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Lectures on Heavy-Ion CollisionsLectures on Heavy-Ion CollisionsPart I: Introduction to relativistic kinetic theory

Theodoros GaitanosTheodoros Gaitanos

1. 1. IntroductionIntroduction2. 2. Preliminaries to the relativistic kinetic theoryPreliminaries to the relativistic kinetic theory

3. 3. Derivation of the relativistic transport equationDerivation of the relativistic transport equation 4. 4. Details on numerical realization & simulationsDetails on numerical realization & simulations 5. 5. Applications to intermediate energy heavy-ion collisionsApplications to intermediate energy heavy-ion collisions

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1. Introduction1. Introduction

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Introduction…

??Genesis of … ?Genesis of … ? Hadronization Hadronization

??quark-gluon plasmaquark-gluon plasma plasma particles→plasma particles→ Stars, galaxies...Stars, galaxies...

??

Search & study...Search & study...Highly compressed & hot matter in the present cosmos/create in Lab

People have long asked...People have long asked...what the universe is made off ? What holds it together ? How it will evolve?

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Introduction…

~1700 neutron stars in our galaxy~1700 neutron stars in our galaxy

Neutron Stars (NS)Neutron Stars (NS)

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Introduction… Neutron Stars (NS)Neutron Stars (NS) stable “cosmic nucleus” made of p,n,estable “cosmic nucleus” made of p,n,e--,...,... (!) densest visible matter (!)(!) densest visible matter (!) 1.5-2 x solar mass inside 1.5-2 x solar mass inside 10km radius10km radius

earth's average density~5.5 g cm-3

earth's radius ~6.371km

2x1015 g cm-3

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Introduction… Units in particle physicsUnits in particle physics

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Introduction…

Temperature units:[1MeV]~[107K]nuclei:T~0MeV(earth:T~180K-330K)

Density units:nuclei:ρ

0 ~ 2.5 1014 g cm-3 = 0.165 fm-3

(earth:ρ ~ g cm-3 )

Units in particle physicsUnits in particle physics

Units:

1 GeV=1.8 10−24 g1 fm = 10-15 m

h- = c = 1

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Introduction…Cosmic matter in the Lab: Heavy-ion collisionsCosmic matter in the Lab: Heavy-ion collisions

Phase diagramPhase diagram

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Introduction…

Phase diagramPhase diagram

Cosmic matter in the Lab: Heavy-ion collisionsCosmic matter in the Lab: Heavy-ion collisions

Initial stage...Initial stage...ρ

0∼0.16fm-3

Τ∼0 MeV

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Cosmic matter in the Lab: Heavy-ion collisionsCosmic matter in the Lab: Heavy-ion collisionsIntroduction…

Phase diagramPhase diagram

compressed stagecompressed stageρρ~(1-10)~(1-10)ρρ00

T~50-150 MeVT~50-150 MeV

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Cosmic matter in the Lab: Heavy-ion collisionsCosmic matter in the Lab: Heavy-ion collisionsIntroduction…

Phase diagramPhase diagram

Back to ground stateBack to ground state(light nuclei + particles)(light nuclei + particles)

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Introduction…Experiments on heavy-ion collisionExperiments on heavy-ion collision

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2. Preliminaries to the relativistic 2. Preliminaries to the relativistic kinetic theorykinetic theory

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Preliminaries…

Involves

Elementary particles & interactions → quantum mechanicsParticle velocities v~c → relativistic kinematics & dynamics

Exact treatment

Relativistic quantum transport theory of a many-body nuclear system

Practical applications...

Relativistic quantum transport theory of a many-body nuclear system

heavy-ion collisions (HIC)heavy-ion collisions (HIC)

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Preliminaries…

Involves

Elementary particles & interactions → quantum mechanicsParticle velocities v~c → relativistic kinematics & dynamics

Exact treatment

Relativistic quantum transport theory of a many-body nuclear system

Practical applications...

Relativistic quantum transport theory of a many-body nuclear system

heavy-ion collisions (HIC)heavy-ion collisions (HIC)

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Preliminaries…

Involves

Elementary particles & interactions → quantum mechanicsParticle velocities v~c → relativistic kinematics & dynamics

Exact treatment

Relativistic quantum transport theory of a many-body nuclear system

Practical applications …

Relativistic quantum transport theory of a many-body nuclear system

heavy-ion collisions (HIC)heavy-ion collisions (HIC)

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Preliminaries…

Practical applications (on computer)

Relativistic quantum transport theory of a many-body nuclear system

heavy-ion collisions (HIC)heavy-ion collisions (HIC)

approximations !approximations !

Involves

Elementary particles & interactions → quantum mechanicsParticle velocities v~c → relativistic kinematics & dynamics

Exact treatment

Relativistic quantum transport theory of a many-body nuclear system

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Preliminaries…classical mechanics ↔ quantum mechanics

elem. particles (t,x) ↔ wave packets Ψ(t,x)

Correspondence principle (Niels Bohr, 1923):Correspondence principle (Niels Bohr, 1923):Wave nature of particles not visible, when de Broglie wave length λ=h/p small compared to considered scales

Considered scales here:nuclear radius d ~ 10-15m =1fm

λ2 ~ d

λ1 < d

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Preliminaries…classical mechanics ↔ quantum mechanics

elem. particles (t,x) ↔ wave packets Ψ(t,x)

Correspondence principle (Niels Bohr, 1923):Correspondence principle (Niels Bohr, 1923):Wave nature of particles not visible, when de Broglie wave length λ=h/p small compared to considered scales

Considered scales here:nuclear radius d ~ (5-10)x10-15m ~ 10-14fm

λ2 ~ d

λ1 < d

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Preliminaries…classical mechanics ↔ quantum mechanics

elem. particles (t,x) ↔ wave packets Ψ(t,x)

Correspondence principle (Niels Bohr, 1923):Correspondence principle (Niels Bohr, 1923):Wave nature of particles not visible, when de Broglie wave length λ=h/p small compared to considered scales

λ2 ~ d

λ1 < d

proton Ekin λ=h/p

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Preliminaries…classical mechanics ↔ quantum mechanics

elem. particles (t,x) ↔ wave packets Ψ(t,x)

Correspondence principle (Niels Bohr, 1923):Correspondence principle (Niels Bohr, 1923):Wave nature of particles not visible, when de Broglie wave length λ=h/p small compared to considered scales

λ2 ~ d

λ1 < d

proton Ekin λ=h/p

classicaldescriptionpossible

J.D. Walecka, Ann. Phys. (N.Y.) 8383 (1974) 497

Preliminaries…Classical mechanics versus relativistic field theory Point-like particles relativistic fields dof: coordinates Velocities

Lagrange function Lagrangian density

Equations of motion Equations of motion

J.D. Walecka, Ann. Phys. (N.Y.) 8383 (1974) 497

Preliminaries…Classical mechanics versus relativistic field theory Point-like particles relativistic fields dof: coordinates Velocities

Lagrange function Lagrangian density

Equations of motion Equations of motion

J.D. Walecka, Ann. Phys. (N.Y.) 8383 (1974) 497

Preliminaries…Classical mechanics versus relativistic field theory Point-like particles relativistic fields dof: coordinates Velocities

Lagrange function Lagrangian density

Equations of motion Equations of motion

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Preliminaries…

Relativistic Hadrodynamics: Lagrangian formalism for fields

Degrees of freedomDegrees of freedomNucleons Dirac Spinor → Ψ

Interaction → σ, ω mesons

Interaction: short range attractive & repulsive for r<0.8 fm

Yukawa's conceptYukawa's conceptscreened Coulomb potential

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Preliminaries…

Relativistic Hadrodynamics: Lagrangian formalism for fields

Degrees of freedomDegrees of freedomNucleons Dirac Spinor → Ψ

Interaction → σ, ω mesons

Interaction: short range attractive & repulsive for r<0.8 fm

Yukawa's conceptYukawa's conceptscreened Coulomb potential

coupling strength particle mass

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Preliminaries…

Relativistic Hadrodynamics: Lagrangian formalism for fields

Degrees of freedomDegrees of freedomNucleons Dirac Spinor → Ψ

Interaction → σ, ω mesons

Interaction: short range attractive & repulsive for r<0.8 fm

Yukawa's conceptYukawa's conceptscreened Coulomb potential

coupling strength particle mass

J.D. Walecka, Ann. Phys. (N.Y.) 8383 (1974) 497

Preliminaries…Relativistic Hadrodynamics: Free Lagrangian for the Dirac field (spin ½ nucleons)

Interaction Lagrangian: minimal coupling (analogy to electrodynamics)

σσ,,ωωµµ

σ → scalar (spin 0) fieldωµ → vector (spin 1) field

Full Lagrangian:

Preliminaries…Relativistic Hadrodynamics: Euler-Lagrange equations of motion for Dirac field Ψ:

→ In-medium Dirac equation for spinor field Ψ:

Preliminaries…Relativistic Hadrodynamics: Euler-Lagrange equations of motion for Dirac field Ψ:

→ In-medium Dirac equation for spinor field Ψ:

Preliminaries…Relativistic Hadrodynamics: Euler-Lagrange equations of motion for Dirac field Ψ:

→ In-medium Dirac equation for spinor field Ψ:

Preliminaries…Relativistic Hadrodynamics: Euler-Lagrange equations of motion for Dirac field Ψ:

→ In-medium Dirac equation for spinor field Ψ:

3. Derivation of the relativistic 3. Derivation of the relativistic transport equationtransport equation

Derivation of the relativistic transport equationStarting basisStarting basis The in-medium Dirac equation:

Using the following equalities:

With the help of the effective Dirac equation:

asumption: smooth fields, Wigner-Function Gradient expansion up to 1. order in ЋB. Blättel, V. Koch, U. Mosel, Rep. Prog. Phys. 56 (1993) 1

Wigner transform of the 1-b-density matrix („Wigner-matrix“):

Derivation of the relativistic transport equationStarting basisStarting basis The MF-approach of QHD in terms of the effective Dirac equation:

Using the following equalities:

With the help of the effective Dirac equation:

asumption: smooth fields, Wigner-Function Gradient expansion up to 1. order in ЋB. Blättel, V. Koch, U. Mosel, Rep. Prog. Phys. 56 (1993) 1

Relativistic generalization of the Wigner function Wigner Matrix:→

Derivation of the relativistic transport equationStarting basisStarting basis The MF-approach of QHD in terms of the effective Dirac equation:

Using the following equalities:

With the help of the in-medium Dirac equation:

asumption: smooth fields, Wigner-Function Gradient expansion up to 1. order in ЋB. Blättel, V. Koch, U. Mosel, Rep. Prog. Phys. 56 (1993) 1

Wigner transform of the 1-b-density matrix („Wigner-matrix“):

Derivation of the relativistic transport equationStarting basisStarting basis The MF-approach of QHD in terms of the effective Dirac equation:

Using the following equalities:

With the help of the effective Dirac equation:

asumption: smoothsmooth fields, Wigner-Function Gradient expansion up to 1. order in Gradient expansion up to 1. order in ЋЋB. Blättel, V. Koch, U. Mosel, Rep. Prog. Phys. 56 (1993) 1

Wigner transform of the 1-b-density matrix („Wigner-matrix“):

Derivation of the relativistic transport equation

Decomposition into imaginary- and real-part

Decomposition of Wigner-“Matrix“ into the elements of the spinor basis

Transformation of variables: (x,p)(x,p*)

Relativistic Vlasov equationRelativistic Vlasov equation

Derivation of the relativistic transport equation

At energies above the Fermi energy: Pauli blocking not effective any more

mean-field dynamics not enough; include 2-body correlations (binary collisionsbinary collisions)

Liouville's Theorem:

So far: no collisions...

Molecular chaos assumption: number of 2-body collisions ~ f(x,p) of colliding particles

Collisions local in soace and time

Include also quantum-mechanical Pauli principle via the blocking factors (1-f(x,p))

Derivation of the relativistic transport equation

At energies above the Fermi energy: Pauli blocking not effective any more

mean-field dynamics not enough; include 2-body correlations (binary collisionsbinary collisions)

Liouville's Theorem:

So far: no collisions...

Molecular chaos assumption: number of 2-body collisions ~ f(x,p) of colliding particles

Collisions local in soace and time

Include also quantum-mechanical Pauli principle via the blocking factors (1-f(x,p))

Derivation of the relativistic transport equation

At energies above the Fermi energy: Pauli blocking not effective any more

mean-field dynamics not enough; include 2-body correlations (binary collisionsbinary collisions)

Liouville's Theorem:

So far: no collisions...

Molecular chaos assumption: number of 2-body collisions ~ f(x,p) of colliding particles

Collisions local in space and time

Include also quantum-mechanical Pauli principle via the blocking factors (1-f(x,p))

Derivation of the relativistic transport equation

Relativistic collision integralRelativistic collision integral

Derivation of the relativistic transport equation

Relativistic collision integralRelativistic collision integral

pp22µµppµµ

pp33µµ

pp44µµ

Derivation of the relativistic transport equation

Relativistic collision integralRelativistic collision integral

pp22µµppµµ

pp33µµ

pp44µµ

Derivation of the relativistic transport equation

Relativistic collision integralRelativistic collision integral

pp22µµppµµ

pp33µµ

pp44µµ

Derivation of the relativistic transport equation

Relativistic collision integralRelativistic collision integral

pp22µµppµµ

pp33µµ

pp44µµ

Derivation of the relativistic transport equation

Relativistic transport equationRelativistic transport equation(Relativistic Boltzmann-Uheling-Uhlenbeck, RBUU)(Relativistic Boltzmann-Uheling-Uhlenbeck, RBUU)

RBUU: propagation of RBUU: propagation of f(x,p*)f(x,p*) under the influence of … under the influence of …

Derivation of the relativistic transport equation

Relativistic transport equationRelativistic transport equation(Relativistic Boltzmann-Uheling-Uhlenbeck, RBUU)(Relativistic Boltzmann-Uheling-Uhlenbeck, RBUU)

RBUU: propagation of f(x,p*) under the influence of RBUU: propagation of f(x,p*) under the influence of a relativistic mean-field a relativistic mean-field and … and …

Derivation of the relativistic transport equation

Relativistic transport equationRelativistic transport equation(Relativistic Boltzmann-Uheling-Uhlenbeck, RBUU)(Relativistic Boltzmann-Uheling-Uhlenbeck, RBUU)

RBUU: propagation of f(x,p*) under the influence of RBUU: propagation of f(x,p*) under the influence of a relativistic mean-fielda relativistic mean-field and and 2-body collisions2-body collisions

Literature on (relativistic) kinetic theory…Literature on (relativistic) kinetic theory…1. Primer1. Primer L. Boltzmann, Wien. Ber. 66 (1872) 275

2. Primer…2. Primer…L. Nordheim, Proc. R. Soc. London A119 (1928) 689

E.A. Uehling, G.E. Uhlenbeck, Phys. Rev. 43 (1933) 552

Theoretical backgroundTheoretical background

Non-Relativistic kinetic theory

L.P. Kadanoff, G. Baym, „Quantum Statistical Mechanics“ (Benjamin, N.Y. 1962)

Relativistic kinetic theory

S.R. de Groot, W.A. van Leeuwen, C.G. van Weert

„Relativistic kinetic theory“ (North Holland, Amsterdam, 1980)

Modern Relativistic Quantum Transport Theory

W. Botermans, R. Malfliet, Phys. Rep. 198 (1990) 115 (difficult to understand…)

First applications to HIC…First applications to HIC…

P. Danielewicz, Ann. Phys. 152 (1984) 239 & 305

G.F. Bertsch, S. Das Gupta, Phys. Rep. 160 (1988) 189

Relativistic applications to HIC…Relativistic applications to HIC…

B. Blättel, V. Koch, U. Mosel, Rep. Prog. Phys. 56 (1993) 1

Derivation of the relativistic transport equation

Lectures on Heavy-Ion CollisionsLectures on Heavy-Ion CollisionsPart II: Applications to HIC

4. Details on numerical realization & simulations5. Applications to intermediate energy HIC

Numerical realization (Test-Particle Ansatz)…Numerical realization (Test-Particle Ansatz)…

Discretization of 8-dim. Phase-space distribution f(x,p*) in terms of N Test-Particles

characterized by D (δ-functions, Gaussians,…)

Collision Integral

(coupled channel problem)+

Liouville-TheoremLiouville-Theorem f(x,p*)=const. along the trajectory on the 8-dim. phase-space:

Apply Test-Particle-Ansatz for f(x,p*) in Vlasov-Equation

Numerical realization (Test-Particle Ansatz)…Numerical realization (Test-Particle Ansatz)…

Discretization of 8-dim. Phase-space distribution f(x,p*) in terms of N Test-Particles

characterized by D (δ-functions, Gaussians,…)

Collision Integral

(coupled channel problem)+

Liouville-TheoremLiouville-Theorem f(x,p*)=const. along the trajectory on the 8-dim. phase-space:

Apply Test-Particle-Ansatz for f(x,p*) in Vlasov-Equation

Numerical realization (Test-Particle Ansatz)…Numerical realization (Test-Particle Ansatz)…

Discretization of 8-dim. Phase-space distribution f(x,p*) in terms of N Test-Particles

characterized by D (δ-functions, Gaussians,…)

Collision Integral

(coupled channel problem)+

Liouville-TheoremLiouville-Theorem f(x,p*)=const. along the trajectory on the 8-dim. phase-space:

Apply Test-Particle-Ansatz for f(x,p*) in Vlasov-Equation

Numerical realization (Test-Particle Ansatz)…Numerical realization (Test-Particle Ansatz)…

Discretization of 8-dim. Phase-space distribution f(x,p*) in terms of N Test-Particles

characterized by D (δ-functions, Gaussians,…)

Collision Integral

(coupled channel problem)+

Liouville-TheoremLiouville-Theorem f(x,p*)=const. along the trajectory on the 8-dim. phase-space:

Apply Test-Particle-Ansatz for f(x,p*) in Vlasov-Equation

RBUU – on the computer…RBUU – on the computer…

InitializationInitialization„test particles“ distributed in x- (Thomas-FermiThomas-Fermi) & p-space (Fermi-Fermi-Dirac at T≠0!!Dirac at T≠0!!)widths of Gaussians… Test particle (TP) propagation acc.:

Collisions (parallel-ensemple algorithm)Collisions (parallel-ensemple algorithm)TP‘s collisions in paralell eventsPoint of closest approach (Kodama,…)

Pauli-blocking factors…(1-fi)

σ=σ(Ε,Θ) (from free scattering, from microscopic DBHF…)

Vlasov propagation (RLV method)Vlasov propagation (RLV method)

d/dt xd/dt xµµ = u = uµµ / u / u00

d/dt pd/dt p**µµ = p* = p*µµ p* p*ννFFµνµν + ∂ + ∂µµm*m*EoS (m*,Fµν…)Time step, solution of diff. Eq., box size for mean field calculation…

Common technical parameterCommon technical parameter

Finite number of TP

Collision Integral

(coupled channel problem)+

RBUU – on the computer…RBUU – on the computer…

InitializationInitialization„test particles“ distributed in x- (Thomas-FermiThomas-Fermi) & p-space (Fermi-Fermi-Dirac at T≠0!!Dirac at T≠0!!)widths of Gaussians… Test particle (TP) propagation acc.:

Collisions (parallel-ensemple algorithm)Collisions (parallel-ensemple algorithm)TP‘s collisions in paralell eventsPoint of closest approach (Kodama,…)

Pauli-blocking factors…(1-fi)

σ=σ(Ε,Θ) (from free scattering, from microscopic DBHF…)

Vlasov propagation (RLV method)Vlasov propagation (RLV method)

d/dt xd/dt xµµ = u = uµµ / u / u00

d/dt pd/dt p**µµ = p* = p*µµ p* p*ννFFµνµν + ∂ + ∂µµm*m*EoS (m*,Fµν…)Time step, solution of diff. Eq., box size for mean field calculation…

Common technical parameterCommon technical parameter

Finite number of TP

Collision Integral

(coupled channel problem)+

RBUU – on the computer…RBUU – on the computer…

InitializationInitialization„test particles“ distributed in x- (Thomas-FermiThomas-Fermi) & p-space (Fermi-Fermi-Dirac at T≠0!!Dirac at T≠0!!)widths of Gaussians… Test particle (TP) propagation acc.:

Collisions (parallel-ensemple algorithm)Collisions (parallel-ensemple algorithm)TP‘s collisions in paralell eventsPoint of closest approach (Kodama,…)

Pauli-blocking factors…(1-fi)

σ=σ(Ε,Θ) (from free scattering, from microscopic DBHF…)

Vlasov propagation (RLV method)Vlasov propagation (RLV method)

d/dt xd/dt xµµ = u = uµµ / u / u00

d/dt pd/dt p**µµ = p* = p*µµ p* p*ννFFµνµν + ∂ + ∂µµm*m*EoS (m*,Fµν…)Time step, solution of diff. Eq., box size for mean field calculation…

Common technical parameterCommon technical parameter

Finite number of TP

Collision Integral

(coupled channel problem)+

RBUU – on the computer…RBUU – on the computer…

InitializationInitialization„test particles“ distributed in x- (Thomas-FermiThomas-Fermi) & p-space (Fermi-Fermi-Dirac at T≠0!!Dirac at T≠0!!)widths of Gaussians… Test particle (TP) propagation acc.:

Collisions (parallel-ensemple algorithm)Collisions (parallel-ensemple algorithm)TP‘s collisions in paralell eventsPoint of closest approach (Kodama,…)

Pauli-blocking factors…(1-fi)

σ=σ(Ε,Θ) (from free scattering, from microscopic DBHF…)

Vlasov propagation (RLV method)Vlasov propagation (RLV method)

d/dt xd/dt xµµ = u = uµµ / u / u00

d/dt pd/dt p**µµ = p* = p*µµ p* p*ννFFµνµν + ∂ + ∂µµm*m*EoS (m*,Fµν…)Time step, solution of diff. Eq., box size for mean field calculation…

Common technical parameterCommon technical parameter

Finite number of TP

Collision Integral

(coupled channel problem)+

Au at rest, T=40/N, one single event!one single event!

Stability of nucleus at rest…Stability of nucleus at rest…

Au@0.4AGeV, T=40/N (1 event !)

Stability of a moving nucleus…Stability of a moving nucleus…

Central heavy-ion collision…Central heavy-ion collision…

Central heavy-ion collision…Central heavy-ion collision…

Central heavy-ion collision…Central heavy-ion collision…

Central heavy-ion collision…Central heavy-ion collision…

Central heavy-ion collision…Central heavy-ion collision…

Central heavy-ion collision…Central heavy-ion collision…

peripheral heavy-ion collision…peripheral heavy-ion collision…

Compressed matter in heavy-ion collision…Compressed matter in heavy-ion collision…

Compressed matter in heavy-ion collision…Compressed matter in heavy-ion collision…

Compressed matter in heavy-ion collision…Compressed matter in heavy-ion collision…

Highly compressed matter:t ~10 fm/cρ

c~(2-3)ρ

0 & T~50 MeV

State of matter at the limitsState of matter at the limits

Compressed matter in heavy-ion collision…Compressed matter in heavy-ion collision…

Particle production in heavy-ion collision…Particle production in heavy-ion collision…

π

ΛΛ

ΛΛ

π

ΛΛ

ΛΛ

ΚΚ

ΚΚ

Λ,Σ,π,Κ,...

Λ,Σ,π,Κ,...

Particle production in heavy-ion collisions…Particle production in heavy-ion collisions…

Channels without strangenessChannels without strangenessElastic baryon-baryon collisions: NN↔NN, N∆↔N∆, ∆∆↔∆∆Inelastic baryon-baryon collisions (hard ∆-production & absorption): NN↔N∆, ΝΝ↔∆∆Inelastic baryon-meson collisions (soft ∆-production & absorption) Nπ↔∆

Channels with strangeness (kaon production)Channels with strangeness (kaon production)

Baryon-Baryon : BBBYK (B=N,∆±,0,++, Y=Λ,Σ±,0, K=K0,+)Pion-Baryon : πBYK (YKπB not included)Kaon-Baryon : BKBK (elastic, no isospin exchange)No channels with antistrangeness (K-)

Particle production in heavy-ion collisions...Particle production in heavy-ion collisions...

Channels without strangenessChannels without strangenessElastic baryon-baryon collisions: NN↔NN, N∆↔N∆, ∆∆↔∆∆Inelastic baryon-baryon collisions (hard ∆-production & absorption): NN↔N∆, ΝΝ↔∆∆Inelastic baryon-meson collisions (soft ∆-production & absorption) Nπ↔∆

Channels with strangeness (kaon production)Channels with strangeness (kaon production)

Baryon-Baryon : BBBYK (B=N,∆±,0,++, Y=Λ,Σ±,0, K=K0,+)Pion-Baryon : πBYK (YKπB not included)Kaon-Baryon : BKBK (elastic, no isospin exchange)No channels with antistrangeness (K-)

All isospin channels for K0 & K+

explicitly included!

Cross sections from:

Tsushima et al., PRC59,1999,369

Tsushima et al., PLB337,1994,245

All isospin channels for K0 & K+

explicitly included!

Cross sections from:

Tsushima et al., PRC59,1999,369

Tsushima et al., PLB337,1994,245

and many more………

Particle production in heavy-ion collisions…Particle production in heavy-ion collisions…

Collective flow of matter in heavy-ion collisions…Collective flow of matter in heavy-ion collisions…

From the side...

Collective flow of matter in heavy-ion collisions…Collective flow of matter in heavy-ion collisions…

From the side from the front

Collective flow of matter in heavy-ion collisions…Collective flow of matter in heavy-ion collisions…

From the side

from the front

??

(sub)threshold (sub)threshold KK++ production, production,

flowsflows

in near futurein near future

Threshold production of multistrange hyperons?

Collective hadron flows???

(sub)threshold (sub)threshold KK++ production, production,

flowsflows

in near futurein near future

Threshold production of multistrange hyperons?

Collective hadron flows???

(sub)threshold (sub)threshold KK++ production, production,

flowsflows

in near futurein near future

Final remarks…Final remarks…

Heavy-ion collisionsHeavy-ion collisions a challenge to explore matter at the limitsa challenge to explore matter at the limits important for nuclear astrophysics (neutron stars)important for nuclear astrophysics (neutron stars)

Theoretical description of HICTheoretical description of HIC Semi-classical dynamical approach for nuclear reactionsSemi-classical dynamical approach for nuclear reactions possible to simulate in powerful clusterpossible to simulate in powerful cluster

Important observables & relation to state of matterImportant observables & relation to state of matter production of particles & exoticsproduction of particles & exotics Collective flow phenomena of nucleons & produced (exotic) particlesCollective flow phenomena of nucleons & produced (exotic) particles

Back up slides

peripheral heavy-ion collision…peripheral heavy-ion collision…

σσ,,ωωµµ

J.D. Walecka, Ann. Phys. (N.Y.) 8383 (1974) 497

Theoretical description of HIC…Relativistic Hadrodynamics: Free Lagrangians

→ for the Dirac field (spin ½ nucleons)

→ for the scalar (spin 0) σ field

→ for the vector (spin 1) ω field

Interaction Lagrangian: simplest case (obeys all invariance principles)