Yoko Ogawa (RCNP/Osaka)

1
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)
2
Introduction
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
Summary
Parity projected relativistic Hartree equations
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Lagrangian
Linear Sigma Model
4
Extended Chiral Sigma Model Lagrangian(ECS)
New nucleon field
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Mean Field Equation
6
Character of the ECS model in nuclear matter
Large incompressibility
Small LS-force
K 650 MeV
ECS
TM1(RMF)

Effective mass M M gss, mw mw gws
80
Saturation property
E/A-M -16.14 MeV
r 0.1414 fm-3
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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)
8
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.
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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.
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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.
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N. Kaiser, S. Fritsch, W. Weise, Nucl. Phys.
A697(2002)255
2p-2h
K 255 MeV
Experiment
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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.
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Hamiltonian
Hamiltonian density
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Total energy
Parity projected wave function
Creation operator for nucleon in a parity
projected state a
Field operator for nucleon
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Parity-projected relativistic mean field equations
Variation after projection
Nucleon part
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Meson part
We solve these self-consistent equations by using
imaginary time step method.
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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