Loading in 5 sec....

the CJT Calculation Beyond MFT and its Results in Nuclear MatterPowerPoint Presentation

the CJT Calculation Beyond MFT and its Results in Nuclear Matter

- 62 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' the CJT Calculation Beyond MFT and its Results in Nuclear Matter' - orson-bailey

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

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 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 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

- Relativistic Hartree approximation (RHA) Matter
propagators: G (N), ( ) , D ( )

Hubei University, Wuhan

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 Matter

- Effective action of composite operators

Where:

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

Hubei University, Wuhan

The application of CJT method in studying nuclear matter Matter

- The formulation (QHD-I model)

the bare propagators:

Hubei University, Wuhan

where Matter

Hubei University, Wuhan

The diagrammatic representation of the gap equations Matter

Hubei University, Wuhan

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

- Approximation 1:

Hubei University, Wuhan

- Approximation 3: Matter
Neglect the momentum dependence of the effective nucleon mass

We have

Hubei University, Wuhan

The stationary condition requires

G is a function of , so we have

which ensures the thermodynamic consistency

Hubei University, Wuhan

- The thermodynamic functions Matter

Hubei University, Wuhan

Hubei University, Wuhan

- When 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 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

(1) calculation

(2)

together with the equations of nucleon self-energy

(3)

(4)

these four equations can be numerically solved

Hubei University, Wuhan

- When calculation

Hubei University, Wuhan

Hubei University, Wuhan calculation

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

谢 谢！ calculation

Hubei University, Wuhan

Download Presentation

Connecting to Server..