. Troltenier, W. Nazarewicz, Z. Szymański, J.P. Draayer, Nucl. Phys. A 567, 591 (1994).
l-forbidden M1 transitions and pseudospin symmetryP. von Neumann-Cosel and J. N. Ginocchio, Phys. Rev. C 62, 014308 (2000)
Neutron number dependence of the energies of the γ-vibrational states in nuclei with Z∼100 and the manifestation of pseudospin symmetryR. V. Jolos, N. Yi. Shirikova, and A. V. Sushkov, Phys. Rev. C 86, 044320 (2012)
Nucleon Dirac Equations
15 2013-07-27
Relativistic mean field / Covariant density functional theory
( ) ( ) i i iV M S p r r
33
1( ) ( ) ( ) ( )2
( ) ( )
V g g e A
S r g
r r r r
r
2013-07-27 16
Dirac Spinor quantum numbers
2/1
2/1
)(~)2/1()(
2/1
lj
lj
ll
jlj
)()(
)()(1)( ~~
ljmn
ljmnN
mnYrF
YrGi
r
r
Pseudo quantum numbers are nothing but the quantum numbers of the lower component.
21
21
2/1 ~,1~,2~,0,2
s2ljln
ljln
21
21
2/3 ~,1~,2~,2,1
d1ljln
ljln
3/21/2,2/32/1 p~d1,s2
1 number node n
2/3,2/1p~2~ n
Ginocchio PRL78(97)436
2013-07-27 17
Origin of the symmetry - Nucleons
FFVMdr
dVrMr
lldrd
drdV
Mdrd
M N
~
41)1~(~
21
21
222
2
For nucleons, d[V(r)S(r)]/dr=0 spin symmetry d[V(r)+S(r)]/dr=0 pseudo-spin symmetry
GGVMdr
dVrMr
lldrd
drdV
Mdrd
M N
222
2
41)1(
21
21
)()()( rSrVrV
)(),( rVMrM NN
)()(
)()(1)( ~~
ljmn
ljmnN
mnYrF
YrGi
r
r
Meng, Sugawara-Tanabe, Yamaji, Ring, Arima, PRC58 (1998) 628R Meng, Sugawara-Tanabe, Yamaji, Arima, PRC59 (1999) 154
2013-07-27 18
Origin of the symmetry - Anti-nucleons
GGVMdr
dVrMr
lldrd
drdV
Mdrd
M
~
41)1~(~
21
21
222
2
FFVMdr
dVrMr
lldrd
drdV
Mdrd
M
222
2
41)1(
21
21
)()()( rSrVrV
)(),( rVMrM AA
For anti-nucleons, d[V(r)S(r)]/dr=0 pseudo-spin symmetry d[V(r)+S(r)]/dr=0 spin symmetry
)()(
)()(1)( ~~
ljmn
ljmnA
mnYrGi
YrF
r
r
Zhou, Meng & Ring PRL92(03)262501
The factor is ~400 times smaller for anti nucleons!
241
M
2013-07-27 19
Origin of the symmetry
FFMlrSrVdrd
rMrSrV
M A
1)()(14
1)()(2 2*
2
FFMlrSrVdrd
rMrSrV
M N
~~1)()(1
41)()(
2 2*
2
For nucleons, the smaller component F
For anti-nucleons, the larger component F
Zhou,Meng&RingPRL92(03)262501
2013-07-27 20
Origin of the symmetry - Anti-nucleons
Zhou, Meng & Ring, PRL92 (03) 262501
0 1 2 3 4 5r [fm]
0
200
400
600
800
1000M
−V +
(r) [
MeV
]
0 1 2 3 4 5
880
900
920
940
sp
df
g
h
ij
kl
s
pd
16O neutron
p1/2 p3/2
2013-07-27 21
Experimental verification: Anti- in 16O
Song, Yao, Meng, CHIN. PHYS. LETT. Vol. 26, No. 12 (2009) 122102
0 1 2 3 4 5
-500
-400
-300
-200
-100
0
0 1 2 3 4 5
-50
-40
-30
-20
-10
0
k
j
i
h
g
f
d
ps
r (fm )
S+V (MeV) anti-L in
16O
d
p
sL in
16O
Experiment: exploration of the relativistic symmetry by hyperon
2013-07-27
Summary / Introduction
Thank you for your attention!22
Origins of nuclear shell structure Spin symmetry in Dirac negative energy spectrum Perturbative interpretation of relativistic symmetries possible Pseudospin symmetry in resonances Pseudospin symmetry in supersymmetric quantum mechanics Pseudospin for deformed nucleus …
Liang, Shen, Zhao, Meng, Phys. Rev. C 87, 014334 (2013) [13 pages] B.-N. Lu, E.-G. Zhao, and S.-G. Zhou, Phys. Rev. Lett. 109, 072501 (2012). Bing-Nan Lu, En-Guang Zhao, Shan-Gui Zhou arXiv:1305.1524
Kenichiro Arita (Nagoya Institute of Technology) Haozhao Liang (RIKEN) Shan-Gui Zhou (Institute of Theoretical Physics, CAS, China)…