Transcript 理研2005.12

Nuclear Dynamics
in Time-Dependent Picture
Takashi Nakatsukasa
University of Tsukuba
Collaborator: Kazuhiro Yabana (U.T.)
The 6th China-Japan Joint Nuclear Physics Symposium, May 16-20, 2006
Time-dependent approach to
quantum mechanical problems


Time rep. vs Energy rep.
Nuclear TDDFT (TDHF)
Giant resonances
Nuclear screening effects at drip line
Time Domain
Basic equations
• Time-dep. Schroedinger eq.
• Time-dep. Kohn-Sham eq.

i  (t )  H (t )
t
Energy Domain
Basic equations
• Time-indep. Schroedinger eq.
• Static Kohn-Sham eq.
H  E
(Eigenvalue equation)
Energy resolution
ΔE〜ћ/T
All energies
Energy resolution
ΔE〜0
A single energy point
Boundary Condition
• No need for BC
• Approximate BC
• Easy for complex systems
Boundary condition
• Exact scattering boundary
condition is possible
• Difficult for complex systems
Applications of the timedependent framework
Fusion reactions:
NPA722 (2003) 261c; PTPS154 (2004) 85; nucl-th/0506073 (PLB)
Linear response in molecules:
JCP114 (2001) 2550; CPL374 (2003) 613
Linear response in nuclei:
PTPS146 (2002) 447; EPJA20 (2004) 163; PRC71 (2005) 024301
In this talk, we focus on the linear density response (RPA).
TDHF with effective interactions
Skyrme TDHF in real space
Time-dependent Hartree-Fock equation

~ r 
 i



i  i (r , t )  hHF [  , , j, s, J ]( t )  Vext (t )  i (r , t )
t
3D space is discretized in lattice
Single-particle orbital:
Mt
i (r, t )  {i (rk , tn )}nk 11,,
Mr , i  1,, N
N: Number of particles
y [ fm ]
Mr: Number of mesh points
Mt: Number of time slices
Spatial mesh size is about 1 fm.
Time step is about 0.2 fm/c
Nakatsukasa, Yabana, Phys. Rev. C71 (2005) 024301
X [ fm ]
Real-time calculation of
response functions
1. Weak instantaneous external
perturbation
(t ) Fˆ (t )
Vext (t )  Fˆ (t )
2. Calculate time evolution of
(t ) Fˆ (t )
3. Fourier transform to energy domain
dB(; Fˆ )
1
  Im  (t ) Fˆ (t ) ei t dt
d

dB(; Fˆ )
d
ω [ MeV ]
Exp for HEOR
LEOR & HEOR
16
in O
Perrin et al. (1977)
300
IS Octupole Strength [ fm6/MeV ]
BKN with continuum
0
Low-lying 3– state
SGII without continuum
SGII int.→ E ≈ 7, 13, 14 MeV
Exp .
10
20
30
E [ MeV ]
40
50
→ E ≈ 6.1, 11.6, 13, 14 MeV
50
σ [ mb ]
16O
Leistenschneider et al,
PRL86 (2001) 5442
0
50
22O
σ [ mb ]
Berman & Fultz, RMP47 (1975) 713
SGII parameter set
Г=0.5 MeV
Note: Continnum is NOT
taken into account !
0
50
σ [ mb ]
28O
0
E1 resonances
in 16,22,28O
0
20
E [ MeV ]
40
Giant dipole resonance in
stable and unstable nuclei
Classical image of GDR
p
n
Neutrons
 n (t )  n (t )  0 n
Time-dep. transition density
16O
δρ> 0
δρ< 0
 p (t )   p (t )  0 p
Protons
28O
Skyrme HF for
8,14Be
8Be
y
z
x
14Be
x
z
x
Neutron
Proton
S.Takami, K.Yabana, and K.Ikeda, Prog. Theor.
Phys. 94 (1995) 1011.
 n (t )  n (t )  0 n
δρ> 0
8Be
δρ< 0
Solid: K=1
Dashed: K=0
14Be
Giant dipole resonance
p
p
“Screening”
N=Z nuclei
n
Neutron-rich
n
E1 polarizability
DE1   i DE1 i
Dynamical screening
Protons
Neutrons
No dynamical screening
Protons
Total Neutrons
Total
With dynamical screening
14Be
14Be
Neutrons
8Be
No dynamical screening
i
 Vext  DE1
8Be
Protons
Total
Neutrons
Protons
Total
Negative polarization of weakly-bound neutrons
Electronic dynamical screening
Nuclear dynamical screening
Eext t 
－
－
Vext ( E1)
+
+
－
+
－
+
－
+
p
n
－
+
－
Eind t 
+
Vnp
Summary
• TDDFT(TDHF)+ABC to study dynamical
aspects of nuclear response in the continuum
• Neutron-proton attractive correlation leads to a
complex dipole motion (“screening”) for
neutron-rich nuclei
• …, though the frequency decomposition is
necessary for a definite answer.
Stable (N=Z)
Neutron-rich (N >> Z)
Boundary Condition
Absorbing boundary condition (ABC)
Absorb all outgoing waves outside
the interacting region
Vext0



~
i  r , t   H  i r  r , t 
t
 i~r 
How is this justified?
All the scattering information resides in the interacting region.
k' S k   (k'k )  2 i ( E ' E ) k' V  (  )

Localized w.f.
dB( E , E )
1
  Im  dt eiEt / (r, t )FE (r),   i( 0)i* (t )  c.c.
dE

i
0
Linear optical absorption
TDDFT accurately describe optical absorption
Dynamical screening effect is significant
PZ+LB94
i




 i (r , t )  h[n(r , t )] i (r , t )
t
with
Dynamical screening
without
i




 i (r , t )  h[n0 (r )] i (r , t )
t
TDDFT
Exp
Without dynamical screening
(frozen Hamiltonian)
T. Nakatsukasa, K. Yabana, J. Chem. Phys. 114(2001)2550.
－－
－
－
－
－
－
Eext t 
++
+
+
+
++
Eind t 
Damping width of GDR near drip line
Enhancement of escape width : Г↑
Phase space
Threshold effect
Enhancement of Landau damping : ГL↓
Large diffuseness of the mean-field potential
→ Many 1p-1h states with the same symmetry
ωGDR ≈ 79 A-1/3 MeV ≈ 2 ω0
1p-1h 2 ω0 excitations
Positive-parity