幻灯片 1 - e Science
Download
Report
Transcript 幻灯片 1 - e Science
Investigation of Pseudospin Symmetry in Nuclei by
the Similarity Renormalization Group
DongPeng Li
School of Physics and Material Science
Anhui University
16. October 2013
Collaborators:
Dr. ShouWan Chen
Dr. ZhongMing Niu
Prof. JianYou Guo
Anhui University
Anhui University
Anhui University
18. Juli 2015
1/26
Outline
Outline
Introduction
Introduction
Theoretical framework of SRG
Analysis of PSS
Summary
18. Juli 2015
2/26
Introduction
Introduction
Pseudospin
symmetry (PSS)
Introduction
Spin symmetry(SS)
(n, l , j l 1/ 2)
O.Haxel,J.H.D.Jensen 1949.PR ; M.Goeppert-Mayer 1949.PR
Pseudospin symmetry(PSS)
(n, l , j l 1/ 2)
(n 1, l 2, j l 3/ 2)
(n n 1, l l 1, j l 1/ 2)
K.T.Hecht 1969.NPA ; A.Arima 1969.PLB
Deformation, superdeformation, identical bands and magic number in exotic
nuclei can be explained by this concept.
18. Juli 2015
3/26
Introduction
Introduction
Progress
in theoretical research
Introduction
Ginocchio 1997.PRL
r V r S r 0 .
Here V r is the repulsive vector and S r is the attractive scalar describe a
nucleon moving in a spherical field.
l is nothing but the orbital angular momentum of the lower component of
the dirac spinor.
Meng 1998.PRC(R) ; 1999.PRC
d
0 .
dr
The quality of the pseudospin approximation is shown to be connected to the
competition between the pseudocentrifugal barrier (PCB) and the pseudospin
orbital potential (PSOP).
1
1 d
≤
E V r dr
r2
With the condition above the pseudospin approximation is good.
18. Juli 2015
4/26
Introduction
Introduction
Progress
in theoretical research
Introduction
Extend the Dirac equation to the deformed case with an axially symmetric shape;
Discuss the competition between the PCB and PSOP.
Sugawara-Tanabe 2000.PRC
Study the PSS by the Dirac equation with the Woods-Saxon potential and find the
near pseudospin degeneracy results from a significant cancellation among the
different terms in the Schrodinger-like equation.
P. Alberto 2001.PRL;2002.PRC
Developed the theory to single antinucleon spectra, find that the SS in
antinucleon spectra is better than PSS in normal nuclear single particle spectra and
they have the same origin.
Zhou 2003.PRL
The pseudospin breaking cannot be treated as a perturbation of the pseudospinsymmetric Hamiltonian.
Liang 2011.PRC(R) ; Ginocchio
2011.J.Phys.Conf.Ser
18. Juli 2015
5/26
Introduction
Introduction
Drawbacks
H E
in the spherical symmetry
d
m
r
dr r
H
d
m r
dr r
1
2m
1
2m
F r
G
r
d2
/ d 1
/
F r EF r
2
m
2
2
dr
2
m
dr
r
r
4
m
d2
/ d 1
/
G r EG r
2
m
2
2
dr
2
m
dr
r
r
4
m
Here the effective masses 2m E m and 2m E m
The coupling between the energy E and the operator.
The singularity in calculating the contribution of every component to the
pseudospin splitting.
18. Juli 2015
6/26
Outline
Outline
Introduction
Introduction
Theoretical framework of SRG
Analysis of PSS
Summary
18. Juli 2015
7/26
Similarity renormalization group
Theoretical framework
Theory
Introduction
The initial Hamiltonian H is transformed by the unitary operator U l according to
H l U l HU l ,
H 0 H
Where l is a flow parameter. Differentiation of the Eq. above gives the flow Eq.
d
H l l , H l
dl
If we choose l in the form
l m, H l
and set H l as a sum of an even operator l and odd operator o l :
H l l o l
where even or odd means : l l
o l o l
For the Dirac Hamiltonian with spherical symmetry, we can finally obtain
0
HP m
0
H
m
A
For details see Ref. Guo 2012.PRC(R)
18. Juli 2015
8/26
Similarity renormalization group
Theoretical framework
Theory
Introduction
p2
1 2
/
//
S 2
S / / 2 2/ / 4S // p 4
/ d
/ d
HP
3
Sp S
Sp 2S
2m 2m2
dr r 4m2 8m2 2m3
dr r 2m3
16m3
8m
p2
1 2
/
//
S 2
S / / 2 2/ / 4S // p 4
/ d
/ d
HA
3
Sp S
Sp 2S
2m 2m2
dr r 4m2 8m2 2m3
dr r 2m3
16m3
8m
where V S and V S . H P possess the exact spin symmetry when / 0 .
SRG+SUSY Liang 2013.PRC ; Shen 2013. PRC
In order to analyzing the nature of PSS, we dispart H P into eight components:
p2
2m
1、Nonrelativestic
limit
2、Dynamical terms
1 2
/ d
Sp
S
2m 2
dr
/
r 4m 2
3、Spin-orbit interaction terms
4、Other terms
S 2
/ d
Sp
2
S
2m3
dr
//
8m 2
/ 2 2 / / 4S //
16m3
S/
r 2m3
p4
3
8m
18. Juli 2015
9/26
Outline
Outline
Introduction
Introduction
Theoretical framework of SRG
Analysis of PSS
Summary
18. Juli 2015
10/26
Analysis of PSS
Numerical
details
Introduction
For convenience in the numerical computations, a Woods-Saxon type
potential is adopted:
r 0 f a , r , r
f a, R, r
with
r 0 f a , r , r
1
rR
1 exp
a
We take the numerical results down here by fitting them to the
neutron spectra of
208Pb.
0 = -66 MEV
0 = 650 MEV
a = a = 0.6 fm
r = r = 7 fm
18. Juli 2015
11/26
Analysis of PSS
Discussion
Introduction
FIG.1.
FIG.2.
FIG.3.
18. Juli 2015
12/26
Analysis of PSS
Discussion
Introduction
FIG.4.
FIG.5.
FIG.6.
18. Juli 2015
13/26
Analysis of PSS
Discussion
Introduction
FIG.7.
FIG.8.
FIG.9.
18. Juli 2015
14/26
Analysis of PSS
Discussion
FIG.10.
FIG.11.
FIG.12.
18. Juli 2015
15/26
Outline
Outline
Introduction
Introduction
Theoretical framework of SRG
Analysis of PSS
Summary
18. Juli 2015
16/26
Summary
Summary
By comparing the contribution of the different components in the diagonal Dirac
Hamiltonian, we found that two dynamic components make similar effect on the
PSS. The same case also appears in the spin-orbit interactions.
The spin-orbit interactions always play a role to improve the PSS, but the
dynamical term improve or destroy the PSS relating to the shape of the potential as
well as the quantum numbers of the state.
We have disclosed the reason why the PSS becomes better for the levels closer to
the continuum.
18. Juli 2015
17/26
Thank you!
18. Juli 2015
18/26