Shan-Gui Zhou

1
Structure of exotic nuclei from relativistic
Hartree Bogoliubov model (I)

• Shan-Gui Zhou
• Email sgzhou_at_itp.ac.cn URL
  http//www.itp.ac.cn/sgzhou
• Institute of Theoretical Physics, Chinese Academy
  of Sciences, Beijing
• Center of Theoretical Nuclear Physics, National
  Laboratory of Heavy Ion Accelerator, Lanzhou

HISS-NTAA 2007 Dubna, Aug. 7-17
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

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

4
Relativistic mean field model
Lagrangian density
http//pdg.lbl.gov
Serot Walecka, Adv. Nucl. Phys. 16 (86) 1
Non-linear coupling for s
Reinhard, Rep. Prog. Phys. 52 (89) 439
Ring, Prog. Part. Nucl. Phys. 37 (96) 193
Vretenar, Afnasjev, Lalazissis Ring Phys. Rep.
409 (05) 101
Field tensors
Meng, Toki, SGZ, Zhang, Long Geng, Prog. Part.
Nucl. Phys. 57 (06) 470
5
Coupled equations of motion
Nucleon
Mesons photon
Vector scalar potentials
Sources (densities)
Solving Eqs. no-sea and mean field
approximations iteration
6
RMF for spherical nuclei
Dirac spinor for nucleon
Radial Dirac Eq.
Vector scalar potentials
7
RMF for spherical nuclei
Klein-Gordon Eqs. for mesons and photon
Sources
Densities
8
RMF potentials
9
RMF for spherical nuclei observables
Nucleon numbers
Radii
Total binding energy
10
Center of mass corrections
Long, Meng, Giai, SGZ, PRC69,034319(04)
11
RMF description of exotic nuclei Why?

• 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

12
Potentials in the RMF model
13
Properties of Nuclear Matter
E/A -16?1 MeV kF 1.35 ?0.05 fm-1
Coester band
Brockmann Machleidt PRC42, 1965 (1990)
14
Isotope shifts in Pb
Sharma, Lalazissis Ring PLB317, 9 (1993)
RMF
15
RMF (RHB) description of nuclei

• 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

Vretenar, Afnasjev, Lalazissis Ring Phys. Rep.
409 (05) 101
Meng, Toki, Zhou, Zhang, Long Geng, Prog.
Part. Nucl. Phys. 57 (06) 470
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

17
Spin and pseudospin in atomic nuclei
Woods-Saxon
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.,
• ? (n1, n) nodal structure
• PS sym. more conserved in deformed nuclei
• Superdeformation, identical bands etc.

Ginocchio, Leviatan, Meng SGZ, PRC69(04)034303
Ginocchio, PRL78(97)436
Chen, Lv, Meng SGZ, CPL20(03)358
Ginocchio Leviatan, PLB518(01)214
19
Pseudo quantum numbers
Pseudo quantum numbers are nothing but the
quantum numbers of the lower component.
Ginocchio PRL78(97)436
20
Origin of the symmetry - Nucleons
Schroedinger-like Eqs.

• For nucleons,
• V(r)-S(r)0 ? spin symmetry
• V(r)S(r)0 ? pseudo-spin symmetry

21
Origin of the symmetry - Anti-nucleons
Schroedinger-like Eqs.

• For anti-nucleons,
• V(r)S(r)0 ? pseudo-spin symmetry
• V(r)-S(r)0 ? spin symmetry

SGZ, Meng Ring PRL92(03)262501
22
Spin symmetry in anti-nucleon more conserved
SGZ, Meng Ring PRL92(03)262501
For nucleons, the smaller component F
For anti-nucleons, the larger component F
23
16O anti neutron levels
SGZ, Meng Ring, PRL91, 262501 (2003)
p1/2 p3/2
M ?V(r)?S(r) MeV
24
Spin orbit splitting
SGZ, Meng Ring, PRL91, 262501 (2003)
25
Wave functions for PS doublets in 208Pb
GinocchioMadland, PRC57(98)1167
26
Wave functions
SGZ, Meng Ring, PRL92(03)262501
27
Wave functions
SGZ, Meng Ring, PRL92(03)262501
28
Wave functions
SGZ, Meng Ring, PRL92(03)262501
29
Wave functions relation betw. small components
He, SGZ, Meng, Zhao, Scheid EPJA28( 2006) 265
30
Wave functions relation betw. small components
He, SGZ, Meng, Zhao, Scheid EPJA28( 2006) 265
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

32
Characteristics of halo nuclei

• Weakly bound large spatial extension
• Continuum can not be ignored

33
BCS and Continuum
Positive energy States
Even a smaller occupation of positive energy
states gives a non-localized density
Bound States
Dobaczewski, et al., PRC53(96)2809
34
Contribution of continuum in r-HFB
When r goes to infinity, the potentials are zero
U and V behave when r goes to infinity
Continuum contributes automatically and the
density is still localized
Bulgac, 1980 nucl-th/9907088
Dobaczewski, FlocardTreiner, NPA422(84)103
35
Contribution of continuum in r-HFB
Positive energy States

• V(r) determines the density
• the density is localized even if U(r) oscillates
  at large r

Bound States
Dobaczewski, et al., PRC53(96)2809
36
Spherical relativistic continuum Hartree
Bogoliubov (RCHB) theory
RHB Hamiltonian
Pairing tensor
Baryon density
Pairing force
37
Spherical relativistic continuum Hartree
Bogoliubov (RCHB) theory
Pairing force
Radial DHB Eqs.
38
Spherical relativistic continuum Hartree
Bogoliubov (RCHB) theory
Densities
Total binding energy
39
11Liself-consistent RCHB description
Meng Ring, PRL77,3963 (96)
RCHB reproduces expt.
40
11Liself-consistent RCHB description
Contribution of continuum
Meng Ring, PRL77,3963 (96)
Important roles of low-l orbitals close to the
threshold
41
Giant halo predictions of RCHB
Halos consisting of up to 6 neutrons
Important roles of low-l orbitals close to the
threshold
Meng Ring, PRL80,460 (1998)
42
Prediction of giant halo
Meng, 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
43
Giant halo from Skyrme HFB and RCHB
Giant halos from non-rela. HFB
Different predictions for drip line
Terasaki, Zhang, SGZ, Meng, PRC74 (2006) 054318
44
Halos in hyper nuclei
Lv, Meng, Zhang SGZ, EPJA17 (2002) 19
Meng, Lv, Zhang SGZ, NPA722c (2003) 366
Additional binding from L
45
Densities and charge changing cross sections
Meng, SGZ, Tanihata, PLB532 (2002)209
Proton density as inputs of Glauber model
46
Summary I

• Relativistic mean field model
• Basics formalism and advantages
• Pseudospin and spin symmetries in atomic nuclei
• Relativistic symmetries cancellation of the
  scalar and vector potentials
• Spin symmetry in anti nucleon spectra is more
  conserved
• Tests of wave functions
• Pairing correlations in exotic nuclei
• Contribution of the continuum r space HFB or RHB
• Spherical relativistic Hartree Bogoliubov theory
• Self consistent description of halo
• Predictions of giant halo and halo in hyper
  nuclei
• Charge changing cross sections