lectures on heavy-ion collisions part i: introduction to relativistic kinetic theory€¦ · ·...
TRANSCRIPT
Istanbul 2012
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
Istanbul 2012
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?
Istanbul 2012
Introduction…
~1700 neutron stars in our galaxy~1700 neutron stars in our galaxy
Neutron Stars (NS)Neutron Stars (NS)
Istanbul 2012
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
Istanbul 2012
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
Istanbul 2012
Introduction…Cosmic matter in the Lab: Heavy-ion collisionsCosmic matter in the Lab: Heavy-ion collisions
Phase diagramPhase diagram
Istanbul 2012
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
Istanbul 2012
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
Istanbul 2012
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)
Istanbul 2012
2. Preliminaries to the relativistic 2. Preliminaries to the relativistic kinetic theorykinetic theory
Istanbul 2012
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)
Istanbul 2012
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)
Istanbul 2012
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)
Istanbul 2012
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
Istanbul 2012
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
Istanbul 2012
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
Istanbul 2012
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
Istanbul 2012
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
Istanbul 2012
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
Istanbul 2012
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
Istanbul 2012
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…
[email protected], T=40/N (1 event !)
Stability of a moving nucleus…Stability of a moving nucleus…
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………
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
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)