SLIDE 1
Gogny-TDHFB による 原子核の非線形振動と緩和
橋本幸男, 笹倉啓介 筑波大学数理物質科学研究科
- 1. Introduction
- 2. From TDHF to TDHFB
＊Ti52 の場合 ＊Si26 の場合 ３．まとめ
Gogny-TDHFB , - - PowerPoint PPT Presentation
Gogny-TDHFB , - - PowerPoint PPT Presentation
Gogny-TDHFB , 1. Introduction 2. From TDHF to TDHFB Ti52 Si26 1 Introduction
SLIDE 2
SLIDE 3
エネルギーの移動 : 相対運動 内部の集団運動・核子の運動
- ne-body dissipation
(2 body collision neglected) その微視的なメカニズムは ??? chaotic motion in TDHF (?)
SLIDE 4
BKN force TDHF
three-level model
SLIDE 5
２．From TDHF to TDHFB
☆対相関の効果を時間依存平均場で見る ⇒ エネルギー移動の仕組みを理解する
SLIDE 6
Equations of motion of matrices U & V
see Ring & Schuck
SLIDE 7
Coulomb part is NOT included
Gogny‐D1S
・basis function：three-dimensional harmonic oscillator wave functions ・space： Gauss part density depende part L‐S part
5
z y x shell
n n n N
SLIDE 8
Q0 ：matrix representation of multipole operator
initial U & V
HFB ground state U, V
初期条件 ・Q20 type impulse on ground state（impulse type） ・CHFB状態（constraint type）
SLIDE 9
Example-1: 20O quadrupole oscillation (small amplitude)
SLIDE 10
Example-2. Spherical case: 26Ne IV dipole response
- S. Peru, H. Goutte, J.F. Berger,
- Nucl. Phys. A788(2007), 44-49.
(Nshll = 5) TDHFB
SLIDE 11
52Ti の場合
☆ 微小振幅・小励起エネルギー ⇒ 大振幅・大励起エネルギーへ
SLIDE 12
Energy [MeV]
energy curve E vs <Q20 > (52Ti (Z = 22, N = 30))
Total Energy Pairing E (p) Pairing E (n)
Q20 [fm2] prolate
- blate
Energy
pairing energy
SLIDE 13
Total Energy Pairing E (p) Pairing E (n)
… pairing in neutrons ( impulse 、Q20 = 140 , 230〜 240 [fm2] ) … NO pairing in neutrons (Q20 = 150 〜 200 [fm2])
initial conditions
impulse (4.32[MeV]) constraints
Energy [MeV] Q20 [fm2]
SLIDE 14
… no pairing in neutrons
- scillation around Q20
= 85 [fm2] … pairing in neutrons
- scillations around Q20
= 0 [fm2]
Q20 [fm2] Q20 [fm2]
SLIDE 15
・two types of oscillations after relaxation process ・effects of pairing correlations in oscillating motions put focus on the occupation probabilities of TDHFB orbitals
SLIDE 16
initial condition：Q20 = 170 [fm2]
Ex = 2.56[MeV] E_pair(proton) = ‐ 3.55[MeV] E_pair(neutron) = 0 [MeV]
Case 1: oscillations around Q20 = 85 [fm2] (constraint Q20 = 170 [fm2])
Q20 [fm2]
time dependence
- f occupation probability（neutrons）
・no pairing in neutrons no jump into ground state pocket ( Q20 = 0[fm^2])
SLIDE 17
・two main trajectories ・Q20
- scillation seesaw in occupation probabilities
Case 2: oscillations around ground state ( Q20 = 0 [fm^2]) (impulse type)
impulse type
Ex = 4.32[MeV] E_pair(proton) = ‐ 4.79 [MeV] E_pair(neutron) = ‐ 2.75 [MeV]
Q20 [fm2]
time dependence
- f occupation probability（neutrons）
SLIDE 18
Case 3: jump into ground state pocket (constraint Q20 = 140 [fm2])
Q20 [fm2]
initial condition： Q20 = 140 [fm2]
Ex = 1.37[MeV] E_pair(proton) = ‐ 3.27 [MeV] E_pair(neutron) = ‐ 0.07 [MeV]
・sudden change in occupation probability Q20 oscillation jumps ・characteristic two orbitals ・in phase with Q20 oscillation
Q20 [fm2]
time dependence
- f occupation probability（neutrons）
SLIDE 19
variations of occupation probabilities of two main trajectories(constrait Q20 = 140 [fm2])
( nx , ny , nz ) = ( 3, 0, 0 ) ( nx , ny , nz ) = ( 0, 3, 0 ) , ( 0, 0, 3 )
prolate
- blate
prolate side … green orbital main
- blate phase … blue orbital main
拡大図
SLIDE 20
change of occupation probability quadrupole oscillation
Energy [MeV] Q20 [fm2] prolate
- blate
s1/2 p3/2 p1/2 d5/2 s1/2 d3/2 f7/2 p3/2
52Ti (Z = 22, N = 30) ⼀粒⼦エネルギー (中性⼦)
EF
SLIDE 21
initial condition： Q20 = 240 [fm2]
Ex = 7.37[MeV] E_pair(proton) = ‐ 4.79 [MeV] E_pair(neutron) = ‐ 0.89 [MeV]
Case 4: slow relaxation (constraint Q20 = 240 [fm2])
slow relaxation ・occupation probabilities of many orbitals change → two main orbitals becomes unclear
準粒⼦軌道の占有率の時間変化（中性⼦）
Q20 [fm2]
SLIDE 22
initial condition： Q20 = ‐ 165[fm2]
Ex = 4.25 [MeV] E_pair(proton) = ‐ 4.32 [MeV] E_pair(neutron) = ‐ 2.16 [MeV]
準粒⼦軌道の占有率の時間変化（中性⼦）
Case 5: from oblate (initial Q20 = ‐ 165 [fm2])
SLIDE 23
Time [fm] Energy [MeV] Q20 [fm2] Initial Q20 = 140
Ex E= 1.37[MeV] Pairing E (p)=‐3.27[MeV] Pairing E (n)=‐0.07[MeV]
Initial Q20 = 240
Ex E= 7.37[MeV] Pairing E (p)=‐4.79[MeV] Pairing E (n)=‐0.89[MeV]
Initial Q20 = 200
Ex E=4.32 [MeV] Pairing E (p)=‐4.19[MeV] Pairing E (n)=0 [MeV]
Impulse type
Ex E= 4.32[MeV] Pairing E (p)= ‐4.79[MeV] Pairing E (n)= ‐2.75[MeV]
SLIDE 24
Amplitudes of slow oscillations with excitation energy from 2.72 to 10.85 [MeV] grow very slowly. (MeV)
SLIDE 25
Si26の場合
Q20 (fm^2)
対エネルギー (MeV) Q20 vs 時間
SLIDE 26
SLIDE 27
まとめ
微⼩振幅から振幅を増加させたときの核の振動運動と、 その時の対相関の働き → Gogny⼒を⽤いたTDHFB法により、
52Ti などの四重極型振動運動
中性⼦の対相関の有無によって、 ⼆種類の振動モードが現れる 基底状態まわりの振動 ・四重極振動と、粒⼦が詰まる軌道の⼊れ替わりが対応 → 断熱的描像 ・中性⼦の対相関の効果によって、四重極振動の周期や、 基底状態まわりに乗り移るまでの時間が決まる