1. Tensor optimized shell model and role of pion in finite nuclei
Hiroshi Toki (RCNP/Osaka)
In collaboration with
Takayuki Myo (Osaka Inst. of Tech.)
Kiyomi Ikeda (RIKEN)

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
We want to calculate heavy nuclei!!
Pion is a key element

3. General feature of nucleon-nucleon 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)
Central dip and D-wave component

4. If we treat tensor interaction
Pion exchange interaction vs. Tensor interaction
Pion is a peudoscalar meson (0-)---spin interaction
Tensor interaction
(high momentum)
Delta interaction
(short range correlation)
Yukawa interaction
(low momentum)
If we treat tensor interaction
we can treat pion

5. The property of tensor interaction
Centrifugal potential pushes away the L=2 wave function

6. Tensor optimized shell model (TOSM)
Ground state is obtained by shell model (HF method)
Treat tensor interaction explicitly using 2p-2h wave functions (3p-3h, 4p-4h are checked small)
The point of success of TOSM is the tensor interaction being of intermediate range

7. Tensor optimized shell model Myo, Toki, Ikeda, Kato, Sugimoto, PTP 117 (2006)
0p-0h + 2p-2h
(size parameter)
Energy variation Gc

8. Convergence of tensor correlation
Higher L states
4 Gaussian functions
We can completely treat the tensor correlations

9. 5He and spin-orbit splitting due to tensor interaction Myo, Kato, Ikeda, PTP 113 (2005)

10. Tensor correlations provide suitable amount of spin-orbit effect
Phase shifts in 4He+n
Tensor correlations provide suitable amount of spin-orbit effect

11. Unitary Correlation Operator Method
(UCOM)
short-range correlator
Bare Hamiltonian
Shift operator depending on the relative distance r
H. Feldmeier, T. Neff, R. Roth, J. Schnack, NPA632(1998)61

12. Short-range correlator : C H. Feldmeier, T. Neff et. al
Short-range correlator : C H. Feldmeier, T. Neff et.al., NPA632(1998)61
Hamiltonian in UCOM
2-body approximation in the cluster expansion of operator

13. Form of R+ in UCOM Afnan-Tang : central only
Function form given by Feldmeier
reproducing deuteron wave function

14. 4He with UCOM

15. Correlation Function and Charge form factor
(0s)4
x C

16. TOSM+UCOM Myo Toki Ikeda, PTP(2008)
Use bare NN interaction (AV8’)
TOSM for tensor interaction (long range)
UCOM for short range repulsion
We take one approximation (two body)
We consider VNNN ( ) in future

17. V coordinate vs. T coordinate
TOSM+UCOM with AV8’ (Myo Toki Ikeda) T
VLS E VC VT
V coordinate vs. T coordinate

18. Picture of nucleus proton Snapshot neutron pionic pair 09.2.20

19. Summarize TOSM
We develop shell model method which describes the strong tensor and short-range correlations explicitly.
Tensor correlation
Tensor-optimized shell model (TOSM)
Short-range correlation
Unitary Correlation Operator Method (UCOM)
We can describe nuclei starting from the bare interaction.
We get a tool to study the importance of pion. (Unification of nuclear physics and hadron physics through chiral symmetry)

20. Hypernuclei and pion T=0 J=1/2 Role of pion through N N N N 09.2.20

21. 4He+Y N p1/2 p3/2 s1/2 N 4He+ 4He+N Large attraction
Spin-orbit effect due to blocking of
particle states by the valence nucleon
Use hole states to utilize pion attraction
for lambda binding

22. 4He+ N N Central Effective int. interaction Hiyama et al. 09.2.20

23. Conclusion We develop TOSM to treat nuclei using NN interaction
We have to treat pion explicitly for hypernuclei (Binding energy) vs. finite nuclei (spin-orbit)
We should develop TOSM for hypernuclei