Neutron enrichment of the neck-originated
intermediate mass fragments
in predictions of the QMD model
I. Skwira-Chalot, T. Cap, K. Siwek-Wilczyńska, J. Wilczyński
for REVERSE-ISOSPIN Collaboration
1. Introduction
2. Results
3. Conclusions
Kazimierz Dolny 29.09.2011
Motivation
There are theoretical suggestions [1] that effect of neutron enrichment of
Intermediate Mass Fragments (IMF) originating from the neck region, emitted
in nucleus-nucleus collisions at energies of several tens of MeV/nucleon, can be
directly associated with the density dependence of the symmetry energy term
in the nuclear equation of state.
We examine predictions of the QMD model in two extreme assumptions
regarding the symmetry energy term: the ASY-HARD and ASY-SOFT.
1. How sensitive is this effect to the symmetry energy term in the equation of
state?
2. Which observables are most suitable for comparisons of the model
predictions with experiments?
[1] M. Di Toro, A Olmi, and R. Roy, Eur. J. A30, 65 (2006).
QMD model. Microscopic model.
Versions of the QMD model:
• BQMD – designed for the description of fragmentation processes at low
energies [2 - 5]
• IQMD – Isospin-QMD – the first QMD which included isospin [6]
• HQMD – combination of the BQMD and the IQMD models – dedicated to
description of pion observables [7]
• RQMD – Relativistic-QMD
• others
[2] M. Begemann-Blaich et al. Phys. Rev. C 48 (1993) 610
[3] W.F.J. MÄuller et al. Phys. Lett. B 298 (1993) 27
[4]. S.C. Jeong et al. Phys. Rev. Lett. 72 (1994) 3468
[5] P.B. Gossiaux et al. Phys. Rev. C 51 (1995) 3357
[6] C. Hartnack, et al., Nucl. Phys. A495 (1989) 303
[7] S. Huber and J. Aichelin. Nucl. Phys. A573 (1994) 587
QMD model of Łukasik [8]
CHIMERA (Code for Heavy Ion Medium Energy ReActions) is a combination of two models:
• Quantum Molecular Dynamics (QMD) model of Aichelin and Stöcker [9, 10]
• Quasi-Particle Dynamics (QPD) of Boal and Glosli [11, 12].
Main assumptions of the CHIMERA code:
1. the scattering of the nucleons can be treated as if they were free
2. the collisions are statistically independent and the interference between two
different collisions can be neglected,
3. the real part of the transition matrix can be replaced by an effective
potential.
The nucleus – nucleus collisions are reconstructed event by event.
[8] J. Łukasik, QMD-CHIMERA code (unpublished); J. Łukasik, Z. Majka, Acta Phys. Pol. B24, 1959 (1993).
[9] J. Aichelin and H. Stöcker, Phys. Lett. 176 B (1988) 14.
[10] J. Aichelin, Phys. Rep. 202 (1991) 233.
[11] D. H. Boal and J. N. Glosli, Phys. Rev. C 38 (1988) 1870.
[12] D. H. Boal and J. N. Glosli, Phys. Rev. C 38 (1988) 2621.
QMD model.
Each nucleon (or quasi-particle) is assumed to be a constant width gaussian wave
packet
 i ( r ,t ) 
1
(2 L )
3/ 4
 ( r  r oi (t )) 2
exp  
4L


 exp

 i

  p oi (t ) r 
 

where: roi – the mean position of the nucleon i,
poi – the mean momentum of the nucleon i,
L - constant parameter, characterizing the width of the wave packet.
The total n -body wave function Ψn is assumed to be the direct product of
coherent states
n 

i
ri , r0 i , p 0 i ,t 
QMD model.
Energy per particle of nuclear matter:
E
A
,  
E
A
  , 0   C sym    2
where: ρ = (ρn + ρp) density of nuclear matter
 
n   p

C sym   
asymmetry
symmetry energy coefficient
SOFT equation of state
ASY HARD
Csym(ρ) = 30.54 MeV
ASY SOFT
Csym(ρ) ~ Csym(ρ0)
 a  b    0
[13]
a = 450 MeV fm3 [14]
b = -1560 MeV fm6
[13] M. Colonna et al., Phys. Rev. C 57 (1997) 1410.
[14] R. Płaneta et al., Phys. Rev. C 77 (2008) 014610.
Simulation and Experiment
System:
124Sn +
Simulated
reaction:
124Sn + 64Ni
Beam
at 35 energy:
MeV/nucleon
64Ni
35 AMeV
Charged Heavy Ion Mass and Energy Resolving Array
beam
target
CHIMERA is a 4π detector.
Consists of 1192 telescopes.
Experimental data were detected only in
FORWARD PART of the detector, which
cover angles in LAB from 10 to 300 (688
telescopes).
Experiment. Identification method.
CsI(Tl)
Si
E-TOF  E, M
E-E  E, Z
Results. Event selection.
In semiperipheral collisions
124
64
Sn  Ni  PLF  TLF  IMF  light particles
Results.
Observables.
In semiperipheral collisions
124
64
Sn  Ni  PLF  TLF  IMF  light particles
The polar angle Ψ is an angle between:
the PLF-TLF separation axis
and
the vector of relative motion
of the IMF-PLF sub-system.
IMFs emitted into Ψ ≈ 1800 originate from the neck formed between PLF-TLF.
Results.
ASY-HARD
ASY-SOFT
Results.
ASY-HARD
ASY-SOFT
Results.
Conclusions.
N
1. The Z ratio is not a sufficiently sensitive observable to discriminate
between different assumptions regarding the symmetry term of the equation
of state.
2. Better observable to test parameters of the symmetry term is the isotopic
ratio for selected pairs of IMFs.
3. The isotopic ratios depend on the assumed form of the symmetry term of
the equation of state.
4. The ASY-SOFT option better describes the experimental results than
ASY-HARD.
Why the Gaussian form for the single particle wave function was adopted?
1. Requirement of the uncertainty principal
 rx  p x 

2
2. One body density distribution consructed from this packets coincides with
the obserwed density profiles.
3. Gaussian wave packets make the calculations feasible.
QMD model. Microscopic model.
Energy per particle of nuclear matter:
E
A
,  
E
A
  , 0   C sym    2
where: ρ = (ρn + ρp) density of nuclear matter
 
n   p
C  

asymmetry
symmetry energy coefficient
SOFT equation of state
ASY HARD
Csym(ρ) = 30.54 MeV
ASY SOFT
Csym(ρ) ~ Csym(ρ0)
[13] M. Colonna et al., Phys. Rev. C 57 (1997) 1410.
[14] R. Płaneta et al., Phys. Rev. C 77 (2008) 014610.

C
0
 a  b
[13]
a = 450 MeV fm3 [14]
b = -1560 MeV fm6
Results.
Experiment
ASY-HARD
ASY-SOFT