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Structure of exotic nuclei from relativistic Hartree Bogoliubov model (I). Shan-Gui Zhou Email: sgzhou@itp.ac.cn ; URL: http://www.itp.ac.cn/~sgzhou Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing

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Structure of exotic nuclei from relativistic hartree bogoliubov model i

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

Shan-Gui Zhou

Email: sgzhou@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


Introduction to itp and cas
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
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
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
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
RMF for spherical nuclei Bogoliubov model (I)

Dirac spinor for nucleon

Radial Dirac Eq.

Vector & scalar potentials


Rmf for spherical nuclei1
RMF for spherical nuclei Bogoliubov model (I)

Klein-Gordon Eqs. for mesons and photon

Sources

Densities


Rmf potentials
RMF potentials Bogoliubov model (I)


Rmf for spherical nuclei observables
RMF for spherical nuclei: observables Bogoliubov model (I)

Nucleon numbers

Radii

Total binding energy


Center of mass corrections
Center of mass corrections Bogoliubov model (I)

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


Rmf description of exotic nuclei why
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

  • Others

    • More easily dealt with

    • Less number of parameters


Potentials in the rmf model
Potentials in the RMF model Bogoliubov model (I)


Properties of nuclear matter
Properties of Nuclear Matter Bogoliubov model (I)

E/A = -161 MeV

kF = 1.35 0.05 fm-1

Coester band

Brockmann & Machleidt

PRC42, 1965 (1990)


Isotope shifts in pb
Isotope shifts in Pb Bogoliubov model (I)

Sharma, Lalazissis & Ring

PLB317, 9 (1993)

RMF


Rmf rhb description of nuclei
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


Contents1
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


Spin and pseudospin in atomic nuclei

Hecht & Adler Bogoliubov model (I)

NPA137(1969)129

Arima, Harvey & Shimizu

PLB30(1969)517

Spin and pseudospin in atomic nuclei

Woods-Saxon


Spin and pseudospin in atomic nuclei1
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
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
Origin of the symmetry - Nucleons Bogoliubov model (I)

Schroedinger-like Eqs.

For nucleons,

  • V(r)-S(r)=0spin symmetry

  • V(r)+S(r)=0pseudo-spin symmetry


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

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


Spin symmetry in anti nucleon more conserved

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

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


16 o anti neutron levels

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

16O: anti neutron levels

SGZ, Meng & Ring, PRL91, 262501 (2003)

p1/2 p3/2

M[V(r)S(r)] [MeV]


Spin orbit splitting

SGZ Bogoliubov model (I), Meng & Ring,

PRL91, 262501 (2003)

Spin orbit splitting


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

Ginocchio&Madland, PRC57(98)1167


Wave functions
Wave functions Bogoliubov model (I)

SGZ, Meng & Ring, PRL92(03)262501


Wave functions1
Wave functions Bogoliubov model (I)

SGZ, Meng & Ring, PRL92(03)262501


Wave functions2
Wave functions Bogoliubov model (I)

SGZ, Meng & Ring, PRL92(03)262501


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

He, SGZ, Meng, Zhao, Scheid

EPJA28( 2006) 265


Wave functions relation betw small components1
Wave functions: relation betw. small components Bogoliubov model (I)

He, SGZ, Meng, Zhao, Scheid

EPJA28( 2006) 265


Contents2
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
Characteristics of halo nuclei Bogoliubov model (I)

  • Weakly bound; large spatial extension

  • Continuum can not be ignored


Bcs and continuum
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
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 hfb1
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
Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory

RHB Hamiltonian

Pairing tensor

Baryon density

Pairing force



Spherical relativistic continuum hartree bogoliubov rchb theory2
Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory

Densities

Total binding energy


11 li self consistent rchb description
11 theoryLi:self-consistent RCHB description

Meng & Ring, PRL77,3963 (96)

RCHB reproduces expt.


11 li self consistent rchb description1
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
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
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
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
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
Densities and charge changing cross sections theory

Meng, SGZ, & Tanihata,

PLB532 (2002)209

Proton density as inputs of Glauber model


Summary i
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