Inputs from SMF BNV simulations Maria Colonna and
Inputs from SMF (BNV) simulations Maria Colonna and Hua Zheng INFN - Laboratori Nazionali del Sud (Catania) ASY-EOS II Collaboration Meeting December 14 -15, 2017 LNS-Catania
Dissipative reaction mechanisms, involving heavy ions, can probe several aspects of the nuclear effective interaction and nuclear EOS Outline § The tool: mean-field models (SMF, BNV) and effective interactions § Study of HIC at 400 Me. V/A, of interest for Asy-EOS II § Sensitivity of selected observables to specific ingredients of the effective interaction (symmetry energy, effective mass splitting)
Mean-field models and effective interactions One-body description ρ1 : one-body density TDHF ETDHF semi-classical approximation k Vlasov δk BUU, SMF Residual interaction: in-medium NN cross section σNN 2 -body correlations, Fluctuations Heff : effective Hamiltonian • Expectation value of physical quantities : • Effective interactions are phenomenological (ex: Skyrme interactions, …) • Fitted parameters incorporate the effects of correlations beyond mean-field functions of isoscalar, spin, isospin densities, currents … DTF, Nuclear matter EOS
The nuclear Equation of State (T = 0) Energy per nucleon E/A (Me. V) Symmetry energy Esym (Me. V) soft poorly known … stiff predictions of several effective interactions symm. matter symm. energy expansion around normal density β = asymmetry parameter = (ρn - ρp)/ρ Ø analogy with Weizsacker mass formula for nuclei (symmetry term) ! or J 25 ≤ J ≤ 35 Me. V 20 ≤ L ≤ 120 Me. V
1. Semi-classical approximation Transport equation for the one-body distribution function f Chomaz, Colonna, Randrup Phys. Rep. 389 (2004) Baran, Colonna, Greco, Di Toro Phys. Rep. 410, 335 (2005) (semi-classical analog of Wigner function) k δk Residual interaction: Correlations, Fluctuations Vlasov Two-body Collision Integral (BUU) vrel 3 (1, 2) 2 (3, 4) 1 Fluctuations in collision integral 4 Boltzmann-Langevin (BL) equation Stochastic Mean-Field (SMF) model Fluctuations are projected in coordinate space (density profile)
2. Molecular Dynamics approaches (AMD, Im. QMD, Co. MD, …) A. Ono, Phys. Rev. C 59, 853(1999) Zhang and Li, PRC 74, 014602(2006) J. Aichelin, Phys. Rep. 202, 233(1991) M. Papa et al. , PRC 64, 024612 (2001), …… stochastic NN collisions Collision integral fully stochastic, but approx. description of mean-field effects… A. Ono, IWM 2011 Colonna, Ono, Rizzo, Phys. Rev. . C 82, 054613 (2010)
Probing the isovector channel of the nuclear effective interaction with SMF model SAMi-J interactions: Skyrme interactions especially devised to improve the spin-isospin properties of nuclei effective mass splitting
stiff Density dependence of Symmetry Energy soft Effective mass splitting stiff, m*n < m*p stiff, m*p < m*n β = 0. 2
p n m* n < m * p m* p < m * n stiff soft k = 2 k. F, β = 0. 2 Momentum dependence of Symmetry potential m* n < m * p Lane potential m*n < m*p m*n > m*p data ρ = ρ0, β = 0. 2 Density dependence of Symmetry potential m* n < m * p n
Collective flows In-plane (transverse) y = rapidity = vparallel /vbeam pt = transverse momentum Out-of-plane (elliptic) X Z V 2 V 1 vs. y = - 1 full out = 0 spherical = + 1 full in V 2 vs pt Flow observables expressed as the 1 st and 2 nd coefficient of the Fourier expansion of the azimuthal distribution of particles d. N/dφ(y, pt ) = 1 + v 1 cos(φ) + 2 v 2 cos(2φ) B-A Li et al. PRL 2002
Mass splitting: N/Z of Fast Nucleon Emission Light isobar 3 H/3 He yields n/p ratio yields 197 Au+197 Au asy-stiff asy-soft 400 AMe. V central, y 0. 3 • m*n>m*p • m*n<m*p asy-stiff asy-soft Observable very sensitive at high p. Tto the mass splitting and not to the asy-stiffness Qualitative trend : ratio increases only with m*n <m*p V. Giordano et al. , PRC 81(2010) see also G. C. Yong et al. , PHYSICAL REVIEW C 80, 044608 (2009)
m*n < m*p stiff m*n > m*p n/p ratio: Preliminary results for 106 Sn+112 Sn 400 AMe. V b = 5 fm, y 0. 3 soft stiff Preliminary results for 132 Sn+124 Sn 400 AMe. V b = 5 fm, y 0. 3 soft m*n > m*p m*n < m*p
Mass splitting impact on Elliptic Flow 197 Au+197 Au, 400 AMe. V, b=5 fm, y(0) 0. 3 Fast nucleon emission m*n<m*p : larger neutron squeeze out at mid-rapidity - Larger neutron repulsion for asy-stiff v 2 vs p. T m*n > m*p y(0) 0. 3 Coulomb effects Comparable results: Interplay between asy-stiffness and effective mass effects ! m*n < m*p Qualitative trend: n flow is more negative than p flow only for the choice m*n < m*p
V 2 : Preliminary results for 132 Sn+124 Sn 400 AMe. V b = 5 fm, y 0. 3 soft m*n > m*p Au + Au stiff soft m*n < m*p stiff
Experimental data and comparison with Ur. QMD calculations P. Russotto et al. Phys. Rev. C 94, 034608 (2016)
To be done … More quantitative and systematic study of the interplay between isovector channel effects: symmetry energy vs effective mass splitting (MD effects) Evolution of the relative role of the two ingredients with the beam energy: Important to extract the density dependence of Esym
Low-energy reaction mechanisms: a study within mean-field models • Fusion vs Quasi fission or Deep Inelastic • Fragmentation • Ternary breaking • Isospin diffusion • Charge equilibration (Fermi energies)
Fusion vs. Quasi Fission: towards the synthesis of SHE 50 Ti +249 Bk 233 Me. V FUSION Umar, Oberacker, Simenel tip side TDHF calculations soft stiff • Fusion probability depends on the deformation/orientation of colliding nuclei Ø Possible summetry energy effects ? ? l (ћ) C. Rizzo et al. , PRC 83, 014604 (2011) SMF calculations with neutron rich systems
Ø A recent investigation: Ternary Quasi Fission SMF Skyrme forces 197 Au + 197 Au collisions - 15 and 23 Me. V/A Mass distribution of fragments Shape by Observables: emitted DF fragment Quadrupole and Octupole moments DF SF A 1 A 2 C. Rizzo et al. , PRC 90 (2014) “PLF-TLF separation time” D F: deformed fragment A 1: lightest fragment S F: “spherical” fragment A 2: heaviest fragment
Ternary breakup in n-rich systems: Sensitivity to Esym & Multidimensional Analysis 124 Sn DF + 64 Ni , E/A = 10 Me. V, b = 6 -8 fm PLF-TLF configuration at separation time PLF Quad. Oct. shifted to the left for stiff Sliced Inverse Regression (SIR) algorithm : a multidimensional analysis technique to discriminate and combine the most sensitive observables P. Cammarata et al. , NIM A 761, 1 -6 (2014)
Ø Dipole excitations in heavy ion reactions (Dyn. Dipole) A 1 TDHF calculations A 2 Simenel et al, PRC 76, 024609 (2007) Initial Dipole D(t) : bremss. dipole radiation If N 1/Z 1 ≠ N 2/Z 2 Compound: stat. GDR Relative motion of neutron and proton centers of mass 130 Me. V + 2 -body collisional damping SMF simulations 132 Sn + 58 Ni , D 0 = 45 fm E/A = 10 Me. V damped oscillations Oberacker et al. , PRC 85, 034609 (2012) 3000 6000 Time (fm/c) C. Rizzo et al. , PRC 83, 014604 (2011)
Dynamical Dipole in heavy ion reactions (DD) • The restoring force is provided by the symmetry term (as in the standard GDR) probe the symmetry energy in the density conditions and configurations reached along the reaction path • Cooling mechanism in the formation of SHE Ø Few experimental data: more systematic analysis needed Ø Theory: a more systematic study of the sensitivity of this mechanism to the ingredients of of the effective interaction and two-body dissipation needed Ground state deformation important ? ? ? DD in the fusion-evaporation of the 40 Ca + 152 Sm heavy system, C. Parascandolo et al. , PRC 93, 044619(2016)
DD oscillations: dependence on the effective interaction MI 132 Sn + 58 Ni , D 0 = 45 fm, E/A = 10 Me. V MD J-L correlations SAMi-J: MI Skyrme (MI) : MD H. Zheng et al. , - free n-n cross section • The DD emission looks sensitive to Esym at ρ = 0. 6 ρsat (damped harmonic oscillator) • Larger strength seen in the MD case: similar to the enhancement factor in the GDR sum rule
Correlations: observables vs. parameters A set of 8 parameterizations in SMF simulations: Skyrme (MI) and SAMi-J 31 + σNN = 40 mb, *2, /2 Observables (A): DD centroid, D”(ω) integral and N/Z of pre-equilibrium nucleon emission Covariance analysis see also Zhang et al, PLB 749, 262 (2015) (n) Blue: negative (n) Red: positive neutrons protons Parameters (B): Symmetry energy slope L, effective mass m* and NN cross section (cs) τcoll : collisional damping time compare with (energy-integrated yield)
q Conclusions Reactions with RIB’s open the opportunity to learn about fundamental properties of the nuclear effective interaction, of interest also in the astrophysical context Ø Low energy collisions: Reaction mechanisms at the borderline with nuclear structure: - role of effective interaction, 2 -body dissipation - n-skin, g. s. deformation -Competition between reaction mechanisms (n-rich neck dynamics) -Pre-equilibrium γ and particle emission Collaborators: Hua Zheng (LNS), Stefano Burrello (LNS), V. Baran (University of Bucharest, Romania)
- Slides: 26