Pions in nuclei and tensor force Hiroshi Toki (RCNP, Osaka) in collaboration with Yoko Ogawa (RCNP, Osaka) Jinniu Hu (RCNP, Osaka) Takayuki Myo (Osaka Inst. Tech.) Kiyomi Ikeda (RIKEN) 10.2.23 toki@yukawa.kyoto

Pion is important !! In Nuclear Physics Yukawa introduced pion as mediator of nuclear interaction for nuclei. (1934) Nuclear Physics started by shell model with strong spin-orbit interaction. 　(1949: Meyer-Jensen: Phenomenological) The pion had not played the central role in nuclear physics until recent years. 10.2.23 toki@yukawa.kyoto

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!! 10.2.23 toki@yukawa.kyoto Pion is a key element

RCNP experiment (good resolution) Giant GT Not simple Y. Fujita et al., E.Phys.J A13 (2002) 411 H. Fujita et al., PRC 10.2.23 toki@yukawa.kyoto

The pion (tensor) is important. S=1 and L=0 or 2 NN interaction Deuteron (1+) 10.2.23 toki@yukawa.kyoto

Deuteron and tensor interaction Pion Tensor spin-spin Central interaction has strong repulsion. Tensor interaction is strong in 3S1 channel. S-wave function has a dip. D-wave component is only 6%. Tensor attraction provides 80% of entire attraction. D-wave is spatially shrank by a half. 10.2.23 toki@yukawa.kyoto

Chiral symmetry (Nambu:1960) Chiral symmetry is the key symmetry to connect real world with QCD physics Chiral model is very powerful in generating various hadronic states Nucleon gets mass dynamically Pion is the Nambu-Goldstone particle of the chiral symmetry breaking 10.2.23 toki@yukawa.kyoto

He was motivated by the BCS theory（１９５８）. Nobel prize (2008) He was motivated by the BCS theory（１９５８）. is the order parameter is the order parameter Particle number Chiral symmetry 10.2.23 toki@yukawa.kyoto

Nambu-Jona-Lasinio Lagrangian Chiral transformation Mean field approximation; Hartree approximation Fermion gets mass. The chiral symmetry is spontaneously broken. Pion appears as a Nambu-Goldstone boson. 10.2.23 toki@yukawa.kyoto

Weinberg transformation Chiral sigma model Y. Ogawa et al. PTP (2004) Pion is the Nambu boson of chiral symmetry Linear Sigma Model Lagrangian Polar coordinate Weinberg transformation 10.2.23 toki@yukawa.kyoto

Non-linear sigma model Lagrangian r = fp + j where M = gsfp M* = M + gs j mp2 = m2 + l fp ms2 = m2 +3 l fp mw = gwfp mw* = mw + gwj ~ Free parameters are and (Two parameters) 10.2.23 toki@yukawa.kyoto

Relativistic Chiral Mean Field Model Wave function for mesons and nucleons p p Mean field approximation for mesons. h h Nucleons are moving in the mean field and occasionally brought up to high momentum states due to pion exchange interaction Bruekner argument 10.2.23 toki@yukawa.kyoto

Relativistic Brueckner-Hartree-Fock theory Brockmann-Machleidt (1990) RBHF Non-RBHF relativity Us~ -400MeV Uv~ 350MeV 10.2.23 toki@yukawa.kyoto RBHF theory provides a theoretical foundation of RMF model.

Density dependent RMF model Brockmann Toki PRL(1992) 10.2.23 toki@yukawa.kyoto

Why 2p-2h states are necessary for the tensor interaction? The spin flipped states are already occupied by other nucleons. Pauli forbidden G.S. Spin-saturated 10.2.23 toki@yukawa.kyoto

Energy minimization with respect to meson and nucleon fields (Mean field equation) 10.2.23 toki@yukawa.kyoto

Energy Energy minimization 10.2.23 toki@yukawa.kyoto

RCMF equation 10.2.23 toki@yukawa.kyoto

Energy minimization with respect to meson and nucleon fields (Mean field equation) (Corrrelation function) 10.2.23 toki@yukawa.kyoto

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 10.2.23 toki@yukawa.kyoto

Short-range correlator : C Hamiltonian in UCOM 2-body approximation in the cluster expansion of operator 10.2.23 toki@yukawa.kyoto

Numerical results (1) 4He 12C 16O Ogawa Toki NP 2009 Adjust binding energy and size. 10.2.23 toki@yukawa.kyoto

Pion tensor provides large attraction to 12C Numerical results 2 O The difference between 12C and 16O is 3MeV/N. P1/2 C The difference comes from low pion spin states (J<3). This is the Pauli blocking effect. P3/2 S1/2 Pion tensor provides large attraction to 12C Pion energy 10.2.23 toki@yukawa.kyoto

Chiral symmetry Ogawa Toki NP(2009) Nucleon mass is reduced N by 20% due to sigma. N Not 45% We want to work out heavier nuclei for magic number. Spin-orbit splitting should be worked out systematically. 10.2.23 toki@yukawa.kyoto

Nuclear matter E/A Hu Ogawa Toki Phys. Rev. 2009 Total Pion 10.2.23 toki@yukawa.kyoto

Deeply bound pionic atom Predicted to exist Toki Yamazaki, PL(1988) Found by (d,3He) @ GSI Itahashi, Hayano, Yamazaki.. Z. Phys.(1996), PRL(2004) Findings: isovector s-wave 10.2.23 toki@yukawa.kyoto

Halo structure in 11Li Myo Kato Toki Ikeda PRC(2008) Deuteron wave function Deuteron-like state is made by 2p-2h states in shell model. 10.2.23 toki@yukawa.kyoto

Tensor interaction Tensor interaction needs 2p-2h excitation of pn pair. P1/2 orbit is used for this Excitation. This orbit is blocked When we want to put two neutrons. S1/2 orbit is free of this. 10.2.23 toki@yukawa.kyoto

Conclusion Pion (tensor) is treated within relativistic chiral mean field model. We extended RBHF theory for finite nuclei. Nucleon mass is reduced by 20% Chiral condensate is similar to the model independent value. (Sigma term~50MeV) Deeply bound pionic atom seems to verify partial recovery of chiral symmetry. 10.2.23 toki@yukawa.kyoto

Picture of nucleus proton Snapshot neutron pionic pair 10.2.23 toki@yukawa.kyoto