Role of Pions in Nuclei and Experimental Characteristics

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Presentation transcript:

Role of Pions in Nuclei and Experimental Characteristics H. Toki (RCNP, Osaka) In collaboration with Y. Ogawa, S. Tamenaga, A. Haga, S. Sugimoto, A. Myo, K. Ikeda 2018/11/24 toki@osaka (Dec.2007)

QCD and Nucleon Quark confinement Chiral symmetry breaking Pions are generated Quarks get mass 2018/11/24 toki@osaka (Dec.2007)

Nucleus with pion exchange among nucleons Nucleon-nucleon interaction Strong short range repulsion (Quark structure) V -50MeV 1fm r Strong tensor interaction (Pion exchange) 2018/11/24 toki@osaka (Dec.2007)

Pion is important !! 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) However, the pion had not played the central role in nuclear physics until recent years. 2018/11/24 toki@osaka (Dec.2007)

Variational calculation of light nuclei with NN interaction C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001) 2018/11/24 toki@osaka (Dec.2007)

Comparison of (p, n) and (3He,t) spectra 58Ni(p, n)58Cu Ep = 160 MeV (IUCF) J. Rapaport et al. NPA (‘83) Counts 58Ni(3He, t)58Cu E = 140 MeV/u (RCNP) Y. Fujita et al., EPJ A 13 (’02) 411. H. Fujita et al., PRC 75 (’07) 034310 GTGR 0 2 4 6 8 10 12 14 Excitation Energy (MeV) 2018/11/24 toki@osaka (Dec.2007)

Difficulty of Nuclear Physics Strong short range repulsion (Quark structure) Feshbach projection V -50MeV 1fm r Shell Model uses only P-space using tamed interaction Strong tensor interaction (Pion exchange) 2018/11/24 toki@osaka (Dec.2007)

Pion exchange interaction vs. Tensor interaction Pion is a peudoscalar meson (0-)---spin interaction Involve large momentum Delta interaction Yukawa interaction 2018/11/24 toki@osaka (Dec.2007)

The property of tensor interaction Centrifugal potential (200MeV@1fm) pushes away the L=2 wave function. 2018/11/24 toki@osaka (Dec.2007)

Tensor optimized shell model Myo, Toki, Ikeda, Kato, Sugimoto, Prog Tensor optimized shell model Myo, Toki, Ikeda, Kato, Sugimoto, Prog.Theor.Phys. (2006) 0p-0h + 2p-2h (size parameter) Energy variation 2018/11/24 toki@osaka (Dec.2007)

Convergence of tensor correlation We can completely take into account the tensor correlations Higher L states 4 Gaussian functions 2018/11/24 toki@osaka (Dec.2007)

5He and spin-orbit splitting due to tensor interaction 2018/11/24 toki@osaka (Dec.2007)

Phase shifts in 4He+n Without tensor correlations, we do not reproduce the phase shifts. Tensor correlations provide suitable amount of spin-orbit effect. 2018/11/24 toki@osaka (Dec.2007)

Characteristics of 11Li Halo structure Borromean system S2n = 0.31 MeV Rm = 3.12±0.16 / 3.53±0.06 fm (9Li: 2.32±0.02 fm) Halo structure Borromean system No bound state in any two-body subsystem 10Li(*)+n 9Li+n+n 0.31 MeV 11Li Breaking of magic number N=8 Simon et al.(exp,PRL83) (1s)2~50%. Mechanism is unclear 2018/11/24 toki@osaka (Dec.2007)

Pairing-blocking : 　　K.Kato,T.Yamada,K.Ikeda,PTP101(‘99)119,　Masui,S.Aoyama,TM,K.Kato,K.Ikeda,NPA673('00)207. TM,S.Aoyama,K.Kat,K.Ikeda,PTP108('02)133, H.Sagawa,B.A.Brown,H.Esbensen,PLB309('93)1. 2018/11/24 toki@osaka (Dec.2007)

11Li G.S. properties (S2n=0.31 MeV) Rm Simon et al. P(s2) Tensor +Pairing E(s2)-E(p2) 2.1 1.4 　0.5 -0.1 [MeV] Pairing interaction couples (0p)2 and (1s)2 states. 2018/11/24 toki@osaka (Dec.2007)

Weinberg transformation Chiral sigma model Y. Ogawa et al. PTP (2004) Pion is the Goldstone boson of chiral symmetry Linear Sigma Model Lagrangian Polar coordinate Weinberg transformation 2018/11/24 toki@osaka (Dec.2007)

Numerical results 40Ca 56Ni Spin-orbit effect Experiment 9.2 40Ca 56Ni 9.0 N=28 N=20 Spin-orbit effect 8.8 8.6 8.4 Experiment 8.2 8.0 7.8 20 30 40 50 60 70 80 90 N=Z A (Mass number) 2018/11/24 toki@osaka (Dec.2007)

There appears strong spin-orbit effect. The spin- Pion energy There appears strong spin-orbit effect. The spin- orbit effect comes from the spherical ansatz (Parity mixing). 2018/11/24 toki@osaka (Dec.2007)

Density distribution and form factor 2018/11/24 toki@osaka (Dec.2007)

Pionic energy is important Kaiser, Fritsch Weise, NPA697 (2002) p-h p-h Finelli, Kaiser Vretener, Weise NPA770(2006) L Parity projection corresponds to taking only L=0 contribution. We should consider all the partial waves. 2018/11/24 toki@osaka (Dec.2007)

Experimental characteristics Normalization (10%) Shell model results have to be reduced by 10% coming from normalization. 2. 2p-2h wave functions have small overlap with shell model states --> widths are small 3. Many GT states from 2p-2h states 4. High momentum components are produced due to pion and short range repulsion Shell Pion Hard core q2 2018/11/24 toki@osaka (Dec.2007)

Summary We can describe now the pions for the structure of nuclei. Tensor correlation in terms of Tensor-optimized shell model (TOSM) We can discribe the recovery of chiral symmetry breaking in terms of the chiral sigma model. We discuss the general features of experiment on nuclei due to pions. 2018/11/24 toki@osaka (Dec.2007)