A. Tamii

1
?????????????????????

• A. Tamii
• Research Center for Nuclear Physics, Osaka
  University

2
Role of the Pion in Nuclei

• Pionic Correlation in Nuclei
• H. Toki et al.
• A kind of 2p-2h diagram mediated by the pion
  exchange, embedded in the ground state and in
  each excited state.
• Tensor interaction at high-q is important due to
  the pion-exchange nature.
• Higher orbits are involved in the Shell-Model.
• The extent of the wave-function of the correlated
  component (high-q) is spatially smaller than the
  description of the Shell-Model.
• Isospins and parities are mixed in the
  calculation of the wave function (due to the
  0-T1 nature of the pion)

Illustrative concept of the pionic correlation in
nuclei
3
??????????????????????????????????

• Conventional ???????????(????pionic
  correlation)????????????????????...
• ?????bulk???
• ??????????????????????...
• ????????????????
• ?????????
• ????????????
• ???????
• ?????Shell-Model???
• Ground State Correlation
• Core-Polarization
• Meson Exchange Current
• Short-range correlation
• (??)

Illustrative concept of the pionic correlation in
nuclei
4
??????????????????????????????????

• Conventional ???????????(????pionic
  correlation)????????????????????...
• ?????bulk???
• ??????????????????????...
• ????????????????
• ?????????
• ????????????
• ???????
• ?????Shell-Model???
• Ground State Correlation
• Core-Polarization
• Meson Exchange Current
• Short-range correlation
• (??)

?????high-q component, transfer reaction
(???) ???????????????? ???????????????????
????????????????...
5
??????????????????????????????????

• Conventional ???????????(????pionic
  correlation)????????????????????...
• ?????bulk???
• ??????????????????????...
• ????????????????
• ?????????
• ????????????
• ???????
• ?????Shell-Model???
• Ground State Correlation
• Core-Polarization
• Meson Exchange Current
• Short-range correlation
• (??)

knock-out reaction, (e,eN), (p,pN), ... transfer
reaction, (p,d), (d,p), ....
6
??????????????????????????????????

• Conventional ???????????(????pionic
  correlation)????????????????????...
• ?????bulk???
• ??????????????????????...
• ????????????????
• ?????????
• ????????????
• ???????
• ?????Shell-Model???
• Ground State Correlation
• Core-Polarization
• Meson Exchange Current
• Short-range correlation
• (??)

Closed Shell ??????????? e.g. 1 states in 4He,
16O, 40Ca, ... ??????????????? e.g.
fragmentation of the 1 states in 48Ca
RCNP-E299 16O(p,p) 40Ca(p,p), H Matsubara et
al., RCNP-E307 40Ca(3He,t), T. Adachi et
al., RCNP-E306 4He(3He,t), A. Tamii et al.,
????4He?????(GT)???
7
??????????????????????????????????

• Conventional ???????????(????pionic
  correlation)????????????????????...
• ?????bulk???
• ??????????????????????...
• ????????????????
• ?????????
• ????????????
• ???????
• ?????Shell-Model???
• Ground State Correlation
• Core-Polarization
• Meson Exchange Current
• Short-range correlation
• (??)

(e,e)?(p,p)????... pion knock-out reaction?...
8
??????????????????????????????????

• Conventional ???????????(????pionic
  correlation)????????????????????...
• ?????bulk???
• ??????????????????????...
• ????????????????
• ?????????
• ????????????
• ???????
• ?????Shell-Model???
• Ground State Correlation
• Core-Polarization
• Meson Exchange Current
• Short-range correlation
• (??)

Illustrative concept of the pionic correlation in
nuclei
(e,eNN)?(p,pNN) ... 2N?0- coupling ? 2 NN-pair ?
?? ?
9
??????????????????????????????????

• ???????(??????Coupling)
• (??)??????????
• (??)?????????????????????
• (??)?????????

? ??????????????? (??????????)
Illustrative concept of the pionic correlation in
nuclei
10
Fine Structure of the Gamow-Teller Resonances
The GT strength in 58Cu has been resolved into
many fragmented narrow peaks with widths of 100
keV.
?Jp1?T1

• How can the
• fragmentation
• peak width
• be explained by theories?

?Sp
?Sn
Y. Fujita et al., EPJ A 13, 411 (2002)
11
Fine structure of the GDR in 28Si
?Jp1-?T1
gamma absorption data H. Harada et al., J. Nucl.
Sci. Tech38_465(2001).
12
Fine structure of the GDR in 28Si
Similar GDR fine structures are observed by
different probes
?Jp1-?T1
gamma absorption data H. Harada et al., J. Nucl.
Sci. Tech38_465(2001). (p,p) data from E249 at
RCNP, H. Matsubara et al. 28Si Sp11.6 MeV,
Sn17.2 MeV
13
(3He,t) spectra in the pf-shell region
T. Adachi, PhD thesis, 2006, Osaka Univ.
14
Inelastic Proton Scattering from 28Si at 0 degrees
Analyzed by H. Matsubara
15
Angular Distribution of IS and IV 1 excitations
DWBA, T0 IS
DWBA, T1 IV
Analyzed by H. Matsubara
Ex 9.50 MeV T0
Ex 11.45 MeV T1
ds/dO mb/sr
ds/dO mb/sr
2.50
0.35
0.11
0.77
Tcm deg
Tcm deg
From angular distribution, isospin value is
identified.
16
Other states identified as 1
1, T0 states
1, T1 states
Analyzed by H. Matsubara
ds/dO mb/sr
ds/dO mb/sr
TCM deg
TCM deg
17
Strength distribution
preliminary
shell model calculation OXBASH USD
interaction
RCNP-E299 H. Matsubara et al., 1 strength
distributions will be measured for each T0 and
1 for 16O, 20Ne, 24Mg, 28Si, 32S, 36Ar, 40Ca
18
?????????(Fragmentation)

• (??)?????????
• ???????????
• ??????????????
• ????????
• ???????????????
• ? ??????????????????
• ? ?????????????
• ?????????? e.g.
• ????? ???????????????... level
  spacing?width?...
• ???????????
• wavelet analysis (?????????????????)
• ??????????????
• ??????????????????
• ? Degree of Fragmentation ?????????

Illustrative concept of the pionic correlation in
nuclei
???????? ????????
19
Exponential Slope of the Strength Distribution
Data RCNP-E249
Calc OXBASH, sd, 0hw
c.f. Levy Statistcs West and Deering, Phys.
Rep. 246(1994)1-100.
20
(No Transcript)
21
Calc. OXBASH
1 T0
1 T1
22
B(s) Ratio T0/T1
Calc. OXBASH
23
Fractal Dimension of a Spectrum
Hilbert Curve Fract. Dim.2.0
Koch Curve Fract. Dim.1.33
How about a spectrum?
Sea Coastline
24
(No Transcript)
25
Fractal Dimension of Spectra
????????????????????? ? wavelet ????????
Fractal Dimension1
26
28Si 1 T1
27
Summary

• ????????????????????????????????
• ????????????????????????????????????????(Fragmenta
  tion)??????????????????????????????????