Transcript shishusu - 中国科学院高能物理研究所

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
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.
A brief introduction to HBT correlation
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.
(k1 , x1 ')
x1
x2
(k2 , x2 ')
A pion of momentum k1 is detected at x ' and another identical pion with
1
'
k
momentum 2 is detected at the space-time point x2 .They are emitted from the
source point x1 and x2 of the extented source.
The total probability amplitude for two identical pions with momenta k1
and k2 to be produced from two source points in the extended source
'
'
and to arrive at their respective detection points x1 and x2 is

x1 , x2

1
i ( x1 )
i ( x2 ) ik1 ( x1  x1' ) ik2 ( x2  x2' )
A(k1 , x1 )e
A(k2 , x2 )e x e
e
2
 A(k1 , x2 )e

'
1
i ( x2 )
A(k2 , x1 )e
i ( x1 ) ik1 ( x1  x2' ) ik2 ( x2  x1' )
e
i ( x1 ) i ( x2 )
'
'
e
e

(
k
k
:
x
x

x
x

1 2
1 2
1 2 )
x1 , x2
  (k1 , k2 : x1' , x2 ' )
e

The two-particle momentum distributionP(k , k ) is defined
k1 , k 2
as the probability distribution for two pions of momenta
to be produced from the extended source and to arrive at
1
x1' , x2'
their respective detection points
2
.
2
1
'
'
P (k1 , k2 ) 
 (k1 , k2 : x1 , x2 )
2!

  (k k
1 2
x1 , x2
: x1 x2  x x2 )
'
1
'
2
Converting the summations into integrals ,we can rewrite the
total probability as a double integral over the source point
coordinates x1 , x2 :
P (k1 , k2 ) 
P (k1 ) P (k2 )(1   dxe
eff ( x : k1 , k2 ) 
i ( k1  k2 ) x
2
 eff ( x : k1 , k2 ) )
 ( x) A(k1 , x) A(k2 , x)
P(k1 ) P(k2 )
The correlation function is defined:
2
P(k1 , k2 )
C2 (k1 , k2 ) 
 1  eff (q : k1k2 )
P(k1 ) P(k2 )
One can introduce another correlation function:
R(k1 , k2 )  C2 (k1 , k2 ) 1  eff (q : k1k2 )
2
In many applications, one parametrizes the effective
density In the from of a Guassian distribution:
eff ( x : k1k2 )
2

y2
z2
t2 
 x

exp 



2
2
2
2 
2 Ry
2 Rz
2 t 


 2 Rx
The correlation function becomes:
C2 (k1 , k2 )  1  Ce
 ( Rx qx ) 2  ( Ry q y ) 2  ( Rz qz ) 2  ( t qt ) 2
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 :
C2 (k1 , k2 )  1
For the analysis of many sets of experimental data, it is
convenient to introduce a ’chaoticity’ patameter λto
modify the correlation function:
C2 (k1 , k2 )  1   e
 ( Rx q x ) 2  ( Ry q y ) 2  ( Rz q z ) 2  ( t qt ) 2
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:
Rout , Rside , Rlong
The concept show of
Rout , Rside , Rlong
Hadronization program ART1.0 of AMPT
Monte-Carlo generator
The evolutive pictures of
hadronization process
The figs of hadrons’ distribution of spacecoordinates 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 spacecoordinates (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) .
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:
The evolutive picture of radii of the reaction area
Summary
Comparing the results with those obtained from the
HBT momentum correlation, we can estimate the freezeout time from the fig above, it is 15±2fm/c .The result
obtained is reasonable.
Thank you！