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Deformed Relativistic Hartree-Bogoliubov Model in Woods-Saxon Basis

Explore the application of deformed relativistic Hartree-Bogoliubov theory in a Woods-Saxon basis for studying exotic nuclei properties, halo formations, and symmetries in nuclei structures. The model incorporates relativistic effects and pairing interactions to analyze ground state properties and predict phenomena like giant halos. Collaborating researchers have made significant progress in understanding the complexities of deformed halo nuclei in a relativistic mean field framework.

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Deformed Relativistic Hartree-Bogoliubov Model in 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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