Toward a deformed relativistic Hartree Bogoliubov theory for exotic nuclei

1
Toward a deformed relativistic Hartree Bogoliubov
theory for exotic nuclei

• Shan-Gui Zhou
• Institute of Theoretical Physics
• Chinese Academy of Sciences
• Beijing

Collaborators J. Meng (Peking Univ., Beijing) P.
Ring (Tech. Univ., Munich)
Asia-Europe Link Workshop in Nuclear Physics and
Astrophysics September 6, 2005, Beijing
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Introduction of 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
• En-Guang Zhao, SGZ
• Super heavy nuclei exotic nuclei nuclear
  astrophysics quark nuclear physics

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Contents

• Introduction
• Exotic nuclei halo, new magic numbers, etc.
• Characteristics of halo phenomena
• Hartree Fock Bogoliubov theory in coordinate
  space
• Contribution of the continuum
• Relativistic Hartree (Bogoliubov) theory in a
  Woods-Saxon basis
• A brief introduction to RMF
• Spherical RMF in a Woods-Saxon basis
• Spin symmetry in anti-nucleon spectrum
• Deformed RHB in a Woods-Saxon basis
• Summary

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Exotic nuclei
Nucleosynthesis e.g., r-process
Shell structure evolution ? new magic numbers
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Characteristics of halo nuclei

• Weakly bound large spatial extension
• Continuum

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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
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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, FlocardTreiner, NPA422(84)103
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Contribution of continuum in r-HFB

• for E gt 0, V(r) always goes exponentially to zero
• V(r) determines the density
• the density is localized even if U(r) oscillates
  at large r

Dobaczewski, et al., PRC53(96)2809
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Relativistic mean field model
Serot Walecka, Adv. Nucl. Phys. 16 (86) 1
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, Zhou, Zhang, Long Geng, Prog.
Part. Nucl. Phys. In press
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Equation of motions
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RMF advantages gt

• Nucleon-nucleon interaction
• Mesons degrees of freedom included
• Nucleons interact via exchanges mesons
• Relativistic effects
• Two potentials scalar and vector potentials gt
• ? the relativistic effects important
  dynamically
• ? New mechanism of saturation of nuclear
  matter gt
• ? Psedo spin symmetry explained neatly and
  successfully
• Spin orbit coupling included automatically
• ? Anomalies in isotope shifts of Pb gt
• Others
• More easily dealt with
• Less number of paramters

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Potentials in the RMF model lt
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Properties of Nuclear Matter lt
E/A -16?1 MeV kF 1.35 ?0.05 fm-1
Brockmann Machleidt PRC42, 1965 (1990)
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Isotope shifts in Pb lt
Sharma, Lalazissis Ring PLB317, 9 (1993)
RMF
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RMF (RHB) description of nuclei

• Ground state properties of nuclei
• Binding energies, radii, neutron skin thickness,
  etc.
• Halo nuclei
• RMF description of halo nuclei
• Predictions of giant halo
• Study of deformed halo long-term struggle
• Symmetries in nuclei
• Pseudo spin symmetry
• Spin symmetry
• 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. In press
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11Liself-consistent RMF description
Meng Ring, PRL77,3963 (1996)
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Prediction of giant halo
Meng Ring, PRL80,460 (1998)
Meng, Toki, Zeng, Zhang Zhou, PRC65,041302R
(2002)
Zhang, Meng, Zhou Zeng, CPL19,312 (2002)
Zhang, Meng Zhou, Sci. China G33,289 (2003)
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Deformed Halo? Deformed core?
Decoupling of the core and valence nucleons?
Misu, Nazarewicz, Aberg, NPA614(97)44
14Be Ne isotopes
Bennaceur et al., PLB296(00)154
Hamamoto Mottelson, PRC68(03)034312
Hamamoto Mottelson, PRC69(04)064302
Nunes, NPA757(05)349
Poschl et al., PRL79(97)3841
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RMF for deformed nuclei in r space

• Mean field Relativistic Hartree Theory
• Axially deformed
• Coupled channel equations
• Relativistic Hartree-Bogoliubov Theory
• Axially deformed
• Coupled channel equations
• Other ways?

Zhou, Meng, Yamaji Yang, CPL17(00)717
Zhou, Meng Yamaji, Proceedings of RIKEN
workshop 2001
Meng, Lv, Zhang Zhou NPA722c,366(03)
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RMF in a Woods-Saxon basis

• Relativistic Hartree Theory for spherical nuclei
• Relativistic Hartree Theory BCS approach for
  axially deformed nuclei
• Relativistic Hartree-Bogoliubov Theory for
  axially deformed nuclei

Zhou, Meng Ring, PRC68,034323(03)
Zhou, Meng Ring In preparation
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SRHSWS
Shooting Method
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SRHSWS
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Spherical RH model in Woods-Saxon basis
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Two basis
Smaller Basis!
Schroedinger WS
nFmax nGmax 1
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Spherical Rela. Hartree Theory 72Ca
Zhou, Meng Ring, PRC68,034323(03)
Woods-Saxon basis reproduces r space
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RMF in a Woods-Saxon basis progress
Spin symmetry in anti nucleon spectra
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16O anti neutron levels
Zhou, Meng Ring, PRL91, 262501 (2003)
p1/2 p3/2
M ?V(r)?S(r) MeV
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Spin orbit splitting
Zhou, Meng Ring, PRL91, 262501 (2003)
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Spin and pseudospin in atomic nuclei
Woods-Saxon
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Pseudo quantum numbers
Pseudo quantum numbers are nothing but the
quantum numbers of the lower component.
Ginocchio PRL78(97)436
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Origin of the symmetry - Nucleons

• For nucleons,
• V(r)?S(r)0 ? spin symmetry
• V(r)S(r)0 ? pseudo-spin symmetry

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Origin of the symmetry - Anti-nucleons

• For anti-nucleons,
• V(r)?S(r)0 ? pseudo-spin symmetry
• V(r)S(r)0 ? spin symmetry

Zhou,MengRing PRL92(03)262501
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Origin of the symmetry
Zhou,MengRing PRL92(03)262501
For nucleons, the smaller component F
For anti-nucleons, the larger component F
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Potentials in RMF theory
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Wave functions
Zhou, Meng Ring, PRL91, 262501 (2003)
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Wave functions relation between smaller
components
He, Zhou, MengZhao, Submitted to PRC
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Deformed RHB in a Woods-Saxon basis
Axially deformed nuclei
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Deformed RHB in a Woods-Saxon basis

• , even
• ?, zero

• , even or odd
• ?, 0 or ?1

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Summary

• Study of exotic nuclei
• The radioactive ion beam facilities around the
  world
• Exotic phenomena in nuclei far from the stability
  line
• Important for astrophysics
• The relativistic mean field model has been
  extensively and quite successfully applied to
  exotic nuclei
• Ground state properties of nuclei
• Halo, giant halo, hyper halo, etc.
• Pseudo spin and spin symmetries
• Deformed relativistic Hartree Bogoliubov theory
  in a Woods-Saxon basis
• Being developed
• Continuum contribution in deformed nuclei,
  deformed halo, shell structure evolution, super
  heavy nuclei, etc.

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Shan-Gui Zhou
ITP-CAS Beijing
Thanks