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

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 2018/11/19

Exotic nuclei 2018/11/19

Characteristics of halo nuclei Weakly bound; large spatial extension Continuum can not be ignored 2018/11/19

Dobaczewski, et al., PRC53(96)2809 BCS and Continuum Positive energy States Even a smaller occupation of positive energy states gives a non-localized density n orders the quasi particle energy; each plot is put from the bottom to the top in the order of canonical energy (or in the order of the node number of the dominant component) Bound States Dobaczewski, et al., PRC53(96)2809 2018/11/19

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 2018/11/19

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 2018/11/19

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 2018/11/19

RMF: advantages > Nucleon-nucleon interaction Relativistic effects 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 … 2018/11/19

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 2018/11/19

11Li：self-consistent RMF description Meng & Ring, PRL77,3963 (1996) 2018/11/19

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 2018/11/19

RMF in a Woods-Saxon basis: progress Shapes Mean field or Beyond Schrödinger W-S basis Dirac Spherical Rela. Hartree SRH SWS SRH DWS √ Axially deformed Rela. Hartree + BCS DRH DWS Rela. Hartree-Bogoliubov DRHB DWS Triaxially deformed Real. Hartree-Bogoliubov TRHB DWS Many difficulties to solve deformed problem in r space Woods-Saxon basis might be a reconciler between the HO basis and r space 2018/11/19

Spherical Rela. Hartree Theory: 72Ca Zhou, Meng & Ring, PRC68,034323(03) Woods-Saxon basis reproduces r space 2018/11/19

Deformed RHB in a Woods-Saxon basis Axially deformed nuclei 2018/11/19

Deformed RHB in a Woods-Saxon basis , even , zero , even or odd , 0 or 1 2018/11/19

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) 2018/11/19

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 2018/11/19

Compare with spherical RCHB model< 20Ne, NL3, Rmax = 10 fm, r = 0.2 fm V0 = 200 MeV fm3, Ecut= 100 MeV 2018/11/19

Compare with deformed RMF in a WS basis< 2018/11/19

Compare with deformed RMF+BCS in a WS basis < 2018/11/19

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. 2018/11/19

Shan-Gui Zhou ITP-CAS Beijing Thanks 2018/11/19