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We construct a relativistic framework which takes into pionic correlations(2p-2h)

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:

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We construct a relativistic framework which takes into pionic correlations(2p-2h)

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  1. 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.

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

  3. 1h-state 1p-1h 2p-2h 2h-state

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

  5. Very important result given by projected chiral mean field model High-momentum components are reflected in the wave function. 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.

  6. Pionic energy systematics Phys. Rev. C76, 014305(2007)

  7. Introduction of higher-spin pion field [MeV] VC hard core 1 2 r[fm] p [3E] VT VNN (r) s+w p r Interaction range Acknowledgment to Professor K. Ikeda Nuclear radius Orbital angular momentum of single-particle state G. E. Brown, Unified Theory of Nuclear Models and Forces, p.90 (North-Holland Publishing Company, 1964).

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

  9. Hamiltonian As for s and w fields, we take the mean field approximation.

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

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

  12. 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.

  13. Summary 1.The pionic correlation favors to including high-momentum components due to the pseudo-scalar nature. 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. As for the future subjects: We should consider the relation between physical observables and high-momentum components.

  14. p1/2 + s1/2 f5/2 + d5/2 p3/2 + d3/2 28 f7/2 + g7/2 20 d3/2 + p3/2 s1/2 + p1/2 d5/2 + f5/2 Example 48Ca(p, p’) Ep = 200 MeV, q = 0 degree (IUCF data, analyzed by Y. Fujita.) 1. There are many tiny peaks. Ground state = | 0p-0h > + 2. High-momentum component Tiny peaks spread in significant wide energy region. We have to know the dependence of the distribution pattern on the momentum space where pionic correlation works.

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