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the CJT Calculation Beyond MFT and its Results in Nuclear Matter. 舒 崧 湖北大学物理学与电子技术院 二零零六年十月二十九日于桂林. Outline. Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter

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The cjt calculation beyond mft and its results in nuclear matter

the CJT Calculation Beyond MFT and its Results in Nuclear Matter

舒 崧

湖北大学物理学与电子技术院

二零零六年十月二十九日于桂林


Outline
Outline Matter

  • Motivation

  • General introduction of CJT formalism

  • The application of CJT method in studying nuclear matter

  • The mean field approximation in the CJT calculation and the comparison to the usual MFT results

  • The beyond MFT calculation and the results in the CJT calculation

  • Summary and outlook

Hubei University, Wuhan


Motivation
Motivation Matter

  • Mean field theory (MFT) in the study of nuclear matter

    QHD model, RHA, HF

  • Develop non-perturbative calculation method beyond MFT in studying nuclear matter

    CJT resummation scheme

Hubei University, Wuhan


Mft in studying nuclear matter
MFT in studying nuclear matter Matter

  • Quantum hadrodynamics (QHD)

    simple Walecka model (QHD-I)

MFT:

B.D.Serot, J.D.Walecka, Adv. Nucl. Phys.,Vol.16 (1986) 1

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

Resumming all the tadpole diagram Matter

where

zero-point energy from vacuum

S. A. Chin, Ann. of Phys. 108 (1977) 403

Hubei University, Wuhan


Introduction of cjt formalism
Introduction of CJT formalism Matter

  • Effective action of composite operators

Where:

J. Cornwall, R. Jackiw and E. Tomboulis, Phys. Rev. D10 (1974) 2428

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

Effective potential (translational invariance) Matter

Stationary condition

Hubei University, Wuhan


The application of cjt method in studying nuclear matter
The application of CJT method in studying nuclear matter Matter

  • The formulation (QHD-I model)

the bare propagators:

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

The thermodynamical potential

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

where Matter

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

From the stationary condition Matter

we have

Hubei University, Wuhan



The mean field approximation in the cjt calculation
The mean field approximation in the CJT calculation Matter

  • Solving the gap equations according to the mean field requirements at the first step

    • Approximation 1:

      replace the full meson propagators by the bare ones

      which means we have neglected the medium effect of the mesons

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

where

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

  • Approximation 3: Matter

    Neglect the momentum dependence of the effective nucleon mass

We have

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

The stationary condition requires

G is a function of , so we have

which ensures the thermodynamic consistency

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

Hubei University, Wuhan


The numerical results
The numerical results Matter

  • When T=0,

The binding energy curve

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

The isotherms of pressure

versus density (liquid-

gas phase transition)

The effective nucleon mass

as a function of temperature

Hubei University, Wuhan


The beyond mft calculation and the results in the cjt calculation
The beyond MFT calculation and the results in the CJT calculation

  • The medium effects of mesons will be included in a thermodynamic consistent way

The effective mass of and meson will be determined by minimizing the thermodynamic potential with respect to the effective mass

these requirements will generate two coupled equations

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

(1) calculation

(2)

together with the equations of nucleon self-energy

(3)

(4)

these four equations can be numerically solved

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

The numerical results calculation

  • When

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

Hubei University, Wuhan



Summary and outlook
Summary and outlook calculation

  • The CJT method has been applied to study the nuclear matter.

  • We have reproduced the MFT results in the CJT calculation after taking certain approximation.

  • The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed.

  • The thermodynamic consistency has been preserved in our calculation.

Hubei University, Wuhan


The cjt calculation beyond mft and its results in nuclear matter

谢 谢! calculation

Hubei University, Wuhan