Mean Field Properties of Exotic Nuclei and the Tensor Force

1
Mean Field Properties of Exotic Nuclei andthe
Tensor Force
28th Int. School of Nuclear Physics Erice
September 16-24, 2006

• Takaharu Otsuka University of Tokyo / RIKEN

2
In recent years, as pointed out by several
speakers already, the evolution of the shell
structure has been one of the major topics of
the physics of exotic nuclei.
In this talk, I would like to discuss

• The origins of the evolution of the nuclear
  shells
• 2-body LS and tensor forces.
• 2. New mean-field model including the tensor
  force.
• How has the island of inversion been changed ?
• The present status of N34 magic number
  prediction.
• 5. Summary

3
Tensor Interaction
r meson ( pp) minor (1/4) cancellation
Ref Osterfeld, Rev. Mod. Phys. 64, 491 (92)
4
The atomic nucleus is bound due to meson
exchange. (Yukawa 1935)
Multiple pion exchanges ? strong effective
central forces in NN interaction (as
represented by s meson, etc.) ? nuclear
binding
Where can we see one pion exchange ?
One pion exchange Tensor force
First-order tensor force effect in spectroscopy ?
manifestation of pions in nuclei
5
Intuitive Picture
wave function of relative motion
large relative momentum
small relative momentum
repulsive
TO et al., Phys. Rev. Lett. 95, 232502 (2005)
6
TO et al., Phys. Rev. Lett. 95, 232502 (2005)
Monopole Interaction of the Tensor Force
j
neutron
j
j
proton
j
Identity for tensor monopole interaction
( j j)
( j j
(2j 1) vm,T (2j
vm,T monopole strength for isospin T
7
Change of proton single-particle energies due to
the tensor force (p r meson exchange) calculatio
n only
taken from GXPF1 interaction
Tensor monopole
Low-lying 2 levels in Ni, M. Sawicka et
al., Phys. Rev. C68, 044304 (03)
68Ni
78Ni
8
Neutron single-particle energies

• Mean-field models
• (Skyrme or Gogny)
• do not reproduce this
• reduction.
• Tensor force effect
• due to vacancies of
• proton d3/2 in 4718Ar29
• 650 (keV) by pr meson
• exchange.

f 5/2
f 7/2
9
Implementation of tensor interaction into mean
field calculations
Gogny interaction (J. Decharge and D. Gogny,
1980)
(1ssttsstt) (Gauss1 Gauss2) Density Dep.
zero range
finite range
Successful descriptions of various properties
with D1S interaction (J.F. Berger et al., Nucl.
Phys. A428, 23c (84))
Tensor interaction is added
All parameters are readjusted
Nuclear matter properties reproduced with
improvement of imcompressibility
Gogny-Tokyo interaction - 2 (GT2)
10
Triplet-Even potential due to the Tensor force
11
Single-particle energies of exotic Ni isotopes
relevance to R-process s.p.e.s binding
energies
TO, Matsuo, Abe, Phys. Rev. Lett. in press (2006)
12
2-body LS force
Vautherin - Brink
One-body mean potential
Proton
Neutron
13
Conventional image of ls splitting change
ls splitting smaller
(Scale-type ls quenching)
14
Wave functions of f7/2 and f5/2 and derivatives
of densities
neutron
proton
f5/2
f7/2
derivatives of densities
Position-type ls quenching
Peaks of derivatives do not get lower, but move
outwards.
Scale-type ls quenching
TO, Matsuo, Abe, Phys. Rev. Lett. in press (2006)
15
Contributions of Central, 2-body LS, and Tensor
components to the change of f7/2 f5/2 gap in
going from N40 to N50 (g9/2 occupancy)
Central and 2-body LS almost the same among
three calculations
Tensor largest effect
TO, Matsuo, Abe, Phys. Rev. Lett. in press (2006)
16
Z51 isotopes
1g7/2 protons
exp.
1h11/2 neutrons
Exp. data from J.P. Schiffer et al., Phys. Rev.
Lett. 92, 162501 (2004)
17
RIA region
GT2
RIBF region
D1S
Neutron h11/2 occupancy
Neutron h9/2 occupancy
TO, Matsuo, Abe, Phys. Rev. Lett. in press (2006)
18
Two Gogny(-type) interactions D1S and GT2
w/o tensor
with tensor
A similar change in the shell model with
SDPF-M int.
TO, Matsuo, Abe, Phys. Rev. Lett. in press (2006)
19
Island of Inversion is being changed
By now, we know
Island of Inversion region of intruder ground
states
Only 9 nuclei in the original model (1990)
Phys. Rev. C 41, 1147 (1990), Warburton, Brown
and Becker
20
31Mg19
Phys. Rev. Lett. 94, 022501 (2005), G. Neyens, et
al.
Outside the original Island of Inversion
Strasbourg unmixed
Tokyo MCSM
USD (only sd shell)
1/2 state comes down by 2 MeV from USD result by
strong mixing between sd and pf shell
configurations due to narrower N20 gap ?
fine details to be refined (odd-A nuclei are
difficult)
21
Exotic Ca Isotopes N 32 and 34 magic numbers ?
GXPF1B int. p3/2-p1/2 part refined from
GXPF1 int. (G-matrix problem)
2
2
Some exp. levels priv. com.
22
Effective single-particle energies of Ca, Ti and
Cr isotopes
Monopole effect of tensor force
34
34
Gap 2 MeV at N32 and 3 MeV at N34
Gap 2 MeV at N32 and 1.5 MeV at N34
23
Comparison with G-matrix polarization correction
KB3G vs. G-matrix (Bonn-C)
GXPF1B vs. G-matrix (Bonn-C)
GXPF1B (MeV)
KB3G (MeV)
G-matrix (MeV)
G-matrix (MeV)
each point a 2-body matrix element
24
Stancu, Brink and Flocard, Phys. Lett. 68B, 108
(1977)
Zero-range spin-momentum tensor coupling term
This is not be a good approximation to the tensor
force itself, but may simulate the monopole
effect of the tensor shown below, picking up
differences in relative momenta.
25
Summary
Nuclear shell evolves in unique ways as compared
to other physical systems (e.g. electrons)
Note that DN must be 10 to see this ? RNB !
Shell evolution due to tensor interactions

• drives j or jway
• intuitive picture ? from p-shell to
  superheavies

N16/20 gap, f7/2-f5/2 in 46Ar-48Ca,
Federman-Pittel mechanism (g7/2 - h11/2
repulsion ? 132Sn), Exotic Ni (Z28 gap) , Z64
submagic, Sb (Sn) RIBF ? RIA

• makes mean-field approaches more exciting and
  important

Shell evolution due to 2-body LS interactions
position-type mechanism ? ls splitting decreases
26
Remark on forces
Tensor force Changes in single particle
properties Simpler
origin dominated by
one pion exchange
(minor contributions from r (pp), )
?? Chiral Perturbation
Physics opened by upcoming RNB machines is
connected at a deeper level to QCD
27
Collaborators
D. Abe Tokyo T. Matsuo Hitachi
Ltd. T. Suzuki Nihon U. R. Fujimoto U.
Tokyo M. Honma U. Aizu H. Grawe
GSI Y. Akaishi KEK
28
END
29
Changes of N51 neutron effective
single-particle energies from Zr to Sn
N51 isotones
repulsion between g7/2 and h11/2
Federman-Pittel mechanism
Lines p r meson tensor
Points exp. level
protons in g9/2
Zr
Sn
shown relative to d5/2
30
2
1
N94 ? 104
0
Neutrons into 1h9/2
N64 ? 82
Neutrons into 1h11/2 ,
31
Weakening of Z64 submagic structure for N90
1h9/2
2d3/2
64
2d5/2
8 neutrons in 2f7/2 reduces the Z64 gap to the
half value
8 protons in 1g7/2 pushes up 1h9/2 by 1 MeV