Neutron enrichment of the neck-originated intermediate mass fragments

in predictions of the QMD model

I. Skwira-Chalot, T. Cap, K. Siwek-Wilczyńska, J. Wilczyńskifor 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.

[1] M. Di Toro, A Olmi, and R. Roy, Eur. J. A30, 65 (2006).

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?

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]

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.

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].

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[8] J. Łukasik, QMD-CHIMERA code (unpublished); J. Łukasik, Z. Majka, Acta Phys.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.

rtp

iL

trrL

tr oioi

i )(exp4

))((exp

)2(1

),(2

4/3

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.

Each nucleon (or quasi-particle) is assumed to be a constant width gaussian wave packet

QMD model.

The total n -body wave function Ψn is assumed to be the direct product of coherent states

tprr iiiin ,,, 00

QMD model.

Energy per particle of nuclear matter:

20,, symCAE

AE

where: ρ = (ρn + ρp) density of nuclear matter

asymmetry

symmetry energy coefficient

pn

symC

SOFT equation of state

ASY HARD Csym(ρ) = 30.54 MeV

[13] M. Colonna et al., Phys. Rev. C 57 (1997) 1410.[14] R. Płaneta et al., Phys. Rev. C 77 (2008) 014610.

ASY SOFT Csym(ρ) ~ Csym(ρ0) [13]

a = 450 MeV fm3 [14] b = -1560 MeV fm6

0ba

Simulation and Experiment

System: Beam energy:124Sn + 64Ni 35 AMeV

Charged Heavy Ion Mass and Energy Resolving Array

Experimental data were detected only in FORWARD PART of the detector, which cover angles in LAB from 10 to 300 (688 telescopes).

beam

target

CHIMERA is a 4π detector. Consists of 1192 telescopes.

Simulated reaction: 124Sn + 64Ni at 35 MeV/nucleon

Experiment. Identification method.

Si

CsI(Tl)

E-TOF E, M E-E E, Z

Results. Event selection.

In semiperipheral collisions

particleslightIMFTLFPLFNiSn 64124

Results.

Observables.

IMFs emitted into Ψ ≈ 1800 originate from the neck formed between PLF-TLF.

the PLF-TLF separation axisand

the vector of relative motion of the IMF-PLF sub-

system.

The polar angle Ψ is an angle between:

In semiperipheral collisions particleslightIMFTLFPLFNiSn 64124

Results.

ASY-HARD ASY-SOFT

Results.

ASY-HARD ASY-SOFT

Results.

Conclusions.

1. The 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.

ZN

Why the Gaussian form for the single particle wave function was adopted?

1. Requirement of the uncertainty principal

2. One body density distribution consructed from this packets coincides with the obserwed density profiles.

3. Gaussian wave packets make the calculations feasible.

2

xx pr

QMD model. Microscopic model.

Energy per particle of nuclear matter:

20,, symCAE

AE

SOFT equation of state

ASY HARD Csym(ρ) = 30.54 MeV

where: ρ = (ρn + ρp) density of nuclear matter

asymmetry

symmetry energy coefficient

pn

C

[13] M. Colonna et al., Phys. Rev. C 57 (1997) 1410.[14] R. Płaneta et al., Phys. Rev. C 77 (2008) 014610.

ASY SOFT Csym(ρ) ~ Csym(ρ0) [13]

a = 450 MeV fm3 [14] b = -1560 MeV fm6

baC

0

Results.

ASY-HARD ASY-SOFT

Experiment