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Parity projected relativistic mean field theory for extended chiral sigma model. Yoko Ogawa (RCNP/Osaka). Hiroshi Toki (RCNP/Osaka). Kiyomi Ikeda (RIKEN). Satoru Sugimoto (RIKEN). Setsuo Tamenaga (RCNP/Osaka). Atsushi Hosaka (RCNP/Osaka). Hong Shen (Nankai/China). Introduction.

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## Yoko Ogawa (RCNP/Osaka)

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**Parity projected relativistic mean field theory**for extended chiral sigma model Yoko Ogawa (RCNP/Osaka) Hiroshi Toki (RCNP/Osaka) Kiyomi Ikeda (RIKEN) Satoru Sugimoto (RIKEN) Setsuo Tamenaga (RCNP/Osaka) Atsushi Hosaka (RCNP/Osaka) Hong Shen (Nankai/China)**Introduction**Toki, Sugimoto and Ikeda demonstrate the occurrence of surface pion condensation. Prog. Theor. Phys. 108 (2002) 903. Application of extended chiral sigma model for finite nuclei(N=Z even-even). Prog. Theor. Phys. 111(2004) 75. The purpose of this study is to understand the properties of finite nuclei by using a chiral sigma model with pion mean field within the relativistic mean field theory. Chiral symmetry : Linear sigma model in hadron physics M. Gell-Mann and M. Levy, Nuovo Cimento 16(1960)705. Pion : Mediator of the nuclear force H. Yukawa, Proc. Phys.-Math.Soc. Jpn., 17(1935)48. Spontaneous chiral symmetry breaking Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122(1961)345. Contents Problem of now framework Parity projection Parity projected relativistic Hartree equations Summary**Lagrangian**Linear Sigma Model**Dynamical mass generation term for omega meson**J. Boguta, Phys. Lett. 120B(1983)34 Non- linear realization Extended Chiral Sigma Model Lagrangian(ECS) New nucleon field**Dirac equation**Klein-Gordon equations Parity mixed single particle wave function Mean Field Equation**Hadron property**gs = M / fp = 10.0968 M = 939 MeV mw = 783MeV mp = 139 MeV fp = 93MeV Free parameter Non-linear coupling ms = 777 MeV ~ • = (ms2 - mp2) / 2fp2 = 33.7847 gw = mw / fp = 8.41935 gw =7.0337 Character of the ECS model in nuclear matter Large incompressibility Small LS-force K = 650 MeV ECS TM1(RMF) ~ Effective mass :M* = M + gss, m*w=mw+ gws ~ 80 % Saturation property E/A-M = -16.14 MeV r = 0.1414 fm-3**ECS model (with pion)**ECS model (without pion) TM1(RMF) Finite Nuclei Y. Ogawa, H. Toki, S. Tamenaga, H. Shen, A. Hosaka, S. Sugimoto and K. Ikeda, Prog. Theor. Phys. Vol. 111, No. 1, 75 (2004)**Single Particle Spectrum**Without pion With pion N = 18 Large incompressibility It is hard energetically to change a density. The state with large L bounds deeper. Anomalous pushed up 1s-state.**The magic number appears at N = 18 instead of N = 20.**Large incompressibility Anomalous pushed up1s 1/2state Parity projection The effect of Dirac sea The Problem and improvement of framework We use the parity mixing intrinsic state in order to treat the pion mean field in the mean field theory because of the pseudovector(scalar) character of pion. We need to restore the parity symmetry and the variation after projection.**Parity Projection**Single particle wave function Total wave function 1h-state 1p-1h 2p-2h 2h-state 0+ 0- H. Toki, S. Sugimoto, K. Ikeda, Prog. Theor. Phys. 108 (2002) 903.**p**0- 0- _ K = 250 + 25 MeV N. Kaiser, S. Fritsch, W. Weise, Nucl. Phys. A697(2002)255 2p-2h K = 255 MeV Experiment**g**7/2 Fermi surface 56Ni p Fermi surface 40Ca 0- 0- In 56Ni case the j-upper state is Fermi level. On the other hand, in 40Ca case the j-upper state is far from Fermi level.**Hamiltonian**Hamiltonian density**Total energy**Parity projected wave function Creation operator for nucleon in a parity projected state a Field operator for nucleon**Parity-projected relativistic mean field equations**Variation after projection Nucleon part**Meson part**We solve these self-consistent equations by using imaginary time step method.**Summary**We show the problem in now framework of ECS model. Large incompressibility. Magic number at N = 20. We derive the parity projected relativistic Hartree equations. Difficulties of relativistic treatment Total energy minimum variation condition gives difficulty to the relativistic treatment, because the relativistic theory involves the negative energy states. We avoid this problem due to elimination of lower component. We however treat the equation which is mathematically equal to the Dirac equation. P. G. reinhard, M. Rufa, J. Maruhn, W. Greiner, J. Friedrich, Z. Phys. A323, (1986)13. K. T. R. Davies, H. Flocard, S. Krieger, M. s. Weiss, Nucl. Phys. A342 (1980)111. Magic number at N = 20 ? Prediction of 0- state

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