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Transcript of Shan-Gui Zhou Email: [email protected]; URL: [email protected] 1.Institute of Theoretical...
Shan-Gui Zhou
Email: [email protected]; URL: http://www.itp.ac.cn/~sgzhou
1. Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing
2. Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou
Structure of exotic nuclei from relativistic Hartree
Bogoliubov model (I)
HISS-NTAA 2007
Dubna, Aug. 7-17
23/4/18 2
Introduction to ITP and CAS Chinese Academy of Sciences (CAS)
Independent of Ministry of Education, but award degrees (Master and Ph.D.) ~120 institutes in China; ~50 in Beijing Almost all fields
Institute of Theoretical Physics (ITP) smallest institute in CAS ~40 permanent staffs; ~20 postdocs; ~120 students Atomic, nuclear, particle, cosmology, condensed matter, biophysics, statistics,
quantum information
Theor. Nucl. Phys. Group Super heavy nuclei Structure of exotic nuclei
23/4/18 3
Contents Introduction to Relativistic mean field model
Basics: formalism and advantages Pseudospin and spin symmetries in atomic nuclei Pairing correlations in exotic nuclei
Contribution of the continuum BCS and Bogoliubov transformation
Spherical relativistic Hartree Bogoliubov theory Formalism and results
Summary I Deformed relativistic Hartree Bogoliubov theory in a Woods-
Saxon basis Why Woods-Saxon basis Formalism, results and discussions
Single particle resonances Analytical continuation in coupling constant approach Real stabilization method
Summary II
23/4/18 4
Relativistic mean field model
http://pdg.lbl.gov
Lagrangian density
Non-linear coupling for
Field tensors
Reinhard, Rep. Prog. Phys. 52 (89) 439
Ring, Prog. Part. Nucl. Phys. 37 (96) 193
Vretenar, Afnasjev, Lalazissis & Ring
Phys. Rep. 409 (05) 101 Meng, Toki, SGZ, Zhang, Long &
Geng, Prog. Part. Nucl. Phys. 57 (06) 470
Serot & Walecka, Adv. Nucl. Phys. 16 (86) 1
23/4/18 5
Coupled equations of motion
Nucleon
Mesons & photon
Vector & scalar potentials
Sources (densities)
Solving Eqs.: no-sea and mean field approximations; iteration
23/4/18 6
RMF for spherical nuclei
Dirac spinor for nucleon
Radial Dirac Eq.
Vector & scalar potentials
23/4/18 7
RMF for spherical nuclei
Klein-Gordon Eqs. for mesons and photon
Sources
Densities
23/4/18 8
RMF potentials
23/4/18 9
RMF for spherical nuclei: observables
Nucleon numbers
Radii
Total binding energy
23/4/18 10
Center of mass correctionsLong, Meng, Giai, SGZ, PRC69,034319(04)
23/4/18 11
Nucleon-nucleon interaction Mesons degrees of freedom included Nucleons interact via exchanges mesons
Relativistic effects Two potentials: scalar and vector potentials
the relativistic effects important dynamically
New mechanism of saturation of nuclear matter
Psedo spin symmetry explained neatly and successfully Spin orbit coupling included automatically
Anomalies in isotope shifts of Pb
Others More easily dealt with Less number of parameters …
RMF description of exotic nuclei: Why?
23/4/18 12
Potentials in the RMF model
r
)()( rSrV
MeV750
MeV50
r
)(rV
)(rSMeV400~
MeV350~
r
)()( rSrV
23/4/18 13
Properties of Nuclear Matter
Brockmann & Machleidt
PRC42, 1965 (1990)
E/A = 161 MeVkF = 1.35 0.05 fm1
Coester band
23/4/18 14
Isotope shifts in Pb
Sharma, Lalazissis & Ring
PLB317, 9 (1993)
RMF
23/4/18 15
Ground state properties of nuclei Binding energies, radii, neutron skin thickness, etc.
Symmetries in nuclei Pseudo spin symmetry Spin symmetry
Halo nuclei RMF description of halo nuclei Predictions of giant halo Study of deformed halo
Hyper nuclei Neutron halo and hyperon halo in hyper nuclei
…
RMF (RHB) description of nuclei
Vretenar, Afnasjev, Lalazissis & Ring
Phys. Rep. 409 (05) 101 Meng, Toki, Zhou, Zhang, Long &
Geng, Prog. Part. Nucl. Phys. 57 (06) 470
23/4/18 16
Contents Introduction to Relativistic mean field model
Basics: formalism and advantages Pseudospin and spin symmetries in atomic nuclei Pairing correlations in exotic nuclei
Contribution of the continuum BCS and Bogoliubov transformation
Spherical relativistic Hartree Bogoliubov theory Formalism and results
Summary I Deformed relativistic Hartree Bogoliubov theory in a Woods-
Saxon basis Why Woods-Saxon basis Formalism, results and discussions
Single particle resonances Analytical continuation in coupling constant approach Real stabilization method
Summary II
23/4/18 17
sl
s1
p1
d1s2
f1
p2
g1
s3
h1
2/1
2/3
2/12/5
2/32/72/3
2/1
2/1
2/5
2/9
2/72/52/32/12/11
2/9
2
2028
8
50
82
92
d2
Spin and pseudospin in atomic nuclei
3/21/2,p~
5/23/2,d~
3/21/2,p~
7/25/2,f~
2
3
21
,2,
,,1
ljln
ljln2/1~:spinpseudo
1~
:orbitpseudo
s
ll
Hecht & AdlerNPA137(1969)129
Arima, Harvey & ShimizuPLB30(1969)517
0
1
2
3
4
Woods-Saxon
1/2s~
23/4/18 18
Spin and pseudospin in atomic nuclei
Spin symmetry is broken Large spin-orbit splitting magic numbers
Approximate pseudo-spin symmetry Similarly to spin, no partner for ? Origin ? Different from spin, no partner for , e.g., ? (n+1, n) & nodal structure
PS sym. more conserved in deformed nuclei Superdeformation, identical bands etc.
2/11/2 s~p nn
21,,1 ljl
Ginocchio, PRL78(97)436
Ginocchio & Leviatan, PLB518(01)214 Chen, Lv, Meng & SGZ, CPL20(03)358
Ginocchio, Leviatan, Meng & SGZ, PRC69(04)034303
3/2p1
23/4/18 19
Pseudo quantum numbers
Pseudo quantum numbers are nothing but the quantum numbers of the lower component.
GinocchioPRL78(97)436
23/4/18 20
Origin of the symmetry - Nucleons
For nucleons, V(r)S(r)=0 spin symmetry V(r)S(r)=0 pseudo-spin symmetry
Schroedinger-like Eqs.
23/4/18 21
Origin of the symmetry - Anti-nucleons
For anti-nucleons, V(r)+S(r)=0 pseudo-spin symmetry V(r)S(r)=0 spin symmetry
SGZ, Meng & RingPRL92(03)262501
Schroedinger-like Eqs.
23/4/18 22
Spin symmetry in anti-nucleon more conserved
For nucleons, the smaller component F
For anti-nucleons, the larger component F
SGZ, Meng & RingPRL92(03)262501
The factor is ~100 times smaller for anti nucleons!
23/4/18 23
16O: anti neutron levels
p1/2 p3/2
M [
V(r
)S(
r)]
[MeV
]SGZ, Meng & Ring, PRL91, 262501 (2003)
p1/2 p3/2
23/4/18 24
Spin orbit splitting SGZ, Meng & Ring, PRL91, 262501 (2003)
23/4/18 25
Wave functions for PS doublets in 208Pb
Ginocchio&Madland, PRC57(98)1167
2/1s2
2/3d1
2/3d1
2/1s2
23/4/18 26
Wave functions SGZ, Meng & Ring, PRL92(03)262501
23/4/18 27
Wave functions SGZ, Meng & Ring, PRL92(03)262501
23/4/18 28
Wave functions SGZ, Meng & Ring, PRL92(03)262501
23/4/18 29
Wave functions: relation betw. small components
He, SGZ, Meng, Zhao, Scheid EPJA28( 2006) 265
23/4/18 30
Wave functions: relation betw. small components
He, SGZ, Meng, Zhao, Scheid EPJA28( 2006) 265
23/4/18 31
Contents Introduction to Relativistic mean field model
Basics: formalism and advantages Pseudospin and spin symmetries in atomic nuclei Pairing correlations in exotic nuclei
Contribution of the continuum BCS and Bogoliubov transformation
Spherical relativistic Hartree Bogoliubov theory Formalism and results
Summary I Deformed relativistic Hartree Bogoliubov theory in a Woods-
Saxon basis Why Woods-Saxon basis Formalism, results and discussions
Single particle resonances Analytical continuation in coupling constant approach Real stabilization method
Summary II
23/4/18 32
Characteristics of halo nuclei
Weakly bound; large spatial extensionContinuum can not be ignored
23/4/18 33
BCS and Continuum
rUr ~1 rVr ~2
Bound States
Positive energy States
Even a smaller occupation of positive energy states gives a non-localized density
Dobaczewski, et al., PRC53(96)2809
23/4/18 34
Contribution of continuum in r-HFB
r
r
r
r
rrrr
rrrrr
E
E
E
E
V
U
E
E
V
U
h
hd
0
0
''
''
'';'';
'';'';' *
3
When r goes to infinity, the potentials are zero
rr EE UEUdr
d
M
2
22
2
rr EE VEVdr
d
M
2
22
2
U and V behave when r goes to infinity
0for'exp
0forcos~
Erk
ErkU
U
UE
r
0for'exp
0forcos~
Erk
ErkV
V
VE
r
Bulgac, 1980 & nucl-th/9907088 Dobaczewski, Flocard&Treiner,
NPA422(84)103
Continuum contributes automatically and the density is still localized
23/4/18 35
Contribution of continuum in r-HFB
Dobaczewski, et al., PRC53(96)2809
rUr ~1 rVr ~2
• V(r) determines the density
• the density is localized even if U(r) oscillates at large r
Positive energy States
Bound States
23/4/18 36
Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory
RHB Hamiltonian
Pairing tensor
Baryon density
Pairing force
23/4/18 37
Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory
Pairing force
Radial DHB Eqs.
23/4/18 38
Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory
Densities
Total binding energy
23/4/18 39
11Li: self-consistent RCHB description
Meng & Ring, PRL77,3963 (96)
RCHB reproduces expt.
23/4/18 40
11Li: self-consistent RCHB description
Meng & Ring, PRL77,3963 (96) Contribution of continuum
Important roles of low-l orbitals close to the threshold
23/4/18 41
Giant halo: predictions of RCHB
Meng & Ring, PRL80,460 (1998)
Halos consisting of up to 6 neutrons
Important roles of low-l orbitals close to the threshold
23/4/18 42
Prediction of giant haloMeng, Toki, Zeng, Zhang & SGZ, PRC65,041302R
(2002)Zhang, Meng, SGZ & Zeng, CPL19,312
(2002)Zhang, Meng & SGZ, SCG33,289
(2003)
Giant halos in lighter isotopes
23/4/18 43
Giant halo from Skyrme HFB and RCHB
Terasaki, Zhang, SGZ, & Meng,
PRC74 (2006) 054318
Giant halos from non-rela. HFB
Different predictions for drip line
23/4/18 44
Halos in hyper nucleiLv, Meng, Zhang & SGZ, EPJA17 (2002)
19Meng, Lv, Zhang & SGZ, NPA722c (2003)
366
Additional binding from
23/4/18 45
Densities and charge changing cross sections
Meng, SGZ, & Tanihata,
PLB532 (2002)209
Proton density as inputs of Glauber model
23/4/18 46
Summary IRelativistic mean field model
Basics: formalism and advantagesPseudospin and spin symmetries in atomic
nucleiRelativistic symmetries: cancellation of the scalar and vector
potentialsSpin symmetry in anti nucleon spectra is more conservedTests of wave functions
Pairing correlations in exotic nucleiContribution of the continuum: r space HFB or RHB
Spherical relativistic Hartree Bogoliubov theorySelf consistent description of haloPredictions of giant halo and halo in hyper nucleiCharge changing cross sections