1. Role of Pions in Nuclei and Experimental Characteristics
H. Toki (RCNP, Osaka)
In collaboration with
Y. Ogawa, S. Tamenaga, A. Haga,
S. Sugimoto, A. Myo, K. Ikeda
2018/11/24
(Dec.2007)

2. QCD and Nucleon Quark confinement Chiral symmetry breaking
Pions are generated
Quarks get mass
2018/11/24
(Dec.2007)

3. Nucleus with pion exchange among nucleons
Nucleon-nucleon interaction
Strong short range repulsion
(Quark structure) V
-50MeV
1fm r
Strong tensor interaction
(Pion exchange)
2018/11/24
(Dec.2007)

4. Pion is important !!
Yukawa introduced pion as mediator of nuclear interaction for nuclei. (1934)
Nuclear Physics started by shell model with strong spin-orbit interaction. (1949:Meyer-Jensen)
However, the pion had not played the central role in nuclear physics until recent years.
2018/11/24
(Dec.2007)

5. Variational calculation of light nuclei with NN interaction
C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001)
2018/11/24
(Dec.2007)

6. Comparison of (p, n) and (3He,t) spectra
58Ni(p, n)58Cu
Ep = 160 MeV (IUCF)
J. Rapaport et al.
NPA (‘83)
Counts
58Ni(3He, t)58Cu
E = 140 MeV/u (RCNP)
Y. Fujita et al.,
EPJ A 13 (’02) 411.
H. Fujita et al.,
PRC 75 (’07)
GTGR
Excitation Energy (MeV)
2018/11/24
(Dec.2007)

7. Difficulty of Nuclear Physics
Strong short range repulsion
(Quark structure)
Feshbach projection V
-50MeV
1fm r
Shell Model uses only
P-space using tamed
interaction
Strong tensor interaction
(Pion exchange)
2018/11/24
(Dec.2007)

8. Pion exchange interaction vs. Tensor interaction
Pion is a peudoscalar meson (0-)---spin interaction
Involve large
momentum
Delta interaction
Yukawa interaction
2018/11/24
(Dec.2007)

9. The property of tensor interaction
Centrifugal potential pushes away the L=2 wave function.
2018/11/24
(Dec.2007)

10. Tensor optimized shell model Myo, Toki, Ikeda, Kato, Sugimoto, Prog
Tensor optimized shell model Myo, Toki, Ikeda, Kato, Sugimoto, Prog.Theor.Phys. (2006)
0p-0h + 2p-2h
(size parameter)
Energy variation
2018/11/24
(Dec.2007)

11. Convergence of tensor correlation
We can completely take into account the tensor correlations
Higher L states
4 Gaussian functions
2018/11/24
(Dec.2007)

12. 5He and spin-orbit splitting due to tensor interaction
2018/11/24
(Dec.2007)

13. Phase shifts in 4He+n
Without tensor correlations, we do not reproduce the phase shifts.
Tensor correlations provide suitable amount of spin-orbit effect.
2018/11/24
(Dec.2007)

14. Characteristics of 11Li Halo structure Borromean system S2n = 0.31 MeV
Rm = 3.12±0.16 / 3.53±0.06 fm (9Li: 2.32±0.02 fm)
Halo structure
Borromean system
No bound state in any two-body subsystem
10Li(*)+n
9Li+n+n
0.31 MeV
11Li
Breaking of magic number N=8
Simon et al.(exp,PRL83) (1s)2~50%.
Mechanism is unclear
2018/11/24
(Dec.2007)

15. Pairing-blocking :
　　K.Kato,T.Yamada,K.Ikeda,PTP101(‘99)119,　Masui,S.Aoyama,TM,K.Kato,K.Ikeda,NPA673('00)207.
TM,S.Aoyama,K.Kat,K.Ikeda,PTP108('02)133, H.Sagawa,B.A.Brown,H.Esbensen,PLB309('93)1.
2018/11/24
(Dec.2007)

16. 11Li G.S. properties (S2n=0.31 MeV)Rm
Simon et al.
P(s2)
Tensor
+Pairing
E(s2)-E(p2)
2.1
1.4
　0.5
-0.1
[MeV]
Pairing interaction couples (0p)2 and (1s)2 states.
2018/11/24
(Dec.2007)

17. Weinberg transformation
Chiral sigma model
Y. Ogawa et al. PTP (2004)
Pion is the Goldstone boson of chiral symmetry
Linear Sigma Model Lagrangian
Polar coordinate
Weinberg transformation
2018/11/24
(Dec.2007)

18. Numerical results 40Ca 56Ni Spin-orbit effect Experiment
9.2
40Ca
56Ni
9.0
N=28
N=20
Spin-orbit effect
8.8
8.6
8.4
Experiment
8.2
8.0
7.8 20 30 40 50 60 70 80 90
N=Z
A (Mass number)
2018/11/24
(Dec.2007)

19. There appears strong spin-orbit effect. The spin-
Pion energy
There appears strong spin-orbit effect. The spin-
orbit effect comes from the spherical ansatz
(Parity mixing).
2018/11/24
(Dec.2007)

20. Density distribution and form factor
2018/11/24
(Dec.2007)

21. Pionic energy is important
Kaiser, Fritsch
Weise, NPA697
(2002)
p-h
p-h
Finelli, Kaiser
Vretener, Weise
NPA770(2006) L
Parity projection corresponds to taking only
L=0 contribution.
We should consider all the partial waves.
2018/11/24
(Dec.2007)

22. Experimental characteristics
Normalization (10%)
Shell model results have to be
reduced by 10% coming from
normalization.
2. 2p-2h wave functions have
small overlap with shell
model states --> widths are small
3. Many GT states from 2p-2h states
4. High momentum components are
produced due to pion and short
range repulsion
Shell
Pion
Hard core q2
2018/11/24
(Dec.2007)

23. Summary We can describe now the pions for the structure of nuclei.
Tensor correlation in terms of Tensor-optimized shell model (TOSM)
We can discribe the recovery of chiral symmetry breaking in terms of the chiral sigma model.
We discuss the general features of experiment on nuclei due to pions.
2018/11/24
(Dec.2007)