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→ success in better description of spin modes in nuclei
● Important roles of tensor force → SFO (p, p-sd)(Suzuki-Fujimoto-Otsuka)
・ Shell evolutions ・ GT transitions and magnetic moments
● Monopole-based universal interaction (VMU)
Monopole terms in Vnn
tensor force
1 2 1 2T JM 1 2
J
(2J 1) j j ;JT | V | j j ;JTV ( j j )
(2J 1)
SFO p-sd shell C T LSV V (central V (tensor V (LS ) ) )
Tensor components
Suzuki, Fujimoto, Otsuka, PR C67 (2003)
Shell evolution inN=8 isotone
πp3/2
N=6
N=8
B(GT) for 12C →12N
present = SFO Suzuki, Fujimoto, Otsuka, PR C67 (2003)
Magnetic moments of p-shell nuclei
SFO*: gAeff/gA=0.95
B(GT: 12C)_cal = experiment
SFO
Space: up to 2-3 hw
PR C55, 2078 (1997)
Suzuki, Chiba, Yoshida,Kajino, Otsuka, PR C74, 034307, (2006).
more repulsion than G in T=1more attraction than G in T=0
● 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
VMU= Monopole based Universal Interaction
Otsuka, Suzuki, Honma,Utsuno, Tsunoda, Tsukiyama, Hjorth-Jensen PRL 104 (2010) 012501
Tensor: bare≈renormalized16
20
• Modification of SFO Full inclusion of tensor force ・ p-sd: tensor-> LS ->
・ sd: Kuo G-matrix T=1 monopole terms more repulsive → SFO-tls
C T LS
T
LS
V V V V
V V V
V V
3=0d3/25=0d5/21=1s1/2
neutron
N dependent en 0.33 0.27 0.22
ESP
• M1 transitions in 17C Anomalous suppression of B(M1) strength
D. Suzuki et al., PL B666 (2008)
2 21 10( ) ( )NB M
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
core-polarization effects
+3rd-order
etc.Hjorth-Jensen et al., Phys. Rep. 261, 125 (1995) T. T. S. Kuo, Nucl. Phys. A103, 71 (1967)
Kuo (HJ): 2nd-order, up to 2hwBonnC: 3rd-order, up to 2-4 hwCD-BonnC: 3rd-order, up to 18hw
- = -
X X
Monopole terms from 3-body force induced by Δ excitations and short-range terms
j j’ j’ j j’ j
j j’ j j’ j j’
21| ' | | | 0pj V hj
E
repulsive
- ...
Monopole terms from 3-body force induced by Δ excitations( A )
j j’ j’ j j j’ j j’
- -
+ +
j’ j j’ j j’ j j’ j
2| | | ' ' |pj V hj j h
( B ) j j’
- ...
….
j j’
2| | | ' ' |ph V jj j j
( C ) j’ j j j’
j j’ j j’
| | ' | | ' ' |pj V jh hj pj V j h hj
Monopoles for sd-shell: T=1
● Oxygen isotopes
ESPE of Oxygen Isotopes
3N →repulsion
E(2+)
Multipoles vs. monopoles
Energies of O isotopes
3-body force → drip line at 24OOtsuka, Suzuki, Holt, Schwenk, Akaishi,
PRL 105, 032501 (2010)
Effects of breaking of 16O core
0hw 2hw 16O 83% 17%
20O 91%24O 97%28O 99%
p-sdp, p-sd: SFOsd: G
How double magic is 24O?Cal: closed (p-d5/2-s1/2 ) core 87%
Monopoles
3-body force →repulsion
● Ca isotopes
Energies of Ca isotopes
E(2+)
48
3N → Shell closure at 48Ca
Multipoles vs. monopoles
EXP. : Steffen et al.NP A404, 413 (1983)
B(M1)
+3N (multipole) → concentration of M1 strength
(A/42)-0.35
Energy levels of odd Ca isotopes
Important roles of multipole components
SPE=PKUO p1/2: 3.8282 MeV p3/2: 1.744 MeV
(spe) : p3/2: +0.6MeV
● He isotopes
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
- -
Higher order terms
Monopoles for π(AV8’) Core=4He
1 2 1 2
T=1 T=0 1 : 3x(-3)=-9
Monopoles in T=0
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 Univ. of Tokyo J. D. Holt ORNL A. Schwenk 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 G-matrix:
V_{low-k} integrating out high momentum components of two-nucleon interaction
2p
0
2pa a a
0
a b a b
a b
QG(E) V V G(E)
E H
QG
E H
| G | | V |
cf . | V |
sum of ladders
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
core-polarization effects
+3rd-order etc.
Hjorth-Jensen et al., Phys. Rep. 261, 125 (1995)
Monopoles for sd-shell: T=1
● Oxygen isotopes
Monopoles for sd-shell: T=1
● Oxygen isotopes
ESPE of Oxygen Isotopes
3N →repulsion
ESPE of Oxygen Isotopes
3N →repulsion
E(2+)
Energies of O isotopes
3-body force → drip line at 24OOtsuka, Suzuki, Holt, Schwenk, Akaishi,
PRL 105, 032501 (2010)
Effects of breaking of 16O core
0hw 2hw 16O 83% 17%18O 87%20O 91%22O 95%24O 97%26O 98%28O 99%
p-sdp, p-sd: SFOsd: G
Energies of Ca isotopes
E(2+)
48
3N → Shell closure at 48Ca
B(GT) for 14N -> 14C
SFO
Negret et al., PRL 97 (2006)
KVI
RCNP
14C → 14N
SFO
14C -> 14Ng.s. Bonn-B 0hw
SFO- tls
*TV f V
- -
Higher order terms
Monopoles for π(AV8’) Core=4He
1 2 1 2
T=1 T=0 1 : 3x(-3)=-9
Monopoles in T=0
Erosion of N=64 magic New magic at N=76