transport phenomena in heavy-ion reactions
DESCRIPTION
Transport phenomena in heavy-ion reactions. Catania, Italy, Jan. 23, 2004. Lijun Shi NSCL MSU and Physics Department, McGill University. Transport theory. Transport theory. Boltzmann equation: Single particle energy Optical potential is: EOS: through total energy E - PowerPoint PPT PresentationTRANSCRIPT
Transport phenomena in heavy-ion reactions
Lijun ShiNSCL MSUandPhysics Department, McGill University
Catania, Italy, Jan. 23, 2004
Page 2
Transport theory Boltzmann equation:
Single particle energy
Optical potential is:
EOS: through total energy E optical potential Uopt
Transport theory
Page 3
Isospin diffusion coefficient DI :
In the limit of weak nonequilibrium and small isospin gradient, isospin flow will be proportional to the isospin gradient
Particle Flow:
Isospin diffusion coef DI:
vi: average velocity of particle imean velocity: v = (1v1 + 2v2)/ Isospin asymmetry: =(n1-n2)/(n1+n2)
Isospin Flow:
Diffusion
Page 4
Numerical results:(diffusion coefficient for free Fermi gas)
Temperature (MeV)
Diffusion coefficient
Mean field enhances isospin diffusion:R = DI(with IEOS) / DI(free gas)
Free gas
Page 5
Isospin diffusion in HIC:
Basic ideas: Peripheral reactions 124Sn+124Sn, 112Sn+112Sn
-- no diffusion 124Sn+112Sn, 112Sn+124Sn
-- diffusion Relative change between
the two systems is due to diffusion effect
Measure isospin in the projectile-like region
Isospin-diffusion
Isospin changed
Isospin Diffusion
Page 6
Isospin dependent Mean Field
IEOS ~ diffusion coefficient ( = / 0)
Isospin-diffusion
Page 7
Ri changes as a function of time (simulation)
Ri is a stable signalNon-diffusion effects: cancelled outRi ~ IEOS ->Diffusion effect
Isospin-diffusionM. B. Tsang, et al.
Projectile isospin asymmetry from simulation = (N-Z)/(N+Z),
Page 8
Compare with experiment data
Exp. Data extracted from isoscaling parameter
Ri(exp)0, incomplete isospin diffusion
Exp. favors iso-SH type IEOS
Iso-stiff type IEOS is favored, especially iso-SH
NS and SKM:iso-soft type IEOS is not favored
Isospin-diffusion
See also discussion by M. B. Tsang
Page 9
Summary: Optical potential for Transport theory and
simulation Asymmetric matter:
symmetry energy, symmetry potential
Isospin diffusion coefficient derived mean field enhances isospin diffusion
Simulating isospin diffusion in HIC
– compared with data, – favors iso-SH type
Page 10
Isospin change in the projectile-like region
Basic ideas: Peripheral reactions 124Sn+112Sn, 112Sn+124Sn
-- diffusion 124Sn+124Sn, 112Sn+112Sn
-- no diffusion Relative change between
the two system is the diffusion effect
Measure the projectile-like region
Isospin-diffusion
app 1
Page 11
Isospin equilibration time scale:
Consider case where DI ~ 0.41 fm.c
1) 1/tH ~ DI / (s * r), where s is the size of the spectator, r is the distance between two spectator, s~4fm, r~4fm,
==> tH ~ 39 fm/c
2) Another way is from diffusion equation with some assumption about the initial isospin profile,
==> tH ~ 35-44 fm/c
BUU simulation does suggest a comparable time scale, for the system 96Ru+96Zr at 100MeV/u, b=5fm,
==> t ~ 40 fm/c.
Diffusion coefficient
app 2
Page 12
Calculate Isospin diffusion coefficient DI :
1) Start from
Boltzmann equations,
2) Variation
of distribution:
3) Self-consistency
equation:
4) Resulting equation
for DI:
Diffusion coefficient
f = ( )
app 3
Page 13
Isoscaling from Relative Isotope Ratios
Factorization of yields into p & n densities
Cancellation of effects from sequential feedings
Robust observables to study isospin effects
R21=Y2/ Y1
pn ZNe Zp
Nn ^ ^
app 4
Page 14
Mean-free-path estimate Classical Two component system model
l1 is the mean free path of particle 1 in the medium of particle 2, C1 is the thermal velocity
Estimate:
T=60MeV, =60mb, n=0.16fm-3,
effective mass m=429MeV ,
==> DI = 0.29fm.c
1212 31
1131
mT
nI ClD
app 5