Maria Colonna Laboratori Nazionali del Sud (Catania )

1. Testing the behavior of n-rich systems away from normal density Maria Colonna Laboratori Nazionali del Sud (Catania) Eurorib’ 10 June 6-11, 2010 --- Lamoura

2. Equation of State (EoS) of asymmetric nuclear matter the nuclear energy density functionals, effective interactions • Self-consistent MF calculations (and extensions) are a powerful framework to understand the structure of medium-heavy nuclei. Isoscalar, spin, isospin densities, currents … Source: F.Gulminelli In this context relativistic <=> non-relativistic …only a matter of functional • Widely employed in the astrophysical context (modelization of neutron stars • and supernova explosion)

3. Often used parametrization: g<1 asy-soft, g>1 asy-stiff asy-stiff asy-soft asy-stiff asy-soft zoom at low density The largest uncertainties concern the isovector part of the nuclear interaction : The symmetry energy Esym = E/A (β=1) – E/A(β=0) E/A (ρ) = Es(ρ) + Esym(ρ) β² β=(N-Z)/A C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book) Esym(ρ) = J γ = L/(3J)

4. Nuclear astrophysics Nuclear structure Nuclei- neutron star connection ! Focus on Esym at low density M.Centelles et al, PRL(2009) I.Vidana et al., PRC80(2009) Correlation between n-skin and L Properties of n-rich nuclei depend on low-density Esym (because of surface effects !) The crust-core transition density decreases with L

5. asy-soft 18 r (2 – r) SKM*(soft) 18 r stiff 18 (2r2 )/(1+r) stiff (superstiff) Esympot = asy-stiff r = ρ/ρ0 Isospin effects in reaction mechanisms at Fermi energies Transient states of nuclear matter in several conditions ! • Symmetry energy parameterizations are implemented into transport codes (Stochastic Mean Field - SMF) and confronted to experimental data for specific reaction mechanisms and related observables Chomaz,Colonna, Randrup Phys. Rep. 389 (2004) • Baran,Colonna,Greco, Di Toro Phys. Rep. 410, 335 (2005) Parametrizations used in SMF simulations γ~0.6 γ~1

6. ISOSPIN TRANSPORT AT FERMI ENERGIES • Reactions between systems with different N/Z • Isospin diffusion (in the low density interface) is driven by the symmetry energy • Information on Esym at low density 1(PLF) Exchange of energy, mass, isospin between 1 and 2 2(TLF) Reaction plane • If x = N/Z or f(N/Z) • Isospin equilibration • 2) Contact time measured by • kinetic energy dissipation • Symmetry energy Path towards equilibrium of the observable x x1,2(t) – xm = (x1,2 – x m) e-t/τ xm = (x1 + x2)/2 t contact time τ dissipation time for observable x • How to access the N/Z of the PLF ? • Isotopic content of light charged particle emission • as a function of the dissipated energy Galichet et al., Phys. Rev. C79, 064615 (2009) INDRA data: Ni + Ni, Ni + Au @ 52, 74 MeV/A

7. Data: • open points higher than full points (n-rich mid-rapidity particles) • Isospin equilibration reached for Ediss/Ecm = 0.7-0.8 ? (open and full dots converge) • Data fall between the two calculations SMF transport calculations: N/Z of the PLF (Quasi-Projectile) Squares: soft Stars: stiff After statistical decay : N = Σi Ni ,Z = Σi Zi Charged particles: Z=1-4 Comparison with data -- stiff (γ=1) + SIMON forward PLF -- soft(γ=0.6) + SIMON forward n-n c.m. PLF PLF CP CP N/ZCP PLF PLF CP CP Calculations:- N/Z increases with the centrality of collision for the two systems and energies (For Ni + Ni pre-equilibrium effects) • In Ni + Au systems more isospin diffusion for asy-soft (as expected) • - (N/Z)CP linearly correlated to (N/Z)QP

8. Path towards equilibrium of the observable x x1,2(t) – xm = (x1,2 – x m) e-t/τ xm = (x1 + x2)/2 Isospin transport ratio R 1(PLF) X1 2(TLF) B. Tsang et al. PRL 92 (2004) Xm X2 R1,2(t) = (x1,2(t)– xm) / |x1,2 – xm| R1,2 = ±e-t/τ τ Esym N/Z of largest fragment Ni + Ni @ 15,40 AMeV P.Napolitani et al., PRC(2010) yred

9. Microscopic BHF calculations Nuclear reactions: Isospin diffusion Li, Lombardo, Schulze, Zuo, PRC77, 034316 (2008) Tsang et al., PRL(2009) Focus on Esym below normal density Strength of PDR Galichet et al.,(2009) Mass formula Neutron skin thickness A.Carbone et al., PRC(R) (2010) and ref.s therein GMR (Li et al, PRL 2007) Pre-equilibrium dipole emission

10. Conclusions • Need to enlarge the systematics of data (and calculations) to • validate the current interpretation and the extraction of Esym • (consensus on Esym~(ρ/ρ0)γ with γ~0.6-1 at low density) • Still large uncertainties at high density (FAIR, NICA, • RIKEN, …) V.Baran (NIPNE HH,Bucharest) M.Di Toro, C.Rizzo, J.Rizzo, (LNS, Catania) M.Zielinska-Pfabe (Smith College) H.H.Wolter (Munich) E.Galichet, P.Napolitani (IPN, Orsay)

11. Time evolution of the one-body distribution function Vlasov Boltzmann Langevin Loss term Transport model: Semi-classical approach to the many-body problem Vlasov Boltzmann Langevin Vlasov: mean field Boltzmann: average collision term Langevin: randomwalk in phase-space D(p,p’,r) D(p,p’,r) w Ensemble average Fluctuation variance: σ2f =<δfδf> SMF model : fluctuations projected onto ordinary spacedensity fluctuations δρ

12. J.Rizzo et al, NPA (2008) Isospin diffusion Pre-equilibrium dipole oscillation V.Baran et al, PRC79, 021603 (2009). M.Colonna et alPRC78,064618(2008) Isospin distillation (liquid-gas) asy-stiff - - -asy-soft Optical potentials (isospin & momentum dependence of forces) Li & Lombardo, PRC78,047603(2008) Probes of the symmetry energy (at low density)

13. Constraints on Esym GDR Fragment N/Z, Central collisions mass formula L=3r0dEsym/dr|r0 GDR P0=r0L/3 Isospin diffusion BHF Pygmy dipole • M.Colonna et alPRC78,064618(2008) • Galichet,Colonna et al • PRC79(2009)064615 • B.Tsang et al • PRL102(2009)122701 • Trippa, Colò, Vigezzi • PRC77(2008)061304 • P.Danielewicz J.Lee • nucl-th/08073743 • A.Klimkiewicz et al • PRC76(2007)051603 • Li,Lombardo et al • PRC77(2008)034316 Symmetry energy at ρ0 (normal density)

14. Lane potential n effective mass different for protons and neutrons data p Symmetry energy and mass splitting E/A (ρ) = Es(ρ) + Esym(ρ) β² β=(N-Z)/A asy-stiff Often used parametrization: g<1 asy-soft, g>1 asy-stiff asy-soft asy-stiff asy-soft C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book) Momentum dependence zoom at low density Symmetry potential m*n < m*p Asy-soft Asy-stiff m*n > m*p

15. 1(PLF) 2(TLF) Ediss Sorting variable and PLF properties The dissipated energy is well correlated to the impact parameter The charge of the reconstructed PLF is in reasonnable agreement with the data Galichet et al., Phys. Rev. C79, 064615 (2009)