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

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

Shan-Gui Zhou

Email: [email protected]; 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

Introduction to ITP and CAS Bogoliubov model (I)

- 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

Contents Bogoliubov model (I)

- 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

Relativistic mean field model Bogoliubov model (I)

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

Coupled equations of motion Bogoliubov model (I)

Nucleon

Mesons &

photon

Vector & scalar potentials

Sources (densities)

Solving Eqs.: no-sea and mean field approximations; iteration

RMF for spherical nuclei Bogoliubov model (I)

Dirac spinor for nucleon

Radial Dirac Eq.

Vector & scalar potentials

RMF for spherical nuclei Bogoliubov model (I)

Klein-Gordon Eqs. for mesons and photon

Sources

Densities

RMF potentials Bogoliubov model (I)

RMF for spherical nuclei: observables Bogoliubov model (I)

Nucleon numbers

Radii

Total binding energy

Center of mass corrections Bogoliubov model (I)

Long, Meng, Giai, SGZ, PRC69,034319(04)

RMF description of exotic nuclei: Bogoliubov model (I)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

- Two potentials: scalar and vector potentials
- Others
- More easily dealt with
- Less number of parameters
- …

Potentials in the RMF model Bogoliubov model (I)

Properties of Nuclear Matter Bogoliubov model (I)

E/A = -161 MeV

kF = 1.35 0.05 fm-1

Coester band

Brockmann & Machleidt

PRC42, 1965 (1990)

RMF (RHB) description of nuclei Bogoliubov model (I)

- 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

Contents Bogoliubov model (I)

- 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

Hecht & Adler Bogoliubov model (I)

NPA137(1969)129

Arima, Harvey & Shimizu

PLB30(1969)517

Spin and pseudospin in atomic nucleiWoods-Saxon

Spin and pseudospin in atomic nuclei Bogoliubov model (I)

- 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.

Ginocchio, Leviatan, Meng & SGZ, PRC69(04)034303

Ginocchio, PRL78(97)436

Chen, Lv, Meng & SGZ, CPL20(03)358

Ginocchio & Leviatan, PLB518(01)214

Pseudo quantum numbers Bogoliubov model (I)

Pseudo quantum numbers are nothing

but the quantum numbers of the lower component.

Ginocchio

PRL78(97)436

Origin of the symmetry - Nucleons Bogoliubov model (I)

Schroedinger-like Eqs.

For nucleons,

- V(r)-S(r)=0spin symmetry
- V(r)+S(r)=0pseudo-spin symmetry

Origin of the symmetry - Anti-nucleons Bogoliubov model (I)

Schroedinger-like Eqs.

For anti-nucleons,

- V(r)+S(r)=0pseudo-spin symmetry
- V(r)-S(r)=0spin symmetry

SGZ, Meng & Ring

PRL92(03)262501

The factor is ~100 times smaller for anti nucleons! Bogoliubov model (I)

Spin symmetry in anti-nucleon more conservedSGZ, Meng & Ring

PRL92(03)262501

For nucleons, the smaller component F

For anti-nucleons, the larger component F

p Bogoliubov model (I)1/2 p3/2

16O: anti neutron levelsSGZ, Meng & Ring, PRL91, 262501 (2003)

p1/2 p3/2

M[V(r)S(r)] [MeV]

Wave functions for PS doublets in Bogoliubov model (I)208Pb

Ginocchio&Madland, PRC57(98)1167

Wave functions Bogoliubov model (I)

SGZ, Meng & Ring, PRL92(03)262501

Wave functions Bogoliubov model (I)

SGZ, Meng & Ring, PRL92(03)262501

Wave functions Bogoliubov model (I)

SGZ, Meng & Ring, PRL92(03)262501

Wave functions: relation betw. small components Bogoliubov model (I)

He, SGZ, Meng, Zhao, Scheid

EPJA28( 2006) 265

Wave functions: relation betw. small components Bogoliubov model (I)

He, SGZ, Meng, Zhao, Scheid

EPJA28( 2006) 265

Contents Bogoliubov model (I)

- 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

Characteristics of halo nuclei Bogoliubov model (I)

- Weakly bound; large spatial extension
- Continuum can not be ignored

BCS and Continuum Bogoliubov model (I)

Positive energy States

Even a smaller occupation of positive energy states gives a non-localized density

Bound States

Dobaczewski, et al., PRC53(96)2809

Contribution of continuum in r-HFB Bogoliubov model (I)

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, Flocard&Treiner, NPA422(84)103

Contribution of continuum in r-HFB Bogoliubov model (I)

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

Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory

RHB Hamiltonian

Pairing tensor

Baryon density

Pairing force

11 theoryLi：self-consistent RCHB description

Contribution of continuum

Meng & Ring, PRL77,3963 (96)

Important roles of low-l orbitals close to the threshold

Giant halo: predictions of RCHB theory

Halos consisting of up to 6 neutrons

Important roles of low-l orbitals close to the threshold

Meng & Ring, PRL80,460 (1998)

Prediction of giant halo theory

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

Giant halo from Skyrme HFB and RCHB theory

Giant halos from non-rela. HFB

Different predictions for drip line

Terasaki, Zhang, SGZ, & Meng,

PRC74 (2006) 054318

Halos in hyper nuclei theory

Lv, Meng, Zhang & SGZ, EPJA17 (2002) 19

Meng, Lv, Zhang & SGZ, NPA722c (2003) 366

Additional binding from L

Densities and charge changing cross sections theory

Meng, SGZ, & Tanihata,

PLB532 (2002)209

Proton density as inputs of Glauber model

Summary I theory

- 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

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