Document

2nd International Conference on
Frontiers in Nuclear Structure,
Astrophysics and Reactions
(FINUSTAR 2)
Aghios Nikolaos, Crete, Greece,
September 10-14, 2007
21世紀COE外国旅費補助・成果報告会
物理学第２教室原子核理論研究室
杉本聡
会議概要１
• 場所：
ギリシアクレタ島アギオス・ニコラウス
Iberostar Mirabello Beach Hotel and Village
• 開催日程：２００７年９月１０～１４日
ミノタウロス
クノッソス宮殿
（部屋数１２００以上）
アギオス・ニコラウス
会議概要２
• 参加人数：１４０名
（フランス1４、イタリア１３、アメリカ・ベルギー・ドイツ各１０、ギリシア９、
日本８、イギリス７、チェコ・フィンランド・南アフリカ各５、他２２カ国４４名）
• 講演数口頭発表７８、ポスター４３
• 招待講演２１、Invited Contribution 9
核構造理論６，核構造実験１０，核反応理論４，核反応
実験６，次期計画４
そのうちγ線分光関係８，天体核関係７
不安定核物理の発展
From http://www.rarf.riken.go.jp/
理研→RIBF
GSI→FAIR
GANIL→SPIRAL2
etc.
Pigmy resonance
From Aumann
6th CNS International Summer SCHOOL CISS07
P. Adrichet al., PRL 95 (2005) 132501
中性子スキンと芯核の相対的な振動運動モード
Study of the tensor correlation
in a neutron-rich sd-shell
region with the chargeand parity-projected HartreeFock methods
Satoru Sugimoto
Kyoto University, Japan
Hiroshi Toki (RCNP, Japan), Kiyomi Ikeda(RIKEN, Japan)
Tensor force
• The strong tensor force is characteristic of
nuclear many-body systems
• The tensor force (pion) plays important roles in
nuclear structure.
– The tensor force produces large attractive energy in
nuclei.
– The tensor force is responsible for the saturation
mechanism of nuclear matter.
• We want to reveal the roles of the tensor force in
nuclei.
– The effect of the tensor force on shell structure.
• Shell evolution (Otsuka, Suzuki et al.)
– The change of the tensor correlation in neutron-rich
nuclei. （テンソル力は陽子‐中性子間に強く働く）
One-pion exchange potential
V
(OPEP)
1 f p 2 r r r r r r e- mp r
(r ) = t ×t 2 (s 1 ×Ñ 1 )(s 2 ×Ñ 2 )
2 1
4p mp
r
ù
é
ú
ê
ì
ü
m
r
m
r
2
ú
p
p
ï
ï
ö
1 f p r r êr r æ
e
4p r ÷
3
3 ïe
ï
ç
ú
=
t 1 ×t 2 ês 1 ×s 2 ç
d(r )÷
+ S12 í 1 +
+
2ý
÷
2
ê
÷
çè r
ïï
3 4p
mp
mp r (mp r ) ïï r ú
ø
ú
ïî
ïþ
ê144444444442 4444444443
4 1444444444442
4
44444444444
4
3
ú
êë
Central
ú
Tensor
û
r r r r
(0)
3(s 1 ×r )(s 2 ×r ) r r
é[sr ´ sr ](2) ´ Y (rˆ)ù
S12 =
s
×
s
=
2
4
p
1
2
2
êë 1 2
ú
û0
r2
j1
j2
å å
m1 = - j1 m2 = - j2
l1 j1m1 , l2 j2 m2 V (OPEP) l1 j1m1 , l2 j2m2 = 0
Tensor correlation
2p-2h correlation
Particle-hole interaction
0d3/2
0d3/2
0d3/2
1s1/2
1s1/2
1s1/2
0d5/2
0d5/2
0d5/2
0p1/2
0p1/2
0p1/2
0p3/2
0p3/2
0p3/2
Proton
Proton
Neutron
0p-0h
Neutron
2p-2h
VT
VT
Proton
Neutron
j j VT j j
j j VT j j
Attractive energy
It cannot be treated in a simple Hartree-Fock
method.
->Go beyond mean field (Charge- and parityprojected Hartree-Fock method)
It can be treated in the
Hartree-Fock method.
->ls-splitting
Charge- and parity-projected
Hartree-Fock (CPPHF) method
• Tensor force is mediated by the pion.
• Pseudo scalar (s)
– To exploit the pseudo scalar character of the pion,
we introduce parity-mixed single particle state.
(over-shell correlation)
• Isovector (t)
– To exploit the isovector character of the pion, we
introduce charge-mixed single particle state.
• Projection
– Because the total wave function made from such
parity- and charge-mixed single particle states
does not have good parity and a definite charge
number. We need to perform the parity and
charge projections before variation.
-> Charge and parity-projected Hartree-Fock
equaiton
Refs. Toki et al., Prog. Theor. Phys. 108 (2002) 903.
Sugimoto et al., Nucl. Phys. A 740 (2004) 77; PRC 75 (2007) 014317; Ogawa et
al., Prog. Thoer. Phys. 111 (2004) 75; Phys. Rev. C 73 (2006) 034301.
n
p
-

p
-

+
n
+
CPPHF results for 4He and 16O
4He
xTE
HF
1.00
(Volkov No. 1
PPHF
0.96
+G3RS)
CPPHF 0.92
16O
Etot
HF
(MV1
+G3RS) PPHF
CPPHF
Etot
KE
Vtot
VC
VT
Rm
P(D)
-27.9 49.7
-77.6
-77.6
0.0 1.45 0.00
-28.3 52.5
-80.8
-75.1
-5.7 1.45 0.68
-28.7 57.8
-86.5
-73.2
-13.3 1.42 3.22
VT
VLS
KE
VC
VCoul
V3B Rm
-123.4 228.9
-416.9
0.0
-0.2
13.4 51.5 2.57
-126.6 236.5
-423.6
-5.3
-0.2
13.5 52.5 2.55
-133.3 256.5
-440.0
-17.8
-0.2
13.9 54.4 2.52
• By performing the parity and charge projection the potential
energy from the tensor force becomes sizable value.
Sugimoto et al., Nucl. Phys. A 740 (2004) 77; PRC 75 (2007) 014317
Density and charge form factor
of 16O
Density
Charge form factor
0
0.20
10
-1
0.15
HF
CPPHF
-2
10
-3
density (fm )
10
HF
CPPHF
|F(q )|
-3
2
0.10
10
-4
10
-5
10
-6
0.05
10
-7
10
0.00
-8
0
1
2
3
R (fm)
4
5
10
0
10
20
2
-2
q (fm )
• The tensor correlation induces higher
momentum component.
30
VT and VLS per particle
in closed-subshell Oxygen isotopes
(14O, 16O, 22O, 24O, 28O)
VT and VLS
VT/A and VLS/A (MeV)
0.2
2p2h tensor correlation

0.0
-0.2
s1/2
-0.4
p3/2
-0.6
-0.8
p1/2
d5/2

0d3/2
1s1/2
d3/2
VT HF
VT CPPHF
VLS CPPHF
-1.0
12 14 16 18 20 22 24 26 28 30
16O
Mass number
• The potential energy from the tensor force has the same order in
magnitude as that from the LS force.
• The tensor potential energy decreases as neutron numbers.
• Excess neutrons around 16O does not contribute to the 2p2h
correlation because there are no protons in the sd shell.
0d5/2
0p1/2
0p3/2
0s1/2
Mixing of the opposite parity
components in single-particle states
0p1/2 1s1/2
0s1/2'


0d3/2
1s1/2
0p3/2'
0.2
Pmix
0p1/2'
0d5/2
0d5/2'
0.1
1s1/2'
0p1/2
0p3/2
0d3/2'
0.0
14
16
18
20
22
24
Mass Number
26
28
16O
 Because the tensor correlation is exploited by parity mixing, the mixing
probability of opposite parity components is one of the measure for the strength
of the tensor correlation.
 j=1/2 states are affected largely by the tensor correlation.
 If a next j=1/2 orbit is occupied newly, the mixing probabilities of the j=1/2 orbit
reduce by a blocking effect.
 The excess neutrons around 16O do not contribute the tensor correlation
strongly.
0s1/2
ls splitting and the tensor force
• The effect of the tensor force on ls splitting
– HF correlation： Tarbutton et al.(HF),
Bouyssy et al.(Relativistic HF), etc.
– Shell evolution induced by the tensor force.（Otsuka,
Suzuki, Abe, Utsuno, etc)
– 2p2h correlaton: Terasawa and Arima, Andō and
Bandō, Myo et al., etc.
• Does ls splitting change in neutron-rich nuclei?
– The experiment at RIKEN
(Michimasa et al. PLB 638 (2006) 146)
D(d) in 17F(16O+p) ~ 5 MeV
→ D(d) in 23F(22O+p) ~ 4 MeV
• We study the effect of the tensor force on the lssplitting with the Hartree-Fock method.
Sugimto et al. PRC (to be published); arXiv:0705.1419
0h
V
0g
0f
1 d
Vl  s
r dr
50MeV, 
V 
0.5fm 2
1
l  s  (l  1) for l  j  1/ 2
2
1
l for l  j  1/ 2
2
Dl s  l  1/ 2
Klinkenberg RMP 24 (1952) 63
The effect of the tensor force
on ls-splitting
j =l+1/2
>
j<=l-1/2
j<’
VT()
j>

VT()
j>’
j<
j>’
j<
j>

VT reduces ls-splitting.
j<’


VT enhances ls-splitting.
1. j<-j<’ or j<-j<’: repulsion
2. j<-j>’: attraction
3. If both j<’ and j>’ orbits are fully
occupied the tensor force does not
act.
cf. Bouyssy et al. PRC 36 (1987) 380
Otsuka et al. PRL 95 (2005) 232502
j<’
VT()
j>’
j<
j>


VT does not act.
17F(16O+p)
23F(22O+p)
VT()
VT()
0d3/2
1s1/2


0d3/2
1s1/2
0d5/2
0d5/2
0p1/2
0p3/2
0p1/2
0p3/2
0s1/2
The tensor force does not act


0s1/2
The tensor force reduces
the ls splitting
Michimasa et al.
(from NPA 787 (2007) 569)
3/2+

0d3/2
1s1/2
0d5/2
5 MeV
23F
5/2+
17F
Bohr & Mottelson vol. 1

Effective Interaction in the HF cal.
• Central part
Modified Volkov No.1, m=0.59
• LS part
iW0s [k 21  d (r12 )k12 ]
d-LS:
W0=115 MeV fm5
to be determied to reproduce D(0p3/2-1-0p1/2-1)
cf. Gogny force D1
• Tensor part
G3RS
7.2MeV
3/2+
5MeV
<VLS>~-3MeV
<VLS>~+4.5MeV
4.2MeV
3/2+
<VLS>~-3.3MeV
5/2+
5/2+
17F
23F
23F
VLS+VT
only VLS
VLS+VT
<VT>~-1.8MeV
<VT>~1.3MeV
• The tensor force reduces the ls-splitting.

cf. D(0d5/2-0d3/2)= 6~7.5 MeV
in 40Ca
VT

0d3/2
1s1/2
0d5/2
Shell evolution induced by the
tensor force?
Otsuka et al. PRL 87 (2001) 082502
Summary
• We study the 2p2h tensor correlation with the CPPHF
method.
• The tensor correlation induces high-momentum
component in single-particle wave functions.
• The 2p2h tensor correlation becomes smaller with
neutron number.
• The tensor force reduces the ls-spitting for the proton
d-orbits by 3MeV in 23F. This reduction is important to
explain the experimental value in the Hartree-Fock
method.
• We also study the effect of the 2p2h tensor
correlation on the ls-splitting with the PPHF method.
It does not affect the ls-splitting largely.

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