1. Relativistic mean field theory and chiral symmetry for finite nuclei
Towards unification of hadron and nuclear physics
Hiroshi Toki (RCNP-Osaka University)
Kiyomi Ikeda (RIKEN & RCNP)
Satoru Sugimoto (RIKEN)
Yoko Ogawa (RCNP)
Setsuo Tamenaga (RCNP)
11/28/2018
Oct. 1 , RCNP-Osaka

2. Variational calculation of light nuclei
Pion
70 ~ 80 %
C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001), nucl-th/
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Oct. 1 , RCNP-Osaka

3. Ｃｈｉｒａｌ ｐｅｒｔｕｒｂａｔｉｏｎ 0- Ｎ．Ｋａｉｓｅｒ， Ｓ． Ｆｒｉｔｓｃｈ ａｎｄ Ｗ．Ｗｅｉｓｅ
Ｃｈｉｒａｌ　ｐｅｒｔｕｒｂａｔｉｏｎ 0-
Ｎ．Ｋａｉｓｅｒ，　Ｓ．　Ｆｒｉｔｓｃｈ　ａｎｄ　Ｗ．Ｗｅｉｓｅ
Ｎ．Ｐ．Ａ６９７（２００２）２５５
11/28/2018
Oct. 1 , RCNP-Osaka

4. Deuteron Veff(r ; 3S1) = VC(r ; 3E) + DVeff(r ; 3S1),
DVeff(r ; 3S1) = VT (r) 8
w(r)
u (r)
The 3S1-3D1 coupling due to tensor force
leads a large attractive force.
11/28/2018
Oct. 1 , RCNP-Osaka

5. Surface pion condensation by Toki, Sugimoto and Ikeda PTP 108 (2002) 903
Lagrangian
Mean field equation
Wave function
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Oct. 1 , RCNP-Osaka

6. Parity Projection
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Oct. 1 , RCNP-Osaka

7. O+ and 0- states as brother states
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Oct. 1 , RCNP-Osaka

8. 5He p1/2 p3/2 s1/2 2 8 20 s1/2 p1/2 p3/2 d3/2 d5/2 f5/2 f7/2
Additional contribution 0-
5He
L .S force
Full energy gain
s1/2
p3/2
p1/2 2
No energy gain
blocked
11/28/2018
Oct. 1 , RCNP-Osaka

9. Weinberg transformation
Chiral sigma model
Linear sigma model
Lagrangian
Polar coordinate
Weinberg transformation
11/28/2018
Oct. 1 , RCNP-Osaka

10. Non-linear sigma model
Lagrangian
r = fp + j
where
M = gsfp M* = M + gs j
mp2 = m2 + l fp2
ms2 = m2 +3 l fp2
mw = gwfp mw* = mw + gwj ~
11/28/2018
Oct. 1 , RCNP-Osaka

11. Without omega mass generation term
Equation of motion obtained by using the E-L equation in nuclear matter
Without omega mass generation term
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Oct. 1 , RCNP-Osaka

12. Linear sigma model
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Oct. 1 , RCNP-Osaka

13. Nuclear matter Chiral sigma model vs. TM1 Density = 0.1414 fm-3
E/A = MeV
K = 650 MeV
ms = 777 MeV
mw = 783 MeV
mp = 139 MeV
M = 939 MeV
fp = 93 MeV
l = (ms2 - mp2) / 2fp2 =
gs = M / fp =
gw = mw / fp = = h gw
h = ~
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Oct. 1 , RCNP-Osaka

14. Finite nuclei
Nucleon
Meson
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Oct. 1 , RCNP-Osaka

15. Finite nuclei h = 1.17319 40Ca 56Ni gp = gA/2fp TM1
9.2
40Ca
56Ni
9.0
8.8
8.6
8.4
8.2
8.0
7.8 20 30 40 50 60 70 80 90
A (Mass number)
with pion (gA = 1.15)
without pion
gp = gA/2fp
11/28/2018
Oct. 1 , RCNP-Osaka

16. Single particle energy
TM1
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Oct. 1 , RCNP-Osaka

17. Extended sigma model with pion
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18. 56Ni Gamow-Teller transition
j> and j< couple and hence the selection rule is jj, j+-1
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Oct. 1 , RCNP-Osaka

19. 11/28/2018
Oct. 1 , RCNP-Osaka

20. Experiments Gamow-Teller distribution; Quenching factor=0.5
Longitudinal vs. transverse spin responses
High resolution GT excitations
H. Fujita et al
RCNP
11/28/2018
Oct. 1 , RCNP-Osaka

21. Proton inelastic scattering
Analyzed by
Y. Fujita
11/28/2018
Oct. 1 , RCNP-Osaka

22. S1/2 N=0.7 The upper components of 3j1/2 for 56Ni. 11/28/2018
Oct. 1 , RCNP-Osaka

23. Magnetic moments for proton
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24. Magnetic mements for neutron
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25. 中性子の単一粒子レベル
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26. Lambda Hypernuclei nucleon lambda OZI rule u u d u d sＭ Ｍ
u u d u d s
g(lambda) = 2/3 g(nucleon)
No pion lambda coupling
11/28/2018
Oct. 1 , RCNP-Osaka

27. Ｌａmbｄａ ｈｙｐｅｒｎｕｃｌei （Ｎｉ５６－Ｌａmbｄａ）
Ｙ．Ｏｇａｗａ　ｅｔ　ａｌ．（２００３）
11/28/2018
Oct. 1 , RCNP-Osaka

28. Conclusion
Chiral sigma model is extended to include the mass generation term for the omega meson
Saturation property is realized with too large a compressibility
The magic number effect is generated by surface pion condensation
All observables related with tensor force
are to be explained by surface pion condensation
11/28/2018
Oct. 1 , RCNP-Osaka

29. The spin-orbit splitting of Lambda hyper nuclei
is small – This fact indicates that the nuclear spin-
orbit splitting is due to surface pion condensation
Pion, which is a Goldstone particle of chiral symmetry, plays the major role for hadron and nuclear physics
11/28/2018
Oct. 1 , RCNP-Osaka

30. Many home works Parity and charge projection Vacuum polarization
Semi-infinite matter
Infinite matter with projection
Observables
Delta and other mesons
11/28/2018
Oct. 1 , RCNP-Osaka

31. Result for 4He Volkov No. 1 + G3RS unit: MeVxT 1
1.25
1.5
1.75 2
xTE
0.93
0.88
0.81
0.73
0.64
Central 1
-18.36
-17.42
-15.92
-14.16
-12.07
Central ss
-11.72
-11.67
-11.52
-11.26
Central tt
-10.31
-9.18
-7.43
-5.28
-2.61
Central ss tt
-33.21
-31.81
-29.73
-27.39
-24.75
Central sum
-73.60
-70.13
-64.75
-58.34
-50.69
Tensor 1
-0.29
-0.36
-0.43
-0.51
-0.59
Tensor tt
-11.98
-19.87
-30.16
-43.36
-59.82
Tensor sum
-12.26
-20.23
-30.59
-43.86
-60.41
LS 1
0.71
1.18
1.78
2.55
3.49
LS tt
0.04
0.08
0.13
0.18
0.22
LS sum
0.75
1.26
1.91
2.72
3.72
Coulomb
0.85
0.86
0.87
Potential sum
-84.27
-88.26
-92.58
-98.62
Kinetic
55.81
59.71
64.39
70.52
78.19
Etotal
-28.46
-28.55
-28.19
-28.10
-28.32
rms Rm (fm)
1.64
1.61
1.58
1.55
1.51
<Y|P|Y>/<Y|Y>
0.67
0.62
0.57
0.52
P(-)
0.105
0.133
0.161
0.188
0.214
rms Rmexp = 1.570.04 fm (NPA 693 (2001) 32)
11/28/2018
Oct. 1 , RCNP-Osaka

32. Density of 4He XT=1.5 XTE=0.81 0+ 0+ H-F 0- 11/28/2018
Oct. 1 , RCNP-Osaka

33. Surface Pion
11/28/2018
Oct. 1 , RCNP-Osaka