1. Relativistic extended chiral mean field model for finite nuclei
Hiroshi Toki (RCNP/Osaka)
Yoko Ogawa (RCNP/Osaka)
Takayuki Myo (Osaka Inst. of Tech.)
Kiyomi Ikeda (RIKEN)
2018/11/30

2. Variational calculation of light nuclei with NN interaction
VMC+GFMC
VNNN
Fujita-Miyazawa
C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001)
Relativistic
Pion is a key element
2018/11/30

3. General feature of nucleon-nucleon interaction
Nucleus using
NN interaction
Strong tensor interaction
(pion: chiral symmetry)
Strong short range repulsion
(quark: confinement)
Deuteron wave function V
1fm r
Strong short range repulsion
(Quark structure) s d
-50
(MeV)
Strong tensor interaction
(Pion exchange)
2018/11/30
Central dip and D-wave component

4. Tensor optimized shell model
Myo Ikeda Toki
Tensor correlation
TOSM
Short-range correlation
UCOM
2018/11/30

5. V coordinate vs. T coordinate
TOSM+UCOM with AV8’ (Myo Toki Ikeda)
Kamada et al.
PRC(2002) T
Few body
Framework
Hiyama
Suzuki
VLS
More
Tensor!! E VC VT
2018/11/30
V coordinate vs. T coordinate

6. Picture of nucleus proton Snapshot neutron pionic pair 2018/11/30

7. Nucleon is made of quarks
QCD -- Confinement + Chiral Symmetry
NJL(Nambu-Jona-Lasinio)
Quarks massive + Pion (NG boson)
Hadronization (Eguchi-Sugawara:1976)
Chiral sigma model (Toki-Weise:2008)
Want to make nucleus with chiral symmetry
2018/11/30

8. Relativistic chiral mean field modeljj
Relativistic chiral mean field model LS
Ogawa Toki
Relativistic mean field model with pion
Toki, Sugimoto, Ikeda, PTP(2002)
Relativistic charge and parity projected chiral mean field model
Ogawa, Toki,.., PRC(2004),PRC(2006)
Spin-orbit splitting and jj-closed shell nuclei
Only surface effect of pion
2018/11/30

9. Pion has volume effect (Pion is important in nuclear matter)
p-h L
Kaiser, Fritsch, Weise, NPA697(2002)
G. Brown, Book
qmax~2kF~3fm-1 (Akaishi)
Tensor force is important!!
qmax R ~ Lmax
2018/11/30

10. Relativistic extended chiral mean field model
Ogawa,Toki (2008)
Linear Sigma Model Lagrangian
Sigma condensation (NJL mechanism) produces finite masses.
2018/11/30
Weinberg transformation

11. Hadrons get mass Non-linear sigma model Two free parameters:
Sigma meson mass
Omega-nucleon coupling
2018/11/30

12. Relativistic extended chiral mean field model Nucleon + sigma and omega
Sigma+omega model
with one pion exchange p h p’ h’
qmax R ~ Lmax
Pionic quantum number
6 for 4He
2018/11/30

13. Self-consistent variational calculation
Mean field equation
Nucleon 2p-2h states
Oset-Toki-Weise formulation, Phys.Rep.(1984)
2018/11/30

14. RECMF model results
bmax~0.7fm
Jmax~6
bs=1.4fm
2018/11/30

15. RECMF model results (2)
2018/11/30

16. RECMF model results (3) M is reduced by 10~15%
Chiral symmetry is partially recovered!
2018/11/30

17. Conclusion
We construct Relativistic Extended Chiral Mean Field model for finite nuclei
We have calculated 4He in RECMF and found quantitatively satisfactory results
We can move to medium heavy nuclei
2018/11/30