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Structure of exotic nuclei from relativistic Hartree Bogoliubov model (II). Shan-Gui Zhou Email: [email protected] ; 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 ii

Structure of exotic nuclei from relativistic Hartree Bogoliubov model (II)

Shan-Gui Zhou

Email: [email protected]; 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

magic numbers in super heavy nuclei
Magic numbers in super heavy nuclei

Zhang et al. NPA753(2005)106

contents
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
deformed halo deformed core
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

hartree fock bogoliubov theory
Hartree-Fock Bogoliubov theory
  • Deformed non-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

harmonic oscillator basis and r space
Harmonic oscillator basis and r-space
  • Average potential in atomic nucleus
    • Woods-Saxon potential: no analytic solution
    • harmonic oscillator potential: a good approx. for stable nuclei; matrix diagonalization
  • Drip line nuclei: large space distribution, contribution of continuum
    • HO basis: localization
    • r-space: complicated and time-consuming (deformation and pairing)
    • Woods-Saxon basis: a reconciler of r-space & HO basis?
  • Basic idea
    • Numerical solutions for spherical WS potential in r space
    • Large-box boundary condition to discretize the continuum
    • WS wave functions used as a complete basis matrix diagonalization problem
dirac ws negative energy states
Dirac-WS: negative energy states

Completeness of the basis (no contradiction with no-sea)

Underbound without inclusion of n.e. states

Results independent of basis parameters

basis dirac ws versus schroedinger ws
Dirac WS

n-max < n+max

Basis: Dirac-WS versus Schroedinger-WS

Smaller Basis!

Schroedinger WS

nFmax = nGmax + 1

spherical rela hartree calc 72 ca
Spherical Rela. Hartree calc.: 72Ca

SGZ, Meng & Ring,

PRC68,034323(03)

Woods-Saxon basis reproduces r space

rmf in a woods saxon basis progress
RMF in a Woods-Saxon basis: progress

SGZ, Meng & Ring,PRC68,034323(03)

SGZ, Meng & Ring, AIP Conf. Proc. 865, 90 (06)

SGZ, Meng & Ring, in preparation

Woods-Saxon basis might be a reconciler between the HO basis and r space

drhb matrix elements
DRHB matrix elements
  • , even

, 0

  • , even or odd

, 0 or 1

pairing interaction
Pairing interaction
  • Phenomenological pairing interaction with parameters: V0, 0, and  ( = 1)

Soft cutoff

Bonche et al., NPA443,39 (1985)

Smooth cutoff

convergence with e cut and compared to spherical rchb results
E+cut: 100 MeV

~16 main shells

dE ~ 0.1 MeV

dr ~ 0.002 fm

Convergence with E+cut and compared to spherical RCHB results
routines checks comparison with available programs
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

contents1
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
analytical continuation in coupling constant
Analytical continuation in coupling constant

Kukulin et al., 1989

Padé approximant

analytical continuation in coupling constant1
Analytical continuation in coupling constant

Zhang, Meng, SGZ, & Hillhouse,

PRC70 (2004) 034308

analytical continuation in coupling constant2
Analytical continuation in coupling constant

Zhang, Meng, SGZ, & Hillhouse,

PRC70 (2004) 034308

real stabilization method
0Real stabilization method

Hazi & Taylor, PRA1(1970)1109

Box boundary condition

Stable against changing of box size: resonance

Stable behavior: width

real stabilization method1
Real stabilization method

Zhang, SGZ, Meng, & Zhao, 2007

RMF (PK1)

real stabilization method2
Real stabilization method

Zhang, SGZ, Meng, & Zhao, 2007

RMF (PK1)

comparisons
Comparisons

RMF (NL3)

ACCC: analytical continuation in coupling constant

S: scattering phase shift

RSM: real stabilization method

Zhang, SGZ, Meng, & Zhao, 2007

summary ii
Summary II
  • Deformed exotic nuclei, particularly halo
    • Weakly bound and large spatial extension
    • Continuum contributing
  • Deformed relativistic Hartree Bogoliubov model in a Woods-Saxon basis for exotic nuclei
    • W-S basis as a reconciler of the r space and the oscillator basis
    • Preliminary results for 44Mg
    • Halo in deformed nucleus tends to be spherical
  • Single particle resonances: bound state like methods
    • Analytical continuation in the coupling constant approach
    • Real stabilization method
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