# Yoko Ogawa (RCNP/Osaka)

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

IntroductionThe purpose of this study is to understand the properties of finite nuclei by using a chiral sigma model with pion mean field within the relativisticmean field theory.Chiral symmetry : Linear sigma model in hadron physicsM. Gell-Mann and M. Levy,Nuovo Cimento 16(1960)705.Spontaneous chiral symmetry breakingPion :Mediator of the nuclear forceY. Nambu and G. Jona-Lasinio, Phys. Rev. 122(1961)345.H. Yukawa, Proc. Phys.-Math.Soc.Jpn., 17(1935)48.Problem of now frameworkParity projectionSummaryParity projected relativistic Hartree equationsContents

LagrangianLinear Sigma Model

Extended Chiral Sigma Model Lagrangian(ECS)New nucleon field

Mean Field Equation

r = 0.1414 fm-3E/A-M = -16.14 MeVK = 650 MeVECSTM1(RMF)Effective mass :M* = M + gss, m*w = mw + gws ~Saturation propertyCharacter of the ECS model in nuclear matterLarge incompressibilitySmall LS-force~ 80 %

Finite NucleiY. 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 SpectrumLarge incompressibilityIt is hard energetically to change a density.The state with large L bounds deeper.Anomalous pushed up 1s-state.N = 18Without pionWith pion

We use the parity mixing intrinsic state in order to treat the pion mean field in themean field theory because of the pseudovector(scalar) character of pion.We need to restore the parity symmetry and the variation after projection. The Problem and improvement of framework

Parity ProjectionSingle particle wave functionTotal wave function0+0-1h-state2h-state1p-1h2p-2hH. Toki, S. Sugimoto, K. Ikeda, Prog. Theor. Phys. 108 (2002) 903.

N. Kaiser, S. Fritsch, W. Weise, Nucl. Phys. A697(2002)2552p-2hK = 255 MeVExperiment

On the other hand, in 40Ca case the j-upper state is far from Fermi level.In 56Ni case the j-upper stateis Fermi level.

Hamiltonian densityHamiltonian

Field operator for nucleonCreation operator for nucleon in a parity projected state aParity projected wave functionTotal energy

Parity-projected relativistic mean field equationsNucleon partVariation after projection

Meson partWe solve these self-consistent equations by using imaginary time step method.

Difficulties of relativistic treatment Total energy minimum variation condition gives difficulty to the relativistictreatment, because the relativistic theory involves the negative energy states.SummaryWe avoid this problem due to elimination of lower component. We howevertreat the equation which is mathematically equal to the Dirac equation.K. T. R. Davies, H. Flocard, S. Krieger, M. s. Weiss, Nucl. Phys. A342 (1980)111.P. G. reinhard, M. Rufa, J. Maruhn, W. Greiner, J. Friedrich, Z. Phys. A323, (1986)13.We derive the parity projected relativistic Hartree equations.We show the problem in now framework of ECS model.Magic number at N = 20 ?Prediction of 0- state Large incompressibility.Magic number at N = 20.