1. Shi Shusu Institute of Particle Physics of HuaZhong Normal University
A Monte Carlo Study on the Expansion of Hadronic Gas in Relativistic Heavy Ion Collisions
Shi Shusu
Institute of Particle Physics of HuaZhong Normal University

2. Basic idea
According to the hadronization program ART1.0 of AMPT Monte-Carlo generator, the evolutive picture of hadronization process can be obtained.
Then the radii of reaction area can be calculated based on the distribution picture of hadrons in different evolutive time.
Comparing the results with those obtained from the HBT momentum correlation, the freeze-out time can be fixed finally.

3. A brief introduction to HBT correlation

4. The principle of HBT correlation
Momentum correlation of identical bosons, e.g. pion interferometry.
The exchange symmetry involving identical particles is the origin of the momentum correlation.

5. A pion of momentum is detected at and another identical pion with momentum is detected at the space-time point They are emitted from the source point and of the extented source.

6. The total probability amplitude for two identical pions with momenta and to be produced from two source points in the extended source and to arrive at their respective detection points and is

7. The two-particle momentum distribution is defined as the probability distribution for two pions of momenta to be produced from the extended source and to arrive at their respective detection points

8. Converting the summations into integrals ,we can rewrite the total probability as a double integral over the source point coordinates :

9. The correlation function is defined:
One can introduce another correlation function:

10. In many applications, one parametrizes the effective
density In the from of a Guassian distribution:
The correlation function becomes:

11. What we has been discussed above is related to chaotic source, and we can prove the two-particle correlation Function for a totally coherent source is :
For the analysis of many sets of experimental data, it is
convenient to introduce a ’chaoticity’ patameter λto
modify the correlation function:

12. The common parametrization of the correlation fucntion Pratt-Bertsch parametrizaition:
The main three components of R is called HBT correlation radii, we denote them by:

13. The concept show of

14. Hadronization program ART1.0 of AMPT Monte-Carlo generator
The evolutive pictures of
hadronization process

16. The figs of hadrons’ distribution of space-coordinates in different time
The interval is 2fm/c，time spans from 1.6fm/c to 29.6fm/c.
The x-axis denotes the values of space-coordinates (fm), the y-axis denote the numbers of the corresponding hadrons.
We use 250 Au-Au collisions events with a center-of-mass energy 200Gev/N(b=0) .

20. Calculation of the radii of reaction area based on the distribution pictures of hadrons in different evolutive time
The calculating method is averaging the space-coordinates of the hadrons in different time. We define:

21. The evolutive picture of radii of the reaction area

22. Summary
Comparing the results with those obtained from the HBT momentum correlation, we can estimate the freeze-out time from the fig above, it is 15±2fm/c .The result obtained is reasonable.

23. Thank you！