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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) 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 • 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 • 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 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 Nucleon Mesons & photon Vector & scalar potentials Sources (densities) Solving Eqs.: no-sea and mean field approximations; iteration
RMF for spherical nuclei Dirac spinor for nucleon Radial Dirac Eq. Vector & scalar potentials
RMF for spherical nuclei Klein-Gordon Eqs. for mesons and photon Sources Densities
RMF for spherical nuclei: observables Nucleon numbers Radii Total binding energy
Center of mass corrections Long, Meng, Giai, SGZ, PRC69,034319(04)
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 • …
Properties of Nuclear Matter E/A = -161 MeV kF = 1.35 0.05 fm-1 Coester band Brockmann & Machleidt PRC42, 1965 (1990)
Isotope shifts in Pb Sharma, Lalazissis & Ring PLB317, 9 (1993) RMF
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
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
Hecht & Adler NPA137(1969)129 Arima, Harvey & Shimizu PLB30(1969)517 Spin and pseudospin in atomic nuclei Woods-Saxon
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, 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 are nothing but the quantum numbers of the lower component. Ginocchio PRL78(97)436
Origin of the symmetry - Nucleons Schroedinger-like Eqs. For nucleons, • V(r)-S(r)=0spin symmetry • V(r)+S(r)=0pseudo-spin symmetry
Origin of the symmetry - Anti-nucleons 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! 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
p1/2 p3/2 16O: anti neutron levels SGZ, Meng & Ring, PRL91, 262501 (2003) p1/2 p3/2 M[V(r)S(r)] [MeV]
SGZ, Meng & Ring, PRL91, 262501 (2003) Spin orbit splitting
Wave functions for PS doublets in 208Pb Ginocchio&Madland, PRC57(98)1167
Wave functions SGZ, Meng & Ring, PRL92(03)262501
Wave functions SGZ, Meng & Ring, PRL92(03)262501
Wave functions SGZ, Meng & Ring, PRL92(03)262501
Wave functions: relation betw. small components He, SGZ, Meng, Zhao, Scheid EPJA28( 2006) 265
Wave functions: relation betw. small components He, SGZ, Meng, Zhao, Scheid EPJA28( 2006) 265
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
Characteristics of halo nuclei • Weakly bound; large spatial extension • Continuum can not be ignored
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
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, Flocard&Treiner, NPA422(84)103
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
Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory RHB Hamiltonian Pairing tensor Baryon density Pairing force
Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory Pairing force Radial DHB Eqs.
Spherical relativistic continuum Hartree Bogoliubov (RCHB) theory Densities Total binding energy
11Li:self-consistent RCHB description Meng & Ring, PRL77,3963 (96) RCHB reproduces expt.
11Li: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 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 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 halos from non-rela. HFB Different predictions for drip line Terasaki, Zhang, SGZ, & Meng, PRC74 (2006) 054318
Halos in hyper nuclei Lv, Meng, Zhang & SGZ, EPJA17 (2002) 19 Meng, Lv, Zhang & SGZ, NPA722c (2003) 366 Additional binding from L
Densities and charge changing cross sections Meng, SGZ, & Tanihata, PLB532 (2002)209 Proton density as inputs of Glauber model
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