We construct a relativistic framework which takes into pionic correlations(2p-2h) account seriously from both interests: 1. The role of pions on nuclei. 2. The partial restoration of chiral symmetry in nuclear medium. There are two strong motivations: 1. Ab initio calculation by Argonne-Illinois group. 2. Gamow-Teller transition strength distribution with high resolution at RCNP. The pionic correlation(2p-2h) in the ground state produces the strong attractive force at medium interaction range(~1 fm). Our framework and its essential points to treat the pionic correlation explicitly. (spherical pion field ansatz) What we are doing now.(including the higher partial states of pions.) Acknowledgments Y. O. is grateful to Prof. K. Ikeda, Prof. Y. Akaishi, Prof. A. Hosaka, Dr. T. Myo, Dr. S. Sugimoto for discussions on tensor force, pions and chiral symmetry. Y. O. is also thankful to members of RCNP theory group.

R. B. Wiringa, S. C. Pieper, J. Carlson, and V. R. Pandaripande, Phys. Rev. C62(014001) Pion 70 ~ 80 % The ab initio calculation by Argonne-Illinois group

1h-state 2h-state 1p-1h 2p-2h

16 O 12 C 4 He Relation between pionic correlation and kinetic energy.

Particle states have a rather compact distribution comparing with that of RMF solution without pionic correlation. Intrinsic single particle-states are expanded in Gaussian basis. High-momentum components are reflected in the wave function. Very important result given by projected chiral mean field model

Pionic energy systematics Phys. Rev. C76, (2007)

Nuclear radius Interaction range Orbital angular momentum of single-particle state [ 3 E] V NN (r) [MeV] hard core VTVT r[fm]     1 2 VCVC Acknowledgment to Professor K. Ikeda Introduction of higher-spin pion field G. E. Brown, Unified Theory of Nuclear Models and Forces, p.90 (North-Holland Publishing Company, 1964).

Ground state wave function We construct the 2p2h states using the RMF basis.

Hamiltonian As for  and  fields, we take the mean field approximation.

p-h transition density matrix element E. Oset, H. Toki, and W. Weise, Phys. Rep. 83, 281(1981). Matrix element

Single-particle states given by RMF basis. Radial parts are expanded in the Gaussian.

Energy minimization conditions First minimization step Second minimization step This minimization is crucial important point in this framework in order to have significant wide variational space. At this step the high-momentum components are included due to pionic correlations.

Summary 2. The pions play the role on the origin of jj-magic structure. 3. The validity of above statement will be conformed theoretically by including the higher partial states of pions. We should consider the relation between physical observables and high-momentum components. As for the future subjects: 1.The pionic correlation favors to including high-momentum components due to the pseudo-scalar nature.

Example 48 Ca(p, p’) E p = 200 MeV,  = 0 degree (IUCF data, analyzed by Y. Fujita.) 1. There are many tiny peaks. Tiny peaks spread in significant wide energy region. Ground state = | 0p-0h > + 2. High-momentum component p 1/2 + s 1/2 f 5/2 + d 5/2 p 3/2 + d 3/2 f 7/2 + g 7/2 s 1/2 + p 1/2 d 3/2 + p 3/2 d 5/2 + f 5/ We have to know the dependence of the distribution pattern on the momentum space where pionic correlation works.