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Shan-Gui Zhou URL: 1.Institute of Theoretical Physics,

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1 Shan-Gui Zhou Email: sgzhou@itp.ac.cn; URL: http://www.itp.ac.cn/~sgzhousgzhou@itp.ac.cnhttp://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

2 2015-6-42 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 2015-6-43 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 2015-6-44 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

5 2015-6-45 Coupled equations of motion Nucleon Mesons & photon Vector & scalar potentials Sources (densities) Solving Eqs.: no-sea and mean field approximations; iteration

6 2015-6-46 RMF for spherical nuclei Dirac spinor for nucleon Radial Dirac Eq. Vector & scalar potentials

7 2015-6-47 RMF for spherical nuclei Klein-Gordon Eqs. for mesons and photon Sources Densities

8 2015-6-48 RMF potentials

9 2015-6-49 RMF for spherical nuclei: observables Nucleon numbers Radii Total binding energy

10 2015-6-410 Center of mass corrections Long, Meng, Giai, SGZ, PRC69,034319(04)

11 2015-6-411  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?

12 2015-6-412 Potentials in the RMF model

13 2015-6-413 Properties of Nuclear Matter Brockmann & Machleidt PRC42, 1965 (1990) E/A =  16  1 MeV k F = 1.35  0.05 fm  1 Coester band

14 2015-6-414 Isotope shifts in Pb Sharma, Lalazissis & Ring PLB317, 9 (1993) RMF

15 2015-6-415  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

16 2015-6-416 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 2015-6-417 Spin and pseudospin in atomic nuclei Hecht & Adler NPA137(1969)129 Arima, Harvey & Shimizu PLB30(1969)517 Woods-Saxon

18 2015-6-418 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. Ginocchio, PRL78(97)436 Ginocchio & Leviatan, PLB518(01)214 Chen, Lv, Meng & SGZ, CPL20(03)358 Ginocchio, Leviatan, Meng & SGZ, PRC69(04)034303

19 2015-6-419 Pseudo quantum numbers Pseudo quantum numbers are nothing but the quantum numbers of the lower component. Ginocchio PRL78(97)436

20 2015-6-420 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.

21 2015-6-421 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 & Ring PRL92(03)262501 Schroedinger-like Eqs.

22 2015-6-422 Spin symmetry in anti-nucleon more conserved For nucleons, the smaller component F For anti-nucleons, the larger component F SGZ, Meng & Ring PRL92(03)262501 The factor is ~100 times smaller for anti nucleons!

23 2015-6-423 16 O: anti neutron levels p 1/2 p 3/2 M  [V(r)  S(r)] [MeV] SGZ, Meng & Ring, PRL91, 262501 (2003) p 1/2 p 3/2

24 2015-6-424 Spin orbit splitting SGZ, Meng & Ring, PRL91, 262501 (2003)

25 2015-6-425 Wave functions for PS doublets in 208 Pb Ginocchio&Madland, PRC57(98)1167

26 2015-6-426 Wave functions SGZ, Meng & Ring, PRL92(03)262501

27 2015-6-427 Wave functions SGZ, Meng & Ring, PRL92(03)262501

28 2015-6-428 Wave functions SGZ, Meng & Ring, PRL92(03)262501

29 2015-6-429 Wave functions: relation betw. small components He, SGZ, Meng, Zhao, Scheid EPJA28( 2006) 265

30 2015-6-430 Wave functions: relation betw. small components He, SGZ, Meng, Zhao, Scheid EPJA28( 2006) 265

31 2015-6-431 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 2015-6-432 Characteristics of halo nuclei  Weakly bound; large spatial extension  Continuum can not be ignored

33 2015-6-433 BCS and Continuum Bound States Positive energy States Even a smaller occupation of positive energy states gives a non-localized density Dobaczewski, et al., PRC53(96)2809

34 2015-6-434 Contribution of continuum in r-HFB When r goes to infinity, the potentials are zero U and V behave when r goes to infinity Bulgac, 1980 & nucl-th/9907088 Dobaczewski, Flocard&Treiner, NPA422(84)103 Continuum contributes automatically and the density is still localized

35 2015-6-435 Contribution of continuum in r-HFB Dobaczewski, et al., PRC53(96)2809 V(r) determines the density the density is localized even if U(r) oscillates at large r Positive energy States Bound States

36 2015-6-436 Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory RHB Hamiltonian Pairing tensor Baryon density Pairing force

37 2015-6-437 Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory Pairing force Radial DHB Eqs.

38 2015-6-438 Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory Densities Total binding energy

39 2015-6-439 11 Li ： self-consistent RCHB description Meng & Ring, PRL77,3963 (96) RCHB reproduces expt.

40 2015-6-440 11 Li ： self-consistent RCHB description Meng & Ring, PRL77,3963 (96) Contribution of continuum Important roles of low-l orbitals close to the threshold

41 2015-6-441 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

42 2015-6-442 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 2015-6-443 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

44 2015-6-444 Halos in hyper nuclei Lv, Meng, Zhang & SGZ, EPJA17 (2002) 19 Meng, Lv, Zhang & SGZ, NPA722c (2003) 366 Additional binding from 

45 2015-6-445 Densities and charge changing cross sections Meng, SGZ, & Tanihata, PLB532 (2002)209 Proton density as inputs of Glauber model

46 2015-6-446 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

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