Transcript Document

Deformed relativistic Hartree
Bogoliubov model in a WoodsSaxon 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 WoodsSaxon basis
A brief introduction to RMF
Spherical RMF in a Woods-Saxon basis
Deformed RHB in a Woods-Saxon basis
Summary
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Exotic nuclei
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Characteristics of halo nuclei
Weakly bound; large spatial extension
Continuum can not be ignored
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BCS and Continuum
1 r  ~ U r 
2 r  ~ V r 
Positive energy States
Even a smaller occupation
of positive energy states
gives a non-localized density
Bound States
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Dobaczewski, et al., PRC53(96)2809
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Contribution of continuum in r-HFB
1 r  ~ U r 
2 r  ~ V r 
Positive energy States
• V(r) determines the density
• the density is localized even
if U(r) oscillates at large r
Bound States
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Dobaczewski, et al., PRC53(96)2809
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Hartree-Fock Bogoliubov theory
 Deformed relativistic HFB in r space
Terasaki, Flocard, Heenen & Bonche, NPA 621, 706 (1996)
Stoitsov, Dobaczewski, Ring & Pittel, PRC61, 034311 (2000)
Terán, Oberacker & Umar, PRC67, 064314 (2003)
 Deformed relativistic Hartree-Bogoliubov or Hartree-FockBogoliubov theory in harmonic oscillator basis
Vretenar, Lalazissis & Ring, PRL82, 4595 (1999)
No deformed relativistic Hartree-Bogoliubov or HartreeFock-Bogoliubov theory in r space available yet
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Relativistic mean field model
1
L   i i     M  i      U ( )  g i i
2
1
1 2

     m   g i   i
4
2
1    1 2   
 
 R R  m     g  i     i
4
2
1
13

 F F  e i
  A i
4
2
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
2015/7/7
Meng, Toki, Zhou, Zhang, Long & Geng,
Prog. Part. Nucl. Phys. In press
8
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
…
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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
…
Meng, Toki, Zhou, Zhang, Long & Geng,
Prog. Part. Nucl. Phys. In press
Vretenar, Afnasjev, Lalazissis & Ring
Phys. Rep. 409 (05) 101
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11Li：self-consistent
RMF description
Meng & Ring, PRL77,3963 (1996)
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Deformed Halo? Deformed core?
Decoupling of the core and valence nucleons？
11,14Be
Ne isotopes
…
Misu, Nazarewicz, Aberg, NPA614(97)44
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
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RMF in a Woods-Saxon basis: progress
Shapes
Mean field or
Beyond
Schrödinger
W-S basis
Dirac
W-S basis
DWS
√
Axially Rela. Hartree + BCS
deformed
DRH DWS
√
Axially Rela. Hartree-Bogoliubov
deformed
DRHB DWS
√
Triaxially Real. Hartree-Bogoliubov
deformed
TRHB DWS
Spherical Rela. Hartree
SRH SWS
SRH
Many difficulties to solve deformed problem in r space
Woods-Saxon basis might be a reconciler between
the HO basis and r space
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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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Deformed RHB in a Woods-Saxon basis
Axially deformed nuclei

 km
  ukm,i aim  vkm,i~ a~im
i 
 ukm,i im rp 
U km  rp 


 m 

 V rp      v m ~ ~ rp 
 k
 i  k ,i  im

1  iGi ( r )Ym ( ) 

im ( rp)  
r   Fi ( r )Ym ( ) 
rp; r ' ' p' U E r ' ' p'
U E rp 
 hrp; r ' ' p'  
  E


d r ' 

*

p
   rp; r ' ' p'  hrp; r ' ' p'    VE r ' ' p' 
 VE rp  
3



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      
    
      
  ukm,i  
  vkm,i~  
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Deformed RHB in a Woods-Saxon basis
  him ,i ' '    I
   mi~ ,i ' '   mi ,i '~ '  
V r   V r Y 

  mi ,i '~ '  
   him~,i '~ '    I
S r    S r Y 

, even
, zero
him ,i ' '     drGi r Gi ' ' r V r   S r   Fi r Fi ' ' r V r   S r A ,  ,  ' , m 

S
r,1 2   Y SM S 1 2 SM
 ; p1 p2 r 
 SM S
mi1 1 ,i2~2 
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, even or odd
, 0 or 1
1
S
    M S ,   SM;S 1 p1 2 p2  drRi1p11 r Ri2p2 2 r SM
 ; p1 p2 r 
2  SM S
p1 p2
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Pairing interaction
Phenomenological pairing interaction with parameters:
V0, 0, , and a cut off parameter Ecut
   r   
 
1
V pp  V0 1   1   r1  r2  1   1 2 
  0  
4


Meng & Ring, PRL77,3963 (1996)
Phenomenological relativistic pairing force with
parameters: c0 and a cut off parameter Ecut

v0
v
pp
pp
2
2
s 1 2
v
V pp  V  V  V
s
pp

 

 c0  C    C  C 1 2  r1  r2 
Cs 
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g
g
, C  
m
m
2
v
Serra & Ring, PRC65,064324 (2002)
17
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
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Compare with spherical RCHB model<
20Ne,
NL3, Rmax = 10 fm, r = 0.2 fm
V0 = 200 MeV fm3, Ecut= 100 MeV
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Compare with deformed RMF in a WS basis<
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Compare with deformed RMF+BCS in a WS
basis <
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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 WoodsSaxon basis
 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
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