11th International Conference on Nucleus-Nucleus Collision
San Antonio, Texas
May 30 (27-June 1), 2012
Shell evolution with tensor and
three-body forces
Takaharu Otsuka
University of Tokyo / MSU
20時14分
Outline
An overview of the evolution of shell structure in
exotic nuclei with large asymmetry in N/Z
Tensor force : robust effect & persistency
3-body force with D-excitation origin
: robust and unique effect
effect of continuum
how large ?
does it maintain features of nuclear forces ?
Monopole component of tensor force
- An intuitive picture -
TO, Suzuki, et al.
PRL 95, 232502
At collision point:
k2
k1
k = k1 – k2 , K = k1 + k2
k2
large relative
momentum k
small relative
momentum k
strong damping
wave function
of relative
coordinate
k1
loose damping
k2
k1
k1
k2
wave function
of relative
coordinate
Response to the renormalization of interactions
Renormalization
processes
- short-range
correlations
- in-medium
corrections
bare interaction for free space
V = Vc + V LS + VT
effective interaction for
a model space
V’ = V’c + V’
LS
+ V’T + VNNN + …
In general, V’x differs from Vx.
If Vx = V’x, Renormalization Persistency holds.
- only good approx. at best, but it makes sense
- new approach to nuclear forces
Treatment of tensor force by V
low k
and Q box (3rd order)
Monopole component
of tensor interactions
in pf shell
Bare (AV8’)
short-range correlation
by V low k
in-medium correction
with intermediate states
(> 10 hw, 3rd order)
V low k : Bogner, Kuo, Schwenk
only for comparison
TO, Suzuki, et al.
PRL 104, 012501 (2010)
Two major components in nuclear force
+…
Renormalization
Persistency
monopole component of
tensor force in nuclear medium
almost equal (no renormalization)
N.Tsunoda, T.O.,
K.Tsukiyama, M.H.-Jensen,
PRC84,044322 (2011)
monopole component of
tensor force in free space
Shell evolution in exotic nuclei due to tensor + central forces
 proton-neutron correlation
Changes of single-particle properties due to these nuclear forces
p3/2
N =28
d3/2
s1/2
f7/2
neutron
d5/2
proton
Z =14
42 Si
14 28
Otsuka, Suzuki and Utsuno,
Nucl. Phys. A805, 127c (2008)
exp. (4+)： RIBF data 2011
doubly
magic ?
repulsive
attractive
Potential Energy Surface
full
Tensor force removed
from cross-shell interaction
Strong oblate
Deformation
Other calculations (RMF, Gogny)
show oblate shape.
42Si
42Si
2+: Bastin, Grévy et al.,
PRL 99 (2007) 022503
PES of
w/o tensor
force
42Si
Tensor force included
(as global VMU)
42Si
spherical
oblate
with tensor
force
prolate
Spectroscopic factors
obtained by (e,e’p) on 48Ca
d3/2
s1/2
(Kramer et al., NP A679, 267 (2001) NIKHEF)
with the same tensor force
Exp.
Th.
d5/2
no tensor in the cross shell part
Exp.
Th.
Proton number 
Nuclear Chart
- Left Lower Part -
Why is the drip line of
Oxygen so near ?
next issue  oxygen anomaly and continuum
v.s. its restoration in fluorine
Neutron number 
Single-Particle Energy for Oxygen isotopes
by microscopic eff. int.
G-matrix+ core-pol. : Kuo, Brown
V
low-k
: Bogner, Kuo, Schwenk
by phenomenological eff. int.
- G-matrix + fit SDPF-M
Utsuno, O., Mizusaki, Honma,
Phys. Rev. C 60, 054315 (1999)
USD-B
Brown and Richter,
Phys. Rev. C 74, 034315 (2006)
trend
The clue : Fujita-Miyazawa 3N mechanism
(D-hole excitation)
p
D particle
m=1232 MeV
S=3/2, I=3/2
D
p
N
N
N
Most important message with Fujita-Miyazawa 3NF
m
m
m’
D
m
Renormalization
of single particle
energy
m’
+
Effective monopole
repulsive interaction
D
m’
m
Pauli blocking
m
same
Monopole part of
Fujita-Miyazawa m’
3-body force
m’
D
m
Ground-state energies of
oxygen isotopes
NN force + 3N-induced NN force
(Fujita-Miyazawa force)
Drip line
(i) D-hole excitation in a
conventional way
(ii) EFT with D
D-hole dominant
role in
determining
oxygen drip line
(iii) EFT incl. contact
terms (N2LO)
continuum
Continuum-coupled shell model (CCSM)
Hamiltonian :
approximated
by Gaussian
basis state-vector (denoted by j ):
bound states + discretized continuum states
wall very far (3000 fm, ~3000 basis states)
d3/2
s1/2
V
r
VNN +
included
240
= 220 + 2n in the space
ground state : 2n in 1s1/2
excited states of 1+ and 2+ :
1s1/2 : solution of Woods-Saxon potential with
observed Sn
diagonalize H
Eigenfunction :
RMS Radius: 16-24O
Woods-Saxon
s1/2
Harmonic Oscillator d5/2
Exp: Ozawa et al., Nucl. Phys. A693, 32 (2001)
Kanungo et al., Phys. Rev. C84, 061304 (2011)
Removal of one proton and one neutron from
26F
knockout reaction @MSU (2009)
9Be(26F,24O)X
C. Hoffman,
M. Thoennessen et al.
16O
less probable
<== large s1/2-d3/2 neutron gap
continuum
16O
H.O.
-p
-n
16O
bound nucleus
26F
16O
doorway state
excited states in 24O
16O
ground state
1s1/2 is bound.
Kanungo et al. (2009)
24
Low-lying Continuum Spectra in 24O
24O,1+
exp
Doorway state ==> continuum states in 24O
24O,
25O,
3/2+
2+
bound approximation:
Normal shell model with the same
Hamiltonian : NO continuum effect
CCSM : With continuum effect
incl. residual interaction
no int. : With continuum effect but
no residual interaction.
Continuum effect is about 1 MeV
No bound excited state.
1+-2+ splitting by 2-body interaction
1+-2+ splitting is in good agreement
with experiments.
25
Summary of the results
Peak Energies of neutron emission
SPE as bound state
2 MeV
Lowering due to continuum effect
Exp. ：MSU (Hoffman et al),
RIKEN (Elekes et al)
Continuum spectra are consistent with the shell evolution
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Ｆｌｕｏｒｉｎｅ ｉｓｏｔｏｐｅｓ
Neutron single-particle energies at N=20 for Z=8~20
solid line : full (central + tensor)
s1/2
-1.1 MeV
d5/2
-1.6 MeV
29F
well bound already
by s. p. e.
31,…F
bound through
mixing with pf shell
energy (MeV)
-2.0 MeV
14
8
A proton in d5/2 moves
neutron orbits by
d3/2
dashed line : central only
20
16
16
20
40Ca
F
d5/2
s1/2
d3/2
Z
TO, Suzuki, et al.
PRL 104, 012501 (2010)
Ca ground-state energy
Holt, TO, Schwenk, Suzuki, submitted
experiment
extrapolation
NN + 3NF
NN only
Summary
1.
Shell structure of exotic nuclei changes (or evolves), even in novel
manners some times, due to particular components of nuclear forces
 Mayer-Jensen’s magic numbers disappear and new ones arise
2. Tensor force : changes spin-orbit splitting
- proton-neutron interaction
- in-medium ~ bare under the concept Renormalization Persistency
-> many cases from p-shell to superheavy
-> 42Si (Bastin, Grévy, et al. 2007 GANIL, Takeuchi et al. 2011-12 RIKEN)
oblate shape rather than spherical sub-magic of Z=14 and N=28
3. Fujita-Miyazawa 3-body force produces repulsive effective
interaction between valence neutrons in general.
-> oxygen drip line at N=16, similar situations e.g. in Ca isotopes
-> contributes to shell evolution
4. Continuum effect sizable even for d3/2 (~ 1 MeV shift for oxygen)
shell evolution in continuum … visible and interesting in future
transfer reactions with RI beams are useful
Collaborators
N. Tsunoda
Tokyo
K. Tsukiyama Tokyo
M. H.-Jensen Oslo
T. Suzuki
M. Honma
Y. Utsuno
B.A. Brown
Nihon U.
Aizu
JAEA
MSU
A. Schwenk Darmstadt
J. Holt
Oak Ridge
K. Akaishi
RIKEN
R. Fujimoto
Hitachi (work @Tokyo)