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Deformed relativistic Hartree Bogoliubov model in a Woods-Saxon basis

Deformed relativistic Hartree Bogoliubov model in a Woods-Saxon basis. Collaborators: J. Meng (Peking Univ., Beijing) P. Ring (Tech. Univ., Munich). Shan-Gui Zhou Institute of Theoretical Physics Chinese Academy of Sciences Beijing. 中日 Nuclear Physics 2006 2006 年 5 月 16 － 20 日，上海.

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Deformed relativistic Hartree Bogoliubov model in a Woods-Saxon basis

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  1. Deformed relativistic Hartree Bogoliubov model in a Woods-Saxon basis Collaborators: J. Meng (Peking Univ., Beijing) P. Ring (Tech. Univ., Munich) Shan-Gui Zhou Institute of Theoretical Physics Chinese Academy of Sciences Beijing 中日Nuclear Physics 2006 2006年5月16－20日，上海

  2. Contents • Introduction • 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 • Deformed RHB in a Woods-Saxon basis • Summary

  3. Exotic nuclei

  4. Characteristics of halo nuclei • Weakly bound; large spatial extension • Continuum can not be ignored

  5. 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

  6. 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

  7. Hartree-Fock Bogoliubov theory • Deformed relativistic HFB in r space • Deformed relativistic Hartree-Bogoliubov or Hartree-Fock-Bogoliubov theory in harmonic oscillator basis Terasaki, Flocard, Heenen & Bonche, NPA 621, 706 (1996) Stoitsov, Dobaczewski, Ring & Pittel, PRC61, 034311 (2000) Terán, Oberacker & Umar, PRC67, 064314 (2003) Vretenar, Lalazissis & Ring, PRL82, 4595 (1999) No deformed relativistic Hartree-Bogoliubov or Hartree-Fock-Bogoliubov theory in r space available yet

  8. 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

  9. RMF: advantages> • 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 paramters • …

  10. 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 • … Meng, Toki, Zhou, Zhang, Long & Geng, Prog. Part. Nucl. Phys. In press Vretenar, Afnasjev, Lalazissis & Ring Phys. Rep. 409 (05) 101

  11. 11Li：self-consistent RMF description Meng & Ring, PRL77,3963 (1996)

  12. Deformed Halo? Deformed core? Decoupling of the core and valence nucleons？ Misu, Nazarewicz, Aberg, NPA614(97)44 11,14Be Ne isotopes … Bennaceur et al., PLB296(00)154 Hamamoto & Mottelson, PRC68(03)034312 Hamamoto & Mottelson, PRC69(04)064302 Poschl et al., PRL79(97)3841 Nunes, NPA757(05)349 Pei, Xu & Stevenson, NPA765(06)29

  13. RMF in a Woods-Saxon basis: progress Many difficulties to solve deformed problem in r space Woods-Saxon basis might be a reconciler between the HO basis and r space

  14. Spherical Rela. Hartree Theory: 72Ca Zhou, Meng & Ring, PRC68,034323(03) Woods-Saxon basis reproduces r space

  15. Deformed RHB in a Woods-Saxon basis Axially deformed nuclei

  16. Deformed RHB in a Woods-Saxon basis • , even , zero • , even or odd , 0 or 1

  17. Pairing interaction • Phenomenological pairing interaction with parameters: V0, 0, , and a cut off parameter Ecut • Phenomenological relativistic pairing force with parameters: c0 and a cut off parameter Ecut Meng & Ring, PRL77,3963 (1996) Serra & Ring, PRC65,064324 (2002)

  18. Routines checks: comparison with available programs > • Compare with spherical RCHB model Spherical, Bogoliubov • Compare with deformed RMF in a WS basis Deformed, no pairing • Compare with deformed RMF+BCS in a WS basis Deformed, BCS for pairing

  19. Compare with spherical RCHB model< 20Ne, NL3, Rmax = 10 fm, r = 0.2 fm V0 = 200 MeV fm3, Ecut= 100 MeV

  20. Compare with deformed RMF in a WS basis<

  21. Compare with deformed RMF+BCS in a WS basis <

  22. Summary • To study exotic nuclei, particularly halo • Weakly bound and large spatial extension • Continuum contribution • 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 • Continuum contribution in deformed nuclei, deformed halo, shell structure evolution, super heavy nuclei, etc.

  23. Shan-Gui Zhou ITP-CAS Beijing Thanks

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