AMD. Skyrme ( ) 2009/03/ / 22

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1 AMD Skyrme ( ) 2009/03/ / 22

2 (?) ( ) 2009/03/ / 22

3 Nuclear Matter in Nuclear Collisions and Neutron Stars 0 60 E sym [MeV] NL3 ChPT DBHF DD ρδ DD TW var AV18+ δ V+3 BF BHF(AV18+3BF) FSU gold x= 1 x= ρ / ρ 0 QMD simulation of nuclear pasta. G. Watanabe et al. Inhomogeneous. (fragments, clusters, pasta) Excited. (finite temperature and/or dynamic) Liquid-gas phase transition. Statistical calculations with AMD for finite systems Relevance of equilibrium in nuclear collisions (Furuta, Ono) Extension of AMD for cluster correlations (Ono) AMD study of neutron star (Hasnaoui, Ono, Furuta, Gulminelli, Chomaz) Implementation of Skyrme force in AMD Isospin effects etc in heavy-ion collisions ( ) 2009/03/ / 22

4 Antisymmetrized Molecular Dynamics Initial State AMD wave function [ { ( Φ(Z) = det exp ν rj Z ) i 2 } χαi (j) ] ij ν Branching c + c 2 + c Z i =.. i νdi + 2 ν K i ν : Width parameter = (2.5 fm) 2 χ αi : Spin-isospin states = p, p, n, n d x Antisymmetrization 0s 0p Stochastic equation of motion for the wave packet centroids Z: d dt Z i = {Z i, H} PB + Z i (t) + (NN collisions) Mean field (Time evolution of single-particle wave functions) Nucleon-nucleon collisions (as the residual interaction) Energy is conserved. No temperature in the equation. Quantum effects are included. ( ) 2009/03/ / 22

5 Mean field + Qauntum branching At each time t 0, for each wave packet k,... Mean field propagation t 0 t 0 + τ + Branching at t 0 + τ τ: Coherence time t 0 t = t 0 t = t 0 + τ Z k Z k ψ k ψ k z z w k (z)dz Mean field Branching τ t = t + τ 1 0 for k = 1,..., A P R Initial State i d dt ψ k(t) = h HF ψ k (t) or f k = hhf f k + hhf f k t p r r p t Branching τ 0 (Strongest branching) τ = τ(ρ) (Density-dependent) τ = τ NN-coll (Decoherence at NN collisions) c + c 2 + c ( ) 2009/03/ / 22

6 AMD and FMD with Skyrme force So far AMD calculations are done with the Gogny force. v ij = (W k + B k P σ H k P τ M k P σ P τ )e (r i r j ) 2 /a 2 k + t ρ (1 + P σ )ρ(r i ) σ δ(r i r j ) k=1,2 V = 1 2 A A A A i=1 j=1 k=1 l=1 Skyrme can be flexible and faster. ij v kl lk B 1 ki B 1 lj A 4 Applications to heavy systems and stellar matter V = V ( ρ(r), τ(r), ρ(r), j(r) ) dr A 2 V (+ ɛa 3 ) ρ(r) = ( ) 3/2 A 2ν π i=1 A j=1 e 2ν(r R ij) 2 B ij B 1 ji, R ij = 1 2 ν (Z i + Z j) ( ) 2009/03/ / 22

7 System size dependence of the CPU time for an evaluation of { Z V ; k = 1, 2,... A } k R = 1.0 A 1/3 fm Time / A [msec] A R Naive expectation A 2 V V = dr V ( ρ(r), τ(r), ρ(r), j(r) ) ρ(r) = ( ) 3/2 A 2ν π i=1 A j=1 e (r R ij) 2 B ij B 1 ji Mesh size r = 0.75 fm, Z = Z = N = N Xeon E5430 Harpertown 2.66 GHz, Using 1 of 8 cores, Almost no load by other processes ( ) 2009/03/ / 22

8 System size dependence of the CPU time for an evaluation of { Z V ; k = 1, 2,... A } k Time / A [msec] R = 1.0 A 1/3 fm 1.2 A 1/3 fm 1.5 A 1/3 fm 2.0 A 1/3 fm 3.0 A 1/3 fm R R Naive expectation A 2 V V = dr V ( ρ(r), τ(r), ρ(r), j(r) ) A ρ(r) = ( ) 3/2 A 2ν π i=1 A j=1 e (r R ij) 2 B ij B 1 ji Mesh size r = 0.75 fm, Z = Z = N = N Xeon E5430 Harpertown 2.66 GHz, Using 1 of 8 cores, Almost no load by other processes ( ) 2009/03/ / 22

9 AMD results for multifragmentation (central collisions) 40 Ca + 40 Ca at 35 MeV/u, b = 0 Xe + Sn at 50 MeV/u, 0 b 4 fm Experiment AMD AMD Charge distribution H S-K Na-P He C-Ne Li,Be,B S- Na-P C-Ne H He Li-B S- Na-P H He Li-B C-Ne dn/dz 1-1 AMD/DS AMD/D INDRA data Hagel et al. PRC50(1994)2017 τ(ρ) τ NN-coll Z Can we reproduce different data with the same model of branching? (Cluster correlations?) AMD (τ 0) AMD (τ NN-coll ) ( ) 2009/03/ / 22

10 Rare isotope production by projectile fragmentation 48 Ca + 9 Be at 140 MeV/nucleon Mocko, Tsang, AO et al., PRC78(2008) Cross section (mb) B C N O F Ne Na Mg AMD Al Si P S Cl Ar K Ca Neutron excess N-Z AMD calc: 17,000 events 40 CPU days (HPC Center at MSU) Experiment: 7 events ( ) 2009/03/ / 22

11 Experimental data of velocity shift Ricciardi et al., PRL 90 (2003) U + Pb and 238 U + Ti at 1 GeV/nucleon Notani et al., PRC 76 (2007) Ar + 9 Be about 90A MeV Dashed line: Morrissey systematics v A v beam v = v beam + v ( ) 2009/03/25 26 / 22

12 Fragment mean velocity and yield 0 90 no cluster cluster 00 no cluster cluster 0 P z /A [MeV/c] Yield [mb] 50 1 Final fragments A A ( ) 2009/03/ / 22

13 p + 27 Al at 180 MeV Y. Tosaka, A. Ono, H. Horiuchi, PRC60 (1999) Z Z (τ coherence 0) ( ) 2009/03/ / 22

14 p + 27 Al at 180 MeV Y. Tosaka, A. Ono, H. Horiuchi, PRC60 (1999) AMD QMD A 1 2 A projectile ( ) 2009/03/ / 22

15 p, α α (5 GeV/u) + Au Tomoyuki Maruyama et al, PTP 97 (1997) 579. QMD p (11.5 GeV) + Au Y. Hirata et al, NPA 707 (2002) 193. (JAM/MF) ( ) 2009/03/ / 22

16 Excited low-density system E Gas (nucleons + clusters) E = 28A MeV W(E) 8A MeV Liquid-gas phase transition E = A MeV E = 4A MeV. MeV 0 MeV 36 Ar W(E) e 2 ae Volume V = 4 π(9 fm)3 3. ( ) 2009/03/ / 22

17 Equilibrium ensembles and caloric curves Ono & Horiuchi Ohnishi & Randrup Schnack & Feldmeier Sugawa & Horiuchi Furuta & Ono Hasnaoui et al T [MeV] T 2 /13 5 E total /A total =(3/2)T T 2 / E * total /A total [MeV] Furuta and Ono, PRC79 (2009) ; PRC74 (2006) ( ) 2009/03/ / 22

18 Production of light charged particles p(62 MeV) + Fe d p(1200 MeV) + Au d ( ) 2009/03/ / 22

19 Cluster correlations in heavy-ion collisions 197 Au Au at 150 MeV/u Exp. Be B p Li d α 3 He t Usual AMD t d d h α α d d t α Be B Li α 3 He t d p ( ) 2009/03/ / 22

20 Cluster formation During the time evolution of AMD, Cluster formation Propagation Breakup B 1 N 1 + B 1 + N 2 + B 2 C 1 + C 2 N 1, N 2 : Colliding nucleons B 1, B 2 : Spectator nucleons/clusters C 1, C 2 : N, (2N), (3N), (4N) N 1 N 2 p 1 p 2 ϕ +q 1 p 1 + q p 2 q ϕ q 2 ϕ 1 C 1 C 2 ϕ 2 B 2 ( ) dσ dσ dω = F kin ϕ 1 ϕ+q 1 2 ϕ 2 ϕ q 2 2 dω NN ( ) 2009/03/ / 22

21 Effects of cluster correlations 40 Ca + 40 Ca, E/A = 35 MeV, filtered violent collisions w/o cluster correlations with cluster correlations experiment S- H S- H S-K H Na-P C-Ne Li-B He Na-P C-Ne Li-B He Na-P He C-Ne Li,Be,B p 6.7 d 1.5 t He 0.3 α 2.7 Coherence time: τ NN-coll p 4.4 d 1.8 t He 0.6 α 5.0 Effects of clusters M p M α IMF Z ( ) 2009/03/ / 22

22 Results for Sn + Sn system 112 Sn Sn at E/A = 50 MeV/nucleon, 0 < b < 2 fm With cluster correlations ΣZ(70 < θ < 1 ) = π dn/dω Sn Sn E/A = 50 MeV 0 < b < 2 fm -2 0 < θ < < θ < 1 Exp Z Gogny n 27.3 p.4 d 6.4 t He 1.2 α Z E kin /A [MeV] Sn Sn E/A = 50 MeV 0 < b < 2 fm < θ < < θ < 1 Gogny exp Z Xe+Sn, INDRA data p 8.4 d 4.4 t He 0.9 α.1 multiplicities of detected particles ( ) 2009/03/ / 22

23 AMD Skyrme AMD ( ) 2009/03/ / 22