K' Nomura1, N' Shimizu1, and T' Otsuka1,2,3,4

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New microscopic foundation of the IBM and the
structure of exotic nuclei
LACM-EFES-JUSTIPEN Workshop _at_ ORNL

• K. Nomura1, N. Shimizu1, and T. Otsuka1,2,3,4

1Univ. Tokyo/2CNS/3RIKEN/4MSU
based on Phys. Rev. Lett. 101, 142501 (2008)
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Outline

• Motivation IBM and Mean Field
• Applications to exotic nuclei
• Applications of the Wavelet analysis
• Summary

3

• Interacting Boson Model (IBM)

• a model of the low-lying collectivity with sd
  bosons as building blocks

Arima and Iachello (1974)
- dynamical symmetries - parameters are
adjusted to experiments

• shell-model foundation (OAI method)

- applied to spherical shapes - open question
for general cases

• Otsuka, Arima, Iachello and Talmi (1978)
• Otsuka, Arima, and Iachello (1978)

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Mean Field (Skyrme) model
- describes intrinsic properties - it is not
easy to obtain excitation spectra
IBM
- calculates levels precisely - needs
microscopic basis for general cases
So far, both have nothing to do with each other
But,
It may be interesting to construct an IBM
Hamiltonian based on the Skyrme model
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Mean-Field Derivation of IBM
fermionic PES
bosonic PES
Mapping
Energy expectation values in the intrinsic states
(PESs) are compared to simulate the effects of
nuclear force Pauli principle.
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fermionic PES
constrained Skyrme Hartree-Fock calculation
in mesh representation (ev8 code Bonche et al.)
- zero-range pairing in the BCS approximation -
mass quadrupole constraint with triaxial
degrees of freedom
bosonic PES
coherent state formalizm
Dieperink and Scholten, etc. (1980)
- IBM-2 Hamiltonian
- Assumptions
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bosonic PES
- relationships of deformation variables
- Skyrme PES is simulated by IBM PES using
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Comparisons of PESs
148Sm
IBM
HF
U(5)
154Sm
SU(3)
- minimum - global pattern of HF PES are
reproduced up to 2 MeV
132Ba
O(6)
134Ba
E(5)
208W
E(5)
minimum
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Evolutions of IBM parameters (Sm)
U(5)
X(5)
SU(3)
Skyrme SLy4
gradual variation
drastic change around N90 ( spherical-deformed
transition )
evolve linearly with N
kept constant
Neutron Number
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Low-lying levels for Sm
U(5)
X(5)
SU(3)
IBM-SLy4
data taken from NuDat 2.4
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PESs for Ba isotopes (SkM)
N54-66
N68-80
HF
HF
IBM
IBM
Spherical
Rotational
Rotational
O(6)
E(5)
Spherical
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Low-lying levels for Ba
SkM
E(5) nucleus 134Ba
SLy4
Signature of spherical ? gamma-soft ? deformed
transition
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Outline

• Motivation IBM and Mean Field
• Applications to exotic nuclei
• Applications of the Wavelet analysis
• Summary

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PESs for exotic W isotopes
SLy4
SkM
HF
HF
IBM
IBM
N130
N130
N132
N132
N134
N134
E(5) symmetry
N136
N136
N138
N138
N140
N140
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Low-lying levels (IBM from SkM)
U(5)
E(5)/O(6)
SU(3)?
E(5)-O(6) pattern is maintained ? never been
seen in stable nuclei
208W? quite similar to 134Ba
No experimental data
? N
208W
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Outline

• Motivation IBM and Mean Field
• Applications to exotic nuclei
• Applications of the Wavelet analysis
• Summary

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Wavelet analysis on PES fit
- superposition of PES using appropriate
wavelet - useful for localized signals
Position
Wavelet function
Scale (frequency)
PES (axially symmetric)
PES fit is carried out in wavelet space
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PES fit in wavelet space (Sm)
Morlet wavelet
HF
IBM
HF
IBM
C2
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Level evolutions for Sm
Paul
uniquely determined
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Summary

• Connection between mean-field (Skyrme) model and
  IBM
• Skyrme model determines IBM parameters, while
  IBM calculates levels precisely.
• - typical cases of dynamical symmetries
• - signatures of critical-point symmetries
• Applications to exotic nuclei
• intriguing features that has never been seen
  in stable nuclei
• - e.g. sustained E(5)-O(6) patterns in W
  Os
• ? to be examined experimentally

END
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Backup Slides
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Relationships of deformation variables
proportional to beta_f
negligible
both are limited to 0 to 60 degrees and have the
similar meanings
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Quantum shape/phase transitions
Castens symmetry triangle

• Phase diagram in IBM parameter space
• Intermediate nuclei are numerically studied

Figs. taken from R.F. Casten, Nature Physics 2
811 (2006)
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Castens triangle
- IBM-2 Hamiltonian
- boson coherent state

• Dieperink and Scholten Ginocchio and Kirson
  Bohr and Mottelson, 1980

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Preliminary results (Sm isotopes)
determined automatically
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PES fit in wavelet space (2)
Mexican Hat
HF
IBM
HF
IBM
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PES fit in wavelet space (3)
Paul
HF
IBM
HF
IBM
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PESs for Ru isotopes (SLy4)
N68-80
N54-66
IBM
HF
IBM
HF
(near-) spherical
(near-) spherical
gamma-unstable
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Levels of Ru isotopes
containing predictions on Ngt70
IBM from SkM
IBM from SLy4