Satoru Sugimoto

1
Study of the Tensor Correlation in Oxygen
Isotopesusing Mean-Field-Type and Shell Model
Methods

• Satoru Sugimoto
• Kyoto University
• 1. Introduction
• 2. Charge- and parity-projected Hartree-Fock
  method (a mean field type model) and its
  application to sub-closed shell oxygen isotopes
• 3.Shell model calculation to 15,16,17O
• 4. Summary

2
Introduction

• The tensor force is important in nuclear
  structure.
• There remain many open problems to be solved.
• How does the tensor correlation change in
  neutron-rich nuclei?
• Shell evolution (Ostuka, PRL 95 232502 (2005)).
• The breakdown of the magic number in 11Li (Myo et
  al.)
• The relation to the ls splitting in 5He (Myo et
  al. PTP 113 (2005) 763)

3
The correlation to be included
2p-2h correlation
cf. Single-particle (H-F) correlation

• In the simple HF calculation, 2p-2h correlations
  are hard to be treated.
• We need to include at least 2p-2h correlations to
  exploit the tensor correlation.?beyond mean
  field model

4
Charge- and parity-symmetry breaking mean field
method

• Tensor force is mediated by the pion.
• Pseudo scalar (s??)
• To exploit the pseudo scalar character of the
  pion, we introduce parity-mixed single particle
  state. (over-shell correlation)
• Isovector (t)
• To exploit the isovector character of the pion,
  we introduce charge-mixed single particle state.
• Projection
• Because the total wave function made from such
  parity- and charge-mixed single particle states
  does not have good parity and a definite charge
  number. We need to perform the parity and charge
  projections.

Refs. Toki et al., Prog. Theor. Phys. 108 (2002)
903. Sugimoto et al., Nucl. Phys. A 740
(2004) 77 nucl-th/0607045. Ogawa et
al., Prog. Thoer. Phys. 111 (2004) 75 Phys.
Rev. C 73 (2006) 034301.
5
Results for 16O

• MV1(VC)G3RS(VT,VLS)
• By performing the parity and charge projection
  the potential energy from the tensor force
  becomes sizable value.

6
VT and VLS per particle

• The potential energy from the tensor force has
  the same order in magnitude as that from the LS
  force.
• The tensor potential energy decreases as neutron
  numbers.

7
Wave function(16O, xT1.5)
s1/2 proton dominant
Opposite parity components mixed by the tensor
force have narrow widths. It suggests that the
tensor correlation needs high-momentum components.
8
Mixing of the opposite parity components in
single-particle states
0p1/2
1s1/2

• If a next j1/2 orbit is occupied newly, the
  mixing probabilities of the j1/2 orbit reduce by
  a blocking effect.
• Mixing of the opposite-parity component may
  affect excitation spectra of nuclei.

9
Shell model calculation

• We perform the shell model calculation including
  1p-1h and 2p-2h configurations to study the
  tensor correlation.
• inclusion of narrow-width single-particle wave
  functions
• The shell model calculation can treat the
  correlation which cannot be treated in a
  mean-field-type calculation.

cf. Myo et al. PTP 113 (2005) 763
10
Model space

• 16O (0p-0h)(1p-1h)(2p2h)17O
  (1p-0h)(2p-1h)(3p2h)15O (0p-1h)(1p-2h)(2p3
  h)
• Core (hole state)
• (0s1/2)4(0p3/2)6(0p1/2)4
• Harmonic oscillator single-particle wave
  functions
• Particle state
• Harmonic oscillator single-particle wave
  functionsGaussian single-particle wave
  functions with narrow (half) width parameters
• These are ortho-normalized by the G-S method

11
Effective interaction

• Central force Volkov No. 1
• A.B. Volkov, Nucl. Phys. 74 ( 1965 ) 33
• Tensor Furutani force
• H. Furutani et al., Prog. Theor. Phys. Suppl. 68
  ( 1980 ) 193
• LS G3RS
• . Tamagaki, Prog. Theor. Phys. 39 ( 1968 ) 91
• No Coulomb force

12
16O

• HO (1s 0d)(1p 0f)(2s 1d 0g)
• NWG bNW bHO/2 1.8 fm
• d-orbit (1s 0d)sNWpNWdNW
• f-orbit (1s 0d)sNWpNWdNWfNW
• By including single-particle orbits with narrow
  width parameters the correlation energy from the
  tensor force becomes large.

13
17,15O (NWG (up to f-orbit))
17O
15O

• DKEDVCDVT0
• ls-splitting nearly equals to DVLS

14
Magnetic Moment

• Magnetic moments change a little in spite of the
  large correlation energy form the tensor force.

A17
A15
15
Summary

• We apply a mean-field model which treats the
  tensor correlation by mixing parities and charges
  in single-particle states (the CPPHF method) to
  oxygen isotopes.
• The opposite parity components induced by the
  tensor force is compact in size. (high-momentum
  component)
• We perform the shell model calculation up to
  2p-2h states to 15,16,17O.
• The tensor correlation energy becomes large by
  including Gaussian single-particle wave functions
  with narrow widths.
• The tensor correlation changes ls splitting and
  magnetic moments in 15,17O a little in spite of
  its large correlation energy.