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Transport phenomena in heavy-ion reactions

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

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Transport phenomena in heavy-ion reactions

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  1. Transport phenomena in heavy-ion reactions Catania, Italy, Jan. 23, 2004 Lijun Shi NSCL MSU and Physics Department, McGill University

  2. Transport theory Transport theory • Boltzmann equation: • Single particle energy • Optical potential is: • EOS: • through total energy E • optical potential Uopt

  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 Flow: Isospin diffusion coef DI: vi: average velocity of particle i mean velocity: v = (r1v1 + r2v2)/ r Isospin asymmetry: d=(n1-n2)/(n1+n2) Diffusion

  4. Numerical results:(diffusion coefficient for free Fermi gas) Mean field enhances isospin diffusion:R = DI(with IEOS) / DI(free gas) Free gas Diffusion coefficient

  5. Isospin-diffusion 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

  6. Isospin-diffusion Isospin dependent Mean Field • IEOS ~ diffusion coefficient ( =  / 0)

  7. Ri changes as a function of time (simulation) Projectile isospin asymmetry d from simulation d = (N-Z)/(N+Z), • Ri is a stable signal • Non-diffusion effects: cancelled out • Ri~ IEOS ->Diffusion effect Isospin-diffusion M. B. Tsang, et al.

  8. Isospin-diffusion 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, especiallyiso-SH NS and SKM: iso-soft type IEOS is not favored See also discussion by M. B. Tsang

  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

  10. Isospin-diffusion 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 app 1

  11. Diffusion coefficient 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 simulationdoes suggest a comparable time scale, for the system 96Ru+96Zr at 100MeV/u, b=5fm, ==> t~ 40 fm/c. app 2

  12. df = ( ) Diffusion coefficient Calculate Isospin diffusion coefficient DI : 1) Start from Boltzmann equations, 2) Variation of distribution: 3) Self-consistency equation: 4) Resulting equation for DI: app 3

  13. R21=Y2/ Y1 ^ ^ Isoscaling from Relative Isotope Ratios Factorization of yields into p & n densities Cancellation of effects from sequential feedings Robust observables to study isospin effects app 4

  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 app 5

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