RBUU Simulation of Heavy-Ion Collisions

for RAON

Lee, Yujeong (Pusan National University)

Lee, Chang-Hwan (Pusan National University)

Kim, Youngman (Institute for Basic Science, Rare Isotope Science Project)

2015 ECT*-APCTP Joint Workshop 2

Contents

• Motivation

• Nuclear Transport Theory

• RBUU(Relativistic Boltzmann-Uehling-Uhlenbeck) Calculation

• Results and Discussion

• Summary

2015 ECT*-APCTP Joint Workshop 3

Motivation

Heavy-Ion Collision(HIC) produceshighly compressed and heated matter(Compact astrophysical objects, early universe …)

▶︎ In operation in 2019▶︎ Maximum beam energy of ~ 200-250 AMeV

Rare isotope accelerator in Korea,

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Properties of nuclear matterestimated by RBUU simulation

2015 ECT*-APCTP Joint Workshop 4

Nuclear transport theory

Non-equilibrium aspects in the evolution of a collision for a many-body system

The system described by a phase-space distribution functiondescribing the distribution of microscopic states

Evolution of system away from thermal equilibriumby transferring energy, momentum, particle, …

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Heavy-ion collision

Non-equilibrium

2015 ECT*-APCTP Joint Workshop 5

Consider nucleon & sigma, omega and rho-meson field

With the Mean Field approximation :

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Phys. Rev. C, 65, 045201 (2002)

2015 ECT*-APCTP Joint Workshop 6

“Pauli blocking factor”

Relativistic Boltzmann-Uehling-Uhlenbeck equation(MF potential, 2-body collisions, Q.M. effect)

Relativistic Vlasov equation (MF potential, no collision)

Relativistic Boltzmann equation (MF potential, 2-body collision)

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

2015 ECT*-APCTP Joint Workshop 7

Numerical calculationMotivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

RBUU code : simulate Heavy-ion collisions- (1995) C. Fuchs : first developed in Munich- (1996-2000) T. Gaitanos, C. Fuchs : density-dep. RMF models, DBHF approaches- (2002-2005) G. Ferini, T. Gaitanos : isospin effects in the production thresholds- (2005-2010) V. Prassa, T. Gaitanos : in-medium isospin effects in cross sections&kaon pot.- (2014) improved stability

Test particle method > Parallel ensemble methodsingle particle phase-space distribution function represented by N covariant Gaussian test particles

▶︎

σ = 1.4fm σk = 0.346fm-1

N=100

2015 ECT*-APCTP Joint Workshop 8

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Liouville’s theoremthe phase-space density of a certain volume element is constantwith time as it follows the trajectory of the system

Vlasov equation with the test particle method & Liouville’s theorem,

Relativistic Hamilton’s equation

2015 ECT*-APCTP Joint Workshop 9

Local temperature by a fit of the RBUU momentum distributionto the Fermi-Dirac distribution, assuming local thermodynamic equilibrium

… T is the only free parameter, μ* is a T-dependent parameterDetermine μ* from the baryon number conservation

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Consider the point x=0… practically, a (5⨉5⨉5)fm3 cubical box around the center

Baryon density

Isospin asymmetry

( )

z

x

y

Nucl. Phys. A, 589, 732, (1995)

2015 ECT*-APCTP Joint Workshop 10

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Nucl. Phys. A, 589, 732, (1995)

“Artificial” temperaturediffused momentum distribution function due to the finite gaussian width>> increment in temperature

artifi

cial

tem

pera

ture

[MeV

]

system temperature [MeV]

◀ For a Fermi function in a rest frame

2015 ECT*-APCTP Joint Workshop 11

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Results (197Au + 197Au @200AMeV)

▼ Time evolution of density distribution

▼ Time evolution of baryon density and isospin asymmetry at the center

(ρ0 : saturation density, ~0.16fm-3)

ρmax ~ 2.0ρ0

ρI ~ 0.107

2015 ECT*-APCTP Joint Workshop 12

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

n(x=

0,k)

2015 ECT*-APCTP Joint Workshop 13

time [fm/c] 40 44 48 52 56 60T [MeV] 26.5 22.1 18.6 15.0 10.6 8.0μ* [MeV] 753.0 783.1 807.3 832.2 854.8 870.7

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Take average on ▶︎ 1-dim. fct. of

𝝌2 = 4.85⨉10-7

( , : all grid points)

100 mesh points in |k|=1~5

E/A [MeV] 250 600

Tmax [MeV] 30.3 52.1

Phy

s. L

ett.

B 4

78 (2

000)

79

2015 ECT*-APCTP Joint Workshop 14

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Results (132Sn + 64Ni @250AMeV)

▼ Time evolution of density distribution

▼ Time evolution of baryon density and isospin asymmetry at the center

(ρ0 : saturation density, ~0.16fm-3)

ρmax ~ 2.1ρ0

ρI ~ 0.100

2015 ECT*-APCTP Joint Workshop 15

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

n(x=

0,k)

2015 ECT*-APCTP Joint Workshop 16

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

time [fm/c] 36 40 44 48 52 56 60

T [MeV] 40.8 28.9 18.5 12.6 9.3 7.4 6.1

μ* [MeV] 771.7 802.9 813.4 842.3 867.2 885.9 899.1

◀ 1-dimensional RBUU & fitted Fermi momentum distribution at the center at time t=36fm/c

𝝌2 = 2.41⨉10-7

▶︎ The first application of a transport model to HIC at low energy.

( , : all grid points)

2015 ECT*-APCTP Joint Workshop 17

Motivation Nuclear transport theory RBUU calculation Results and discussion Summary and outlook

Summary

• Simulation of HIC experiments by using the RBUU code for estimation of properties of nuclear matter that is expected to be created in .

• Baryon density, isospin asymmetry, local temperature for197Au on 197Au @200AMeV & 132Sn on 64Ni @250AMeV reactions: ρmax ~ 2ρ0, ρI ~ 0.1, Tloc ~ 20-40MeV

• Phase structure of nuclear matter in terms of three thermodynamic variables: temperature, baryon chemical potential and isospin chemical potential

• Ongoing development of advanced transport calculation code for better results

Thank you 감사합니다