Transcript Document

Possibility to extract thermal temperature
in central heavy-ion collisions
J. Su(苏军) and F.S. Zhang(张
丰收)
College of Nuclear Science and Technology,
Beijing Normal University,
Beijing, China
E-mail: [email protected]
Outline
 Introduction
Thermometer determination
 Theoretical model
 Results and discussions
 Conclusions and outlooks
Introduction
Definition of Temperature
1.Statistical mechanics:
with fixed number of particles N at an energy E
2.The kinetic theory of gases :
In a classical ideal gas, the temperature is related to its
average kinetic energy
<Ek>=number of degree of freedom * 1/2kBT
In heavy-ion reactions at low and
intermediate energy
Dense and hot nuclear matter
?
R =?
What
happened?
Size?
Lifetime?
T=?
Shape?
Detectors
Equation of State
Of Nuclear Matter
E(r,T,p)=？
Liquid-to-Gas
Phase transition?
Challenges
The nuclear systems are special.
Finite, Open, Transient, Expanding
1. Is the equilibrium reached during the reactions?
2. Are there any memory effects?
3. How to define the nuclear temperature?
4. How to extract the thermal temperature?
5. How to define and sign a possible phase transition in a finite, open,
transient and expanding system?
……
To understood the reaction mechanism of the multifragmentation
Thermometer determination
• Experimental Methods：
 Kinetic approaches, Based on the canonical ensemble
Slope thermometer
Fluctuation temperature
G. D. Westfall, Phys. Lett. B 116, 118 (1982).
S. Wuenschel et al., Nuclear Physics A 843, 1 (2010).
 Population approaches, Based on the grand-canonical
ensemble,
Double ratios of isotopic yields
Population of excited states
Isobaric yields from a given soure
S. Albergo et al., Nuovo Cimento A 89, 1 (1985).
D.J. Morrissey et al., Phys. Lett. B 148, 423 (1984).
M. Veselsky et al., Phys. Lett. B 497, 1 (2001).
 Based on the decay model
From the evaporation cascade
K.-H. Schmidt et al., Nucl. Phys. A 710, 157 (2002).
 Kinetic approaches
Originally proposed in 1937 in case of n-induced reactions
(Maxwell-Boltzmann distribution)
dY
dE kin
= f ( E kin ) exp[ 
Slope thermometer
G. D. Westfall, Phys. Lett. B 116, 118 (1982).
B. V. Jacak et al., Phys. Rev. Lett. 51, 1846 (1983).
Fluctuation thermometer
S. Wuenschel et al., Nuclear Physics A 843 (2010) 1–13
E kin
T
]
Slope thermometer
The slope temperature is
extracted by fitting the
slope of the particle spectra.
dY
dE kin
= f ( E kin ) exp[ 
E kin
]
T
The spectra shape can be
Influenced by collective
dynamical effects
G. D. Westfall, Phys. Lett. B 116, 118 (1982)
B. V. Jacak et al., Phys. Rev. Lett. 51, 1846 (1983)
Fluctuation thermometer
Using the momentum fluctuation,
the nuclear temperature can also
be derived.
S. Wuenschel et al., Nuclear Physics A 843 (2010) 1–13
Population approaches
Based on the grand-canonical ensemble
To assume the following type of population of excited states
rN =
1
Z
exp[ 
N  E
T
• Double ratios of isotopic yields
• Population of excited states
• Isobaric yields from a given soure
]
 Double ratios of isotopic yields
density
Ratio between the 2 different emitted fragments
Temperature
S. Albergo et al., Nuovo Cimento A 89, 1 (1985)
Theoretical Model (IQMD+Gemini)
excited pre-fragments
hot nuclear system
final products
v=0.1-0.5c
Projectile
Target
50 fm/c
de-excitation
Multifragmentation
200 fm/c
Isospin-dependent Quantum Molecular Dynamics model
THERMAL SHOCK
COMPRESSION
EXPANSION
PRE-EQ UILIB RIUM EMISSION
EQ UILIBRIUM EMISSION ?
t
FREEZEOUT
statistical decay model (GEMINI)
SECONDARY
EMISSION
SEPARATION
Isospin dependent quantum
molecular dynamics model
Quantum molecular dynamics model (QMD)
The QMD model represents the many body state of the
system and thus contains correlation effects to all orders. In
QMD, nucleon i is described by a Gaussian form of wave
function.
After performing Wigner transformations, the density
distribution of nucleon i is:
From QMD model to IQMD model
 mean field (corresponds to interactions)
U ( r , z ) = U
loc
U
Yuk
U
Uloc : density dependent potential
UYuk: Yukawa (surface) potential
UCoul: Coulomb energy
USym: symmetry energy
UMD: momentum dependent interaction
two-body collisions
Pauli blocking
Coul
 U
Sym
U
MDI
To check the theoretical model
IQMD+GEMINI
 Charge distribution
 Multiplicity
Good agreement!
 Energy spectra
J. Su, B. A. Bian, and F. S. Zhang, PRC 83, 014608 (2011)
Results and Discussions
r≠r0, T > 0,  >0
v=0.1-0.5c
Projectile
E(r, T, ) = ?
Target
?
How to extract the thermal temperature?
1. Some characters: isospin effects? mass effects? T(, N)
2. Possible thermometer: from kinetic characteristics?
Ptot= Pthermal +PFermi +Pflow +Pcoulomb
3. Revisit of the definition: equilibrium? any memory effects?
4. ???
Isospin effects? Mass effects? T(, N)
Assumption: the traditional definition of temperature is suitable.
Systems:
projectile fragmentation (Ca, Zr, Sn, Pb + Ca)
Energy:
600 MeV/u
Observable: THeLi Double ratios of isotopic yields
Ca, Zr, Sn, Pb (600MeV/u)+40Ca
Isospin dependent
Mass dependent
Why?
More work
Jun Su et al. Phys. Rev. C 83, 014608 (2011)
Results and Discussions
r≠r0, T > 0,  >0
v=0.1-0.5c
Projectile
E(r, T, ) = ?
Target
?
How to extract the thermal temperature?
1. Some characters: isospin effects? mass effects? T(, N)
2. Possible thermometer: from kinetic characteristics?
Ptot= Pthermal +PFermi +Pflow +Pcoulomb
3. Revisit of the definition: equilibrium? any memory effects?
4. ???
Possible thermometer
dY
dE kin
= f ( E kin ) exp[ 
E kin
Tslope≠Tthermal !
]
T slope
Ptot= Pthermal +PFermi +Pflow +Pcoulomb
 If we can distinguish the thermal motion from the total motion,
we can extract thermal temperatures from kinetic characteristics.
1. PFermi
2. Pflow
T slope =
A  Af 2
A 1 5
E flow ( )  (
1
R
2
5 T
2
E F (1 
2
2
)
12 E F
sin   cos  )
2
3. Pcoulomb ?
Jun Su et al. Phys. Rev. C 85, 017604 (2011)
2

To Distinguish the Fermi motion
f ( p )  exp( 
p
1
f ( p) 
2
)
(1  exp( p / 2 m T ))
2
2mT
Fermi distribution
Maxwell distribution
Ek =
T slope =
p
2
 2m
f ( p)
A  Af 2
A 1 5
dp
d
d
5 T
2
E F (1 
2
2
)
12 E F
 We can get the relation between the slope temperature
and the quantum slope temperature.
quantum slope temperature ≈ thermal temperature
Jun Su et al. Phys. Rev. C 85, 017604 (2011)
To compare the nuclear thermometers
Assumption: the traditional definition of temperature is suitable.
Systems:
central heavy-ion collisions (Xe+Sn, Au+Au)
Energy:
30 - 80 MeV/u
Observable: difference between THeLi and Tslope (Tflu)
Maxwell distribution: T>THeLi
Fermi distribution: T~THeLi
It is Possible to extract the
thermal temperature from
kinetic characteristics.
Pflow?
Pcoulomb ?
More work
Jun Su et al. Phys. Rev. C 85, 017604 (2011)
Results and Discussions
r≠r0, T > 0,  >0
v=0.1-0.5c
Projectile
E(r, T, ) = ?
Target
?
How to extract the thermal temperature?
1. Some characters: isospin effects? mass effects? T(, N)
2. Possible thermometer: from kinetic characteristics?
Ptot= Pthermal +PFermi +Pflow +Pcoulomb
3. Revisit of the definition: equilibrium? any memory effects?
4. ???
Equilibrium?
Systems:
central heavy-ion collisions (Xe+Sn, Au+Au)
Energy:
20 - 150 MeV/u
Observable: degree of stopping
ratio of transverse to parallel quantities
RE =
 E
2 E
var tl =
 dN / dy x
 dN / dyz
RE or vartl = 1
equilibrium
RE or vartl ≠ 1
non-equilibrium
memory effects?
effect 1: correlation between the
memory loss ratio and the normalized
flow energy.
effect 2: prolate shape of the
fragmenting source, polar angle
dependence of flow energy.
Open question
Condition: a Finite, Open, Transient, Expanding and Non-equilibrium
system
The traditional statistical description is not suitable.
Challenge: 1. Equilibrium in another degrees of freedom?
2. How far is the system from equilibrium?
3. Statistical description?
4. Definitions of temperature and phase transition?
……
More work is needed!
Conclusions and outlooks
1. To verify different methods for determination of T
Kinetic method, Population of excited states,
Double ratios of isotopic yields
2. In each method, to know the reliability for different
conditions
3. New methods are welcome for determination of T and it
is still very far to get a proper definition of liquid-gas
phase transitions in nuclear system
HINP-BG in BNU
2011-05-01
Thank you
for your attention !