Post on 03-Feb-2016
description
Nuclear Dynamicsin 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 rep. vs Energy rep. Nuclear TDDFT (TDHF)
Giant resonances
Nuclear screening effects at drip line
Time-dependent approach to quantum mechanical problems
Basic equations• Time-dep. Schroedinger eq.• Time-dep. Kohn-Sham eq.
Energy resolution ΔE 〜 ћ/T All energies
Boundary Condition• No need for BC• Approximate BC• Easy for complex systems
Basic equations• Time-indep. Schroedinger eq. • Static Kohn-Sham eq.
(Eigenvalue equation)
Energy resolution ΔE 〜 0 A single energy point
Boundary condition• Exact scattering boundary co
ndition is possible• Difficult for complex systems
Time Domain Energy Domain
)()( tHtt
i EH
Applications of the time-dependent framework
TDHF with effective interactions
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).
Skyrme TDHF in real space
X [ fm ]
y [
fm ]
3D space is discretized in lattice
Single-particle orbital:
N: Number of particles
Mr: Number of mesh points
Mt: Number of time slices
Nitt MtnMrknkii ,,1,)},({),( ,1
,1
rr
),()()](,,,,[),( exHF ttVthtt
i iti rJsjr �
Time-dependent Hartree-Fock equation
Spatial mesh size is about 1 fm.
Time step is about 0.2 fm/c
Nakatsukasa, Yabana, Phys. Rev. C71 (2005) 024301
ri~
Real-time calculation of response functions
1. Weak instantaneous external perturbation
2. Calculate time evolution of
3. Fourier transform to energy domain
dtetFtd
FdB ti
)(ˆ)(Im1)ˆ;(
)(ˆ)( tFt
)(ˆ)(ext tFtV
)(ˆ)( tFt
ω [ MeV ]
d
FdB )ˆ;(
LEOR & HEOR in 16O
Exp for HEOR
BKN with continuum
SGII without continuum
0 10 5020 30 40E [ MeV ]
IS O
ctu
pole
Str
eng
th [
fm6/M
eV
]
300
Low-lying 3–
stateSGII int.→ E ≈ 7, 13, 14 MeV
Exp . → E ≈ 6.1, 11.6, 13, 14 MeV
Perrin et al. (1977)
E1 resonances in 16,22,28O
0 20 400
50
0
050
50
E [ MeV ]
σ [
mb
]σ
[ m
b ]
σ [
mb
]16O
22O
28O
SGII parameter set
Г=0.5 MeV
Note: Continnum is NOT taken into account !
Leistenschneider et al, PRL86 (2001) 5442
Berman & Fultz, RMP47 (1975) 713
Giant dipole resonance instable and unstable nuclei
npClassical image of GDR
Neutrons
Protons
δρ> 0
δρ< 016O
ppp tt 0)()(
nnn tt 0)()( Time-dep. transition density
28O
Skyrme HF for 8,14Be
S.Takami, K.Yabana, and K.Ikeda, Prog. Theor. Phys. 94 (1995) 1011.
8Be
14Be
Neutron Proton
x
z
x
y
x
z
Solid: K=1Dashed: K=0
nnn tt 0)()(
8Be
14Be
δρ> 0
δρ< 0
Giant dipole resonance
n
p
n
p
“Screening”N=Z nuclei Neutron-rich
E1 polarizability
Neutrons
Protons
8Be
No dynamical screening With dynamical screening
NeutronsProtons
Protons
Protons
Neutrons
Neutrons
Total Total
Total Total
1
11
Eext
iiEiE
DV
DD
14Be 14Be
8Be
Negative polarization of weakly-bound neutrons
No dynamical screening Dynamical screening
tEext
+
+
+
+
+
+
+
-
-
-
-
-
-
-
tEind
)1(ext EV
npV
n p
Electronic dynamical screening Nuclear dynamical screening
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)
)()'(2)( VEEiS k'kk'kk'
Boundary Condition
0extV
ri~
Absorbing boundary condition (ABC)
Absorb all outgoing waves outside the interacting region
trriHtrt
i ,~,
How is this justified?
All the scattering information resides in the interacting region.
iiiE
iEt cctFtedtdE
EEdB..)(),(),(Im
1),( *)0(
0
/
rr
Localized w.f.
T. Nakatsukasa, K. Yabana, J. Chem. Phys. 114(2001)2550.
Linear optical absorption
ExpTDDFT
Without dynamical screening(frozen Hamiltonian)
TDDFT accurately describe optical absorptionDynamical screening effect is significant
),()],([),( trtrnhtrt
i ii
),()]([),( 0 trrnhtrt
i ii
withwithout
Dynamical screening
tEext
++
+
++
+
+
--
--
-
-
-
tEind
PZ+LB94
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
Positive-parity
1p-1h 2 ω0 excitations