Transcript Structure of Neutron-Rich Isotopes and Three

Structure of Neutron-rich
Isotopes and
Roles of Three-body Forces
Toshio Suzuki
Nihon University
Trento, July 13, 2011
○ Shell-model interactions
important roles of tensor force
need more repulsion in T=1 monopoles
need more attraction in T=0 monopoles
1. Repusive Corrections in T=1 Monopoles
and Structure of C isotopes
with the use of a ‘phenomenological’ interaction
Three-body forces → repulsion
2. ・Structure of O and Ca isotopes and three-body
forces
‘G + FM-3N (Δ excitaions by 2π exchanges)’
・He, Sn isotopes and remaining problems
1. Repusive Corrections in T=1 Monopoles
and Structure of C isotopes
・ Important roles of tensor forces
e.g. a new p-shell Hamiltonian: SFO
・ Need for repulsion in T=1 monopoles
G-matrix vs. phenomenological interactions
・ Monopole-based-universal interaction (VMU)
・ Phenomenological shell model interaction for
neutron-rich carbon isotopes: SFO-tls
・ Structure of C isotopes
New shell model Hamiltonians Monopole terms in Vnn
→ success in better
 ( 2 J  1)  j j ; JT | V | j j ; JT 
description of spin modes V ( j j ) 
 ( 2 J  1)
in nuclei
1 2
T
M
J
1 2
J
Important roles of
tensor force
→ SFO (p, p-sd)
(Suzuki-Fujimoto-Otsuka)
●
・Shell evolutions
・GT transitions and
magnetic moments
●
Monopole-based
universal interaction
(VMU)
tensor force
1 2
SFO
p-sd shell
Suzuki, Fujimoto, Otsuka, PR C67 (2003)
V  V C (cen tral ）  V T ( ten so r ）  V L S ( L S ）
Tensor components
Shell evolution in
N=8 isotone
N=8
N=6
πp3/2
Magnetic moments of
p-shell nuclei
B(GT) for 12C →12N
SFO
present = SFO
Suzuki, Fujimoto,
Otsuka, PR C67 (2003)
PR C55,
2078 (1997)
Space: up to 2-3 hw
SFO*: gAeff/gA=0.95
B(GT: 12C)_cal = experiment
Suzuki, Chiba, Yoshida,Kajino,
Otsuka, PR C74, 034307, (2006).
●
Tensor force + repulsive
corrections in T=1
monopoles
→ SFO-tls
・Structure of neutron-rich
C isotopes
・Exotic M1 transitions in
17C
3 body forces induced by
Δ excitations
→ repulsion in T=1
monopoles
●
more repulsion than G in T=1
more attraction than G in T=0
VMU= Monopole based Universal Interaction
Tensor:
bare≈renormalized
16
20
Otsuka, Suzuki, Honma,
Utsuno, Tsunoda,
Tsukiyama, Hjorth-Jensen
PRL 104 (2010) 012501
• Modification of SFO
Full inclusion of tensor force
・p-sd: tensor->pr
LS -> srw
V  VC VT V LS
VT  V p V r
V LS  V s w  r
・sd:
Kuo G-matrix
T=1 monopole terms
more repulsive
→ SFO-tls
3=0d3/2
5=0d5/2
1=1s1/2
neutron
ESP
N dependent en
0.33 0.27 0.22
• M1 transitions in 17C
Anomalous suppression of B(M1) strength
2
B ( M 1) (10  N )
D. Suzuki et al., PL
B666 (2008)
2
N ote :
d 5 / 2 1s 1 / 2  s p a c e
|1/ 2

 | d 5 / 2
2
(0

)  1s 1 / 2 
 d 5 / 23  3 / 2  , 5 / 2  , 9 / 2 
|3/2

 | d 5 / 2
2
(2
|d5/2
2
(2


)  1s 1 / 2 
,4

)d5/2 
B (M 1 :1 / 2   3 / 2  )  0
Suzuki, Otsuka,
PR C78 (2008) 061301(R)
2. Structure of O and Ca isotopes and
three-body forces
Shell model
G-matrix vs. G-matrix + three-body force
G = BonnC, CD-Bonn for Ca; 3rd-order Q-box
G = Kuo, BonnC, CD-Bonn for O
Hjorth-Jensen, Kuo, Osnes Phys. Rep. 261 (1995) 125.
FM (Fujita-Miyazawa) three-body force
Δ-excitation by two-pion exchange
・Effective neutron single-particle energies
・Ground state energies
・Ex (2+)
・M1 transition in 48Ca
+3rd-order
core-polarization effects
Kuo (HJ): 2nd-order, up to 2hw
BonnC: 3rd-order, up to 2-4 hw
CD-BonnC: 3rd-order, up to 18hw
Hjorth-Jensen et al., Phys. Rep. 261, 125 (1995)
T. T. S. Kuo, Nucl. Phys. A103, 71 (1967)
etc.
Monopole terms from 3-body force induced
by Δ excitations and short-range terms
j j’
j’ j
X X
j j’
1
E
j
j
j’
= －
－
j j’
j’
2
| pj ' | V | hj  |  0
repulsive
Monopole terms from 3-body force
induced
by
Δ
excitations
（A）
（B）
j
j’
－
j’
j
－
j
j’
j
＋
j’
j
j’
．．．
－
＋
….
j’
j
j’
j
j’
j
 | pj | V | hj ' j ' h  |
（C）
j’
j
j
j’
2
j
j
j’
 | ph | V | jj ' j ' j  |
j’
－
j
j’
．．．
j
j’
 pj | V | jh  hj  pj ' | V | j ' h  hj '  |
2
● Oxygen
isotopes
Monopoles for sd-shell: T=1
ESPE of Oxygen Isotopes
3N →repulsion
E(2+)
Multipoles vs. monopoles
Energies of O isotopes
3-body force → drip line at 24O
Otsuka, Suzuki, Holt, Schwenk, Akaishi,
PRL 105, 032501 (2010)
Effects of breaking of 16O core
p-sd
p, p-sd: SFO
sd: G
0hw 2hw
16O 83% 17%
20O
91%
24O 97%
28O 99%
How double magic is 24O?
Cal: closed (p-d5/2-s1/2） core 87%
● Ca isotopes
Monopoles
3-body force →repulsion
Energies of Ca isotopes
E(2+)
48
3N → Shell closure at 48Ca
Multipoles vs. monopoles
B(M1)
+3N (multipole) →
concentration of M1 strength
EXP.： Steffen et al.
NP A404, 413 (1983)
(A/42)-0.35
Energy levels of odd Ca isotopes
Important roles of multipole components
● He isotopes
SPE=PKUO
p1/2: 3.8282 MeV
p3/2: 1.744 MeV
(spe) : p3/2: +0.6MeV
Erosion of N=64 magic
New magic at N=76?
Remaining Problems
• T=0 monopoles
Need attractive correction
• Microscopic derivation of single-particle
energies (J. D. Holt)
• Extension of the configuration space
sd -> sd+f7/2,p3/2 (J. D. Holt)
fp -> fp+g9/2 (J. D. Holt)
G-matrix for non-degenerate orbits (Tsunoda)
p-sd, sd-pf, pf-g9/2
Monopoles in T=0
Higher order terms
－
－
1  2
T=1
1 :
1  2
T=0
3x(-3)=-9
Monopoles for π(AV8’)
Core=4He
Summary
• Three-body force can describe well
the g.s. energies of O and Ca (and He)
isotopes, drip-line at 24O, shell closure
at 48Ca, as well as M1 transition
strength in 48Ca.
• Structure of C isotopes can be well
described by an improved
Hamiltonian with proper tensor
forces and repulsive corrections in
T=1 monopoles.
Collaborators
T. Otsuka
J. D. Holt
A. Schwenk
Univ. of Tokyo
ORNL
Darmstadt
殻模型
H = T + U(r) + Σi>jVij = H0 + V
一体場 + 残留相互作用
U(r) = Uc(r) +ULS(r)L・S
殻模型相互作用
・Microscopic interaction derived from NN interaction
1. Renormalization of repulsive core part of NN interaction
Q 2p
G-matrix: G (E )  V  V
G (E )
E  H0
 a  a 
Q 2p
E  H0
Ga
 a | G | b  a | V |  b 
cf .   a | V |  b   
sum of ladders
V_{low-k}
integrating out high momentum components of two-nucleon
interaction
+3rd-order
core-polarization effects
Hjorth-Jensen et al., Phys. Rep. 261, 125 (1995)
Good energy levels except for a few cases:
e.g. closed-shell struture of 48Ca can not be obtained
Problems in saturation (binding energies)
・Phenomenological interaction
single particle energies + fitted two-body matrix elements
e.g. p-shell: Cohen-Kurath
p-sd:
Millener-Kurath
sd:
USD
etc.
● Oxygen
isotopes
Monopoles for sd-shell: T=1
● Oxygen
isotopes
Monopoles for sd-shell: T=1
ESPE of Oxygen Isotopes
3N →repulsion
ESPE of Oxygen Isotopes
3N →repulsion
E(2+)
Energies of O isotopes
3-body force → drip line at 24O
Otsuka, Suzuki, Holt, Schwenk, Akaishi,
PRL 105, 032501 (2010)
Effects of breaking of 16O core
p-sd
p, p-sd: SFO
sd: G
0hw 2hw
16O 83% 17%
18O 87%
20O 91%
22O 95%
24O 97%
26O 98%
28O 99%
Energies of Ca isotopes
E(2+)
48
3N → Shell closure at 48Ca
14C
→ 14N
SFO
B(GT) for 14N -> 14C
KVI
SFO
RCNP
Negret et al., PRL 97 (2006)
14C
-> 14Ng.s. Bonn-B 0hw
SFO-ｔｌｓ
VT  f * V p  r
Monopoles in T=0
Higher order terms
－
－
1  2
T=1
1 :
1  2
T=0
3x(-3)=-9
Monopoles for π(AV8’)
Core=4He
Erosion of N=64 magic
New magic at N=76