Shan-Gui Zhou

Email: sgzhou@itp.ac.cn; 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

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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