Production of clusters and pions in heavy-ion collisions

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1 Production of clusters and pions in heavy-ion collisions Akira Ono Department of Physics, Tohoku University NPCSM 16: YIPQS long-term and Nishinomiya-Yukawa memorial workshop on "Nuclear Physics, Compact Stars, and Compact Star Mergers 16", Oct Nov. 18, 16, YITP, Kyoto, Japan Clusters (d, t, 3 He, α) in heavy-ion collisions and in AMD Pion production based on AMD calculation (+JAM) Recent progress in the comparison of many transport codes Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 1 / 34

2 Various densities in heavy-ion collisions Nuclear EOS (at T = ) (E/A)(ρ p,ρ n ) = (E/A) (ρ) + S(ρ)δ 2 + ρ = ρ p + ρ n, δ = (ρ n ρ p )/(ρ n + ρ p ). Constrains on S(ρ) at Horowitz et al., J. Phys. G: Nucl. Part. Phys. 41 (14) ρ?????????? ρ > ρ n,p(center) [fm 3 ] fm/c fm/c fm/c 3 fm/c 4 fm/c 132 Sn Sn, 3 MeV/u, b (N/Z)central Symmetry Energy [MeV].2 (a)..... (b) n, SLy4m (L=46) p, SLy4m (L=46) n, SLy4'm (L=8) p, SLy4'm (L=8) 1.2 n/p, SLy4m (L=46) n/p, SLy4'm (L=8) t [fm/c] 4 3 SLy4 (L=46 MeV) L=8 MeV ρ [fm -3 ] fm/c Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 2 / 34

3 Probing high-density dynamics by pions Bao-An Li, PRL88 (2) Pion ratio π /π + has been proposed as a good probe of symmetry energy at high densities ρ n /ρ p ratio in the high density region Production/absorption of and π: (N = n or p) N + N N + N + N N + N + π N + π Simple expectation: π /π + (N/Z ) 2 First-chance N N N N Nπ Chemical equilibrium n,p(center) [fm 3 ] fm/c fm/c fm/c 3 fm/c 4 fm/c 132 Sn Sn, 3 MeV/u, b (N/Z)central Symmetry Energy [MeV].2 (a)..... (b) n, SLy4m (L=46) p, SLy4m (L=46) n, SLy4'm (L=8) p, SLy4'm (L=8) 1.2 n/p, SLy4m (L=46) n/p, SLy4'm (L=8) t [fm/c] 4 3 SLy4 (L=46 MeV) L=8 MeV ρ [fm -3 ] fm/c Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 3 / 34

4 Clustering phenomena in excited states of nuclear systems Multi fragmentation in heavy ion collision Excitation energy/temperature Liquid-gas phase α condensation matter Molecular resonance Cluster decay Threshold energy Collective mode (GR, PR) Molecular orbitals Weakly bound systems developed clusters deformation Shell evolusion Halo, skin nn correlation shell structure custer breaking neutron-rich Kanada-En yo, Kimura, Ono, Prog. Theor. Exp. Phys. 12 1A2 (12) Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 4 / 34

5 Interacting and reacting clusters in heavy-ion collisions INDRA data, Hudan et al., PRC67 (3) FOPI data, Reisdorf et al., NPA 848 () 366. Partitioning of protons Xe + Sn Au + Au MeV/u 2 MeV/u p % 21% α % % d, t, 3 He % 4% A > 4 6% 18% d α d t h d t d α α The system may be composed of many clusters. Clusters are not only created but also broken by reactions. n + p + X d + X d + n + X t + X d + p + X h + X t + p + X α + X h + n + X α + X d + d + X α + X 2n + p + X t + X n + 2p + X h + X d + n + p + X α + X 2n + 2p + X α + X d + d p + t d + d n + h p + t n + h d + t n + α d + h p + α d + t 2n + h d + h 2p + t d + α t + h Transport models with clusters +decay Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 / 34

6 Transport with clusters (pbuu) BUU with clusters Danielewicz and Bertsch, NPA 33 (1991) 712. Coupled equations for f n (r,p, t), f p (r,p, t), f d (r,p, t), f t (r,p, t), f h (r,p, t) are solved by the test particle method. f n t + v f n r U n r f n p = I n coll [f n, f p, f d, f t, f h ] without clusters f p t f d t + v f p r U p r f p p = I p coll [f n, f p, f d, f t, f h ] + v f d r U d r f d p = I coll d [f n, f p, f d, f t, f h ] f t t + v f t r U t r f t p = I coll t [f n, f p, f d, f t, f h ] f h t + v f h r U h r f h p = I coll h [f n, f p, f d, f t, f h ] with clusters Coupland, Lynch, Tsang, Danielewicz, Zhang, PRC 84 (11) 463. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 6 / 34

7 Antisymmetrized Molecular Dynamics (very basic version) Ono, Horiuchi, Maruyama, Ohnishi, Prog. Theor. Phys. 87 (1992) 118. AMD wave function [ { ( Φ(Z ) = det exp ν r j Z ) i 2 ] }χ αi (j ) i j ν Z i = νd i + i 2ħ ν K i ν : Width parameter = (2. fm) 2 χ αi : Spin-isospin states = p, p,n,n Equation of motion for the wave packet centroids Z d dt Z i = {Z i,h } PB + (NN collisions) {Z i,h } PB : Motion in the mean field Φ(Z ) H Φ(Z ) H = + (c.m. correction) Φ(Z ) Φ(Z ) H: Effective interaction (e.g. Skyrme force) NN collisions W i f = 2π ħ Ψ f V Ψ i 2 δ(e f E i ) V 2 or σ N N (in medium) Pauli blocking Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 7 / 34

8 Failure of fragmentation AMD with usual NN collisions (very basic version) Central Xe + Sn at MeV/u fm/c 4 fm/c 8 fm/c 1 fm/c 16 fm/c fm/c 24 fm/c Multiplicity Xe + Sn MeV/u A Multiplicity n p d t 3 He Exp. AMD Z Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 8 / 34

9 NN collisions without or with cluster correlations W i f = 2π ħ Ψ f V Ψ i 2 δ(e f E i ) In the usual way of NN collision, only the two wave packets are changed. { } { } Ψ f = ϕ k1 (1)ϕ k2 (2)Ψ(3,4,...) 3 Phase space or the density of states for two nucleon system Molecular Dynamics (ignoring antisymmetrization for simplicity of presentation.) K BE E rel V Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 9 / 34

10 NN collisions without or with cluster correlations W i f = 2π ħ Ψ f V Ψ i 2 δ(e f E i ) In the usual way of NN collision, only the two wave packets are changed. { } { } Ψ f = ϕ k1 (1)ϕ k2 (2)Ψ(3,4,...) 3 Phase space or the density of states for two nucleon system Exact Quantum Mechanics Molecular Dynamics (ignoring antisymmetrization for simplicity of presentation.) Extension for cluster correlations Include correlated states in the set of the final states of each NN collision. { } Ψ f ϕ k1 (1)ψ d (2,3)Ψ(4,...),... K V BE E rel Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 9 / 34

11 NN collisions with cluster correlations N 1 + B 1 + N 2 + B 2 C 1 + C 2 Similar to Danielewicz et al., NPA33 (1991) 712. N 1, N 2 : Colliding nucleons B 1, B 2 : Spectator nucleons/clusters C 1, C 2 : N, (2N), (3N), (4N) (up to α cluster) Transition probability B 1 N 1 p () 1 ϕ +q 1 N 2 p () 2 ϕ q 2 B 2 ϕ 1 ϕ 2 C 1 C 2 W (NBNB CC) = 2π ħ CC V NBNB 2 δ(e f E i ) vdσ ϕ 1 ϕ+q 1 2 ϕ 2 ϕ q 2 2 M 2 δ(e f E i )p 2 rel dp reldω M 2 = NN V NN 2 : Matrix elements of NN scattering (dσ/dω) NN in medium (or in free space) p rel = 1 2 (p 1 p 2 ) = p rel ˆΩ q = p 1 p () 1 = p() 2 p 2 ϕ +q 1 = exp(+iq r N 1 )ϕ () 1 ϕ q 2 = exp( iq r N 2 )ϕ () 2 Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 / 34

12 NN collisions with cluster correlations (more explanations) For each NN collision, cluster formation is considered. N 1 + B 1 + N 2 + B 2 C 1 + C 2 W i f = 2π ħ CC V N N NBNB 2 δ(e f E i ) Ono, J. Phys. Conf. Ser. 4 (13) 123 Ikeno, Ono et al., PRC 93 (16) We always have a Slater determinant of nucleon wave packets. A cluster in the final states is represented by placing wave packets at the same phase space point. Consequently the processes such as d + X n + p + X and d + X d + X are automatically taken into account. No parameters have been introduced to adjust individual reactions. There are many possibilities to from clusters in the final states. Non-orthogonality of the final states should be carefully handled. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

13 Construction of Final States Clusters (in the final states) are assumed to have (s) N configuration. B 1 (n ) B 2 (n ) B 1 B 2 B 1 B 1 N(p ) B 3 (n ) N B 3 N B 2 B 3 N B 3 Φ q After p () p () + q Φ 1 N + B 1 C 1 Φ 2 N + B 2 C 2 Φ 3 N + B 3 C Final states are not orthogonal: N i j Φ i Φ j δ i j The probability of cluster formation with one of B s: P ˆP = i j Φ 1 i Ni j Φ j, P = Φq ˆP Φ q i 1 P Don t make a cluster (with any n ). Φ i Φq 2 Choose one of the candidates and make a cluster. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

14 Correlations to bind several clusters d α d t h d t d α α E rel Clusters may form a loosely bound state. e.g., 7 Li = α + t 2. MeV Need more probability of α + t 7 Li C j R i j, P i j C i Step 1 Clusters (and nucleons) C i and C j are linked, if C i is one of the 3 clusters closest to C j, and (i j), and if the distance is 1 fm < R i j < 7 fm, and if they are slowly moving away, P 2 i j /2µ i j < MeV and R i j P i j >. Step 2 Linked clusters (CC) are identified. Following steps are taken only for CC with mass number 6 A 9 or 19 A 23. Step 3 Transition of the internal state of CC by eliminating the (radial component of) internal momentum P i for i CC in the c.m. of CC with some care of the momentum conservation. Next Energy conservation. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

15 Correlations to bind several clusters d α d t h d t d α α E rel Clusters may form a loosely bound state. e.g., 7 Li = α + t 2. MeV Need more probability of α + t 7 Li CC C j Step 4 Search a third particle for E-conservation A cluster C k is selected, depending on the distance and momentum ( R k and P k ) relative to CC. If the selected C k already belongs to a CC, this whole CC is treated as the third particle for E-conservation. Step Scale the radial component of the relative momentum between CC and C k for the total energy conservation. P k = P k + P k βp k + P k R i j, P i j C i R k, P k C k Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

16 Effect of cluster correlations: central Xe + Sn at MeV/u Without clusters With clusters fm/c 4 fm/c 8 fm/c 1 fm/c 16 fm/c fm/c 24 fm/c fm/c 4 fm/c 8 fm/c 1 fm/c 16 fm/c fm/c 24 fm/c Multiplicity Xe + Sn MeV/u A Multiplicity n p d t 3 He Multiplicity Xe + Sn MeV/u A Multiplicity n p d t 3 He Exp. AMD Z 2 Exp. AMD Z Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

17 Results for multifragmentation in central collisions Xe + Sn Multiplicity Multiplicity Xe + Sn 32 MeV/u A Multiplicity n p d t 3 He 2 Exp. AMD Z Xe + Sn MeV/u A Multiplicity MeV/u n p d t 3 He 2 Exp. AMD Z MeV/u Ca + Ca at 3 MeV/u Multiplicity Ca + 4 Ca E/A = 3 MeV Exp. AMD Z Au + Au at 2 MeV/u Multiplicity Au + Au 2 MeV/u Exp. AMD n p d t 3 He Z Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 / 34 A Multiplicity Data: Hudan et al., PRC 67 (3) Hagel et al., PRC (1994) 17. Reisdorf et al., NPA 848 () 366.

18 Collisions at higher energies fm/c fm/c fm/c 132 Sn+ 124 Sn, E/A = 3 MeV, b 3 fm/c 4 fm/c fm/c Pions are measured to probe high-density nuclear matter by the SπRIT experment. n,p(center) [fm 3 ] (a) n, SLy4m (L=46) p, SLy4m (L=46) n, SLy4'm (L=8) p, SLy4'm (L=8) Many protons are bound in clusters. In Au+Au at 2 MeV/u (FOPI data), p: 21%, α: %, d+t+ 3 He: 4% The SπRIT project: TPC in SAMURAI magnet. 1.8 (b) (N/Z)central n/p, SLy4m (L=46) n/p, SLy4'm (L=8) t [fm/c] Momentum dependence of Skyrme (SLy4) interaction has been corrected for high energy collisions, in a similar way to Gale, Bertsch, Das Gupta, PRC 3 (1987) Talk by T. Isobe at NuSYM Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

19 Collisions at higher energies fm/c fm/c fm/c 132 Sn+ 124 Sn, E/A = 3 MeV, b n,p(center) [fm 3 ] (N/Z)central (a). (b) fm/c 4 fm/c n, SLy4m (L=46) p, SLy4m (L=46) n, SLy4'm (L=8) p, SLy4'm (L=8) 1.2 n/p, SLy4m (L=46) n/p, SLy4'm (L=8) t [fm/c] Momentum dependence of Skyrme (SLy4) interaction has been corrected for high energy collisions, in a similar way to Gale, Bertsch, Das Gupta, PRC 3 (1987) fm/c 4 r 2 ( A N n A Z p) [fm 1 ] t = fm/c n p diff., SLy4m (L=46) n p diff., SLy4'm (L=8) vradial, SLy4m (L=46) vradial, SLy4'm (L=8) r [fm] vrad [c] Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

20 Collisions at higher energies fm/c fm/c fm/c 132 Sn+ 124 Sn, E/A = 3 MeV, b n,p(center) [fm 3 ] (N/Z)central (a). (b) fm/c 4 fm/c n, SLy4m (L=46) p, SLy4m (L=46) n, SLy4'm (L=8) p, SLy4'm (L=8) 1.2 n/p, SLy4m (L=46) n/p, SLy4'm (L=8) t [fm/c] Momentum dependence of Skyrme (SLy4) interaction has been corrected for high energy collisions, in a similar way to Gale, Bertsch, Das Gupta, PRC 3 (1987) fm/c 4 r 2 ( A N n A Z p) [fm 1 ] t =2 fm/c n p diff., SLy4m (L=46) n p diff., SLy4'm (L=8) vradial, SLy4m (L=46) vradial, SLy4'm (L=8) r [fm] vrad [c] Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

21 Collisions at higher energies fm/c fm/c fm/c 132 Sn+ 124 Sn, E/A = 3 MeV, b n,p(center) [fm 3 ] (N/Z)central (a). (b) fm/c 4 fm/c n, SLy4m (L=46) p, SLy4m (L=46) n, SLy4'm (L=8) p, SLy4'm (L=8) 1.2 n/p, SLy4m (L=46) n/p, SLy4'm (L=8) t [fm/c] Momentum dependence of Skyrme (SLy4) interaction has been corrected for high energy collisions, in a similar way to Gale, Bertsch, Das Gupta, PRC 3 (1987) fm/c 4 r 2 ( A N n A Z p) [fm 1 ] t =3 fm/c n p diff., SLy4m (L=46) n p diff., SLy4'm (L=8) vradial, SLy4m (L=46) vradial, SLy4'm (L=8) r [fm] vrad [c] Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

22 Collisions at higher energies fm/c fm/c fm/c 132 Sn+ 124 Sn, E/A = 3 MeV, b n,p(center) [fm 3 ] (N/Z)central (a). (b) fm/c 4 fm/c n, SLy4m (L=46) p, SLy4m (L=46) n, SLy4'm (L=8) p, SLy4'm (L=8) 1.2 n/p, SLy4m (L=46) n/p, SLy4'm (L=8) t [fm/c] Momentum dependence of Skyrme (SLy4) interaction has been corrected for high energy collisions, in a similar way to Gale, Bertsch, Das Gupta, PRC 3 (1987) fm/c 4 r 2 ( A N n A Z p) [fm 1 ] t =4 fm/c n p diff., SLy4m (L=46) n p diff., SLy4'm (L=8) vradial, SLy4m (L=46) vradial, SLy4'm (L=8) r [fm] vrad [c] Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

23 N/Z Spectrum Ratio (AMD with clusters) (N/Z)gas ( N Z ) SLy4m (L=46) SLy4'm (L=8) 4 < cm <13 E cm /A [MeV] gas = Y n(v) + Y d (v) + 2Y t (v) + Y h (v) + 2Y α (v) Y p (v) + Y d (v) + Y t (v) + 2Y h (v) + 2Y α (v) N/Z of spectrum of emitted particles is similar to the neutron-proton density difference at the compression stage. 4 r 2 ( A N n A Z p) [fm 1 ] t =2 fm/c n p diff., SLy4m (L=46) n p diff., SLy4'm (L=8) vradial, SLy4m (L=46) vradial, SLy4'm (L=8) r [fm] ρ [fm -3 ] Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34 Symmetry Energy [MeV] SLy4 (L=46 MeV) L=8 MeV vrad [c]

24 N/Z Spectrum Ratio (AMD without clusters) (N/Z)gas ( N Z ) SLy4m (L=46) SLy4'm (L=8) 4 < cm <13 E cm /A [MeV] gas = Y n(v) + Y d (v) + 2Y t (v) + Y h (v) + 2Y α (v) Y p (v) + Y d (v) + Y t (v) + 2Y h (v) + 2Y α (v) N/Z of spectrum of emitted particles is NOT similar to the neutron-proton density difference at the compression stage. 4 r 2 ( A N n A Z p) [fm 1 ] t =2 fm/c n p diff., SLy4m (L=46) n p diff., SLy4'm (L=8) vradial, SLy4m (L=46) vradial, SLy4'm (L=8) r [fm] ρ [fm -3 ] Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34 Symmetry Energy [MeV] SLy4 (L=46 MeV) L=8 MeV vrad [c]

25 Do clusters exist in high density region? Equation for a deuteron in uncorrelated medium f (p) ψ(p) P [e( 1 2 P + p) + e( 1 ] 2 P p) ψ(p) ] + [1 f ( 1 2 P + p) f ( 1 2 P p) dp (2π) 3 p v p ψ(p ) = E ψ(p) E d = B.E. deuteron binding energy [MeV] ρ =.7 fm 3 ρ =.4 fm 3 ρ =.1 fm deuteron c.o.m. wave number [fm -1 ] n =.1 fm -3 n =.7 fm -3 n =.4 fm -3 n =.1 fm -3 E = E d P/ħ Momentum (P) dependence of B.E. Röpke, NPA867 (11) 66. Clusters may exist even in high density matter if they have sufficient momenta so that the effect of Pauli principle is weak. However, clusters in high density region will be soon broken by a collisions with other particles. Does it make sense to consider such short-lived correlations? Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

26 Do clusters exist in high density region? Equation for a deuteron in uncorrelated medium f (p) ψ(p) P [e( 1 2 P + p) + e( 1 ] 2 P p) ψ(p) ] + [1 f ( 1 2 P + p) f ( 1 2 P p) dp (2π) 3 p v p ψ(p ) = E ψ(p) Deuteron in medium (at T = ) Deuteron Momentum P [MeV/c] deuteronization deuteron Cooper pair p [MeV/c] F Danielewicz and Bertsch, NPA 33 (1991) Clusters may exist even in high density matter if they have sufficient momenta so that the effect of Pauli principle is weak. However, clusters in high density region will be soon broken by a collisions with other particles. Does it make sense to consider such short-lived correlations? Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

27 Turn off clusters at high density Always produce clusters Produce clusters only at ρ < ρ Multiplicity Au + Au 4 MeV/u A Multiplicity n p d t 3 He Multiplicity Au + Au 4 MeV/u A Multiplicity n p d t 3 He Exp. AMD 1 Exp. AMD Z Z When the cluster production is turned off at high density ρ >.16 fm 3, M p (overproduction) M α M d and M t don t increase. We need some fine tuning of the cluster production. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 / 34

28 Transport equations for N, and π Coupled equations for f N (r,p, t), f (r,p, t), f π (r,p, t) f N t f t f π t + h N p f N + h p f + h π p f π r h N [f N, f, f π ] r r h [f N, f, f π ] r r h π[f N, f, f π ] r f N p = I N [f N, f, f π ] f p = I [f N, f, f π ] f π p = I π[f N, f, f π ] N N N N N N N Nπ Assumption: and pion productions are rare (in low-energy collisions), so that they can be treated as perturbation. I N [f N, f, f π ] = I el N [f N,,] + λi N [f N, f, f π ] f N = f () (1) + λf N N +, f = O(λ), f π = O(λ) Ikeno, Ono, Nara, Ohnishi, PRC 93 (16) Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

29 AMD + JAM Zeroth order equation for f N f () N t + h N p f () N h N [f () N,,] r r () f N p = I el () N [f N,,] solved by AMD First order equations for f and f π solved by JAM for given f () N f t f π t + h p f + h π p f π r h () [f r h () π[f N, f, f π ] f r p = I [f () N, f, f π ] N, f, f π ] f π r p = I π[f () N, f, f π ] Send nucleon test particles from AMD to JAM at every 2 fm/c, with AMD JAM corrections for the conservation of baryon number and charge. Ikeno, Ono, Nara, Ohnishi, Φ AMD (t) (r 1,p 1 ),(r 2,p 2 ),...,(r A,p A ) (r 1,p 1 ),(r 2,p 2 ),...,(r A,p A ) π, PRC 93 (16) (r 1,p 1 ),(r 2,p 2 ),...,(r A,p A ) t t Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

30 About JAM JAM: Jet AA Microscopic transport model Y. Nara, N. Otuka, A. Ohnishi, K. Niita, S. Chiba, PRC61 () Applied to high-energy collisions (1 8A GeV) Hadron-Hadron reactions are based on experimental data and the detailed balance. e.g., dσ N N N dm No mean field (default). = C I M 2 p i s 16π 2 π m 2 Γ(m) (m 2 m 2 )2 + m 2 Γ(m) 2 p f (m) M 2 sγ 2 = A (s m 2 )2 + sγ 2 s-wave pion production (N N N Nπ) is turned off. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

31 Pions from JAM and AMD+JAM calculations Au + Au central collisions Data: Reisdorf et al., NPA 848 () 366. π π + The energy violation, due to the mismatch of AMD and JAM, is about 2 MeV/nucleon on average at t fm/c in collisions at 3 MeV/nucleon. This corresponds to the % overestimation of the pion multiplicity. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

32 About potentials for and π N τ1 + N τ2 N τ3 + τ4 τ1 N τ3 + π τ4 U (N) τ 1 +U (N) τ 2 U (N) τ 3 +U ( ) τ 4 U ( ) τ 1 U (N) τ 3 +U (π) τ 4 +q 1 U C + q 2 U C + q 3 U C + q 4 U C +q 1 U C + q 3 U C + q 4 U C U ( ) τ : Isospin(τ)-dependent potential due to the strong interaction U C : Coulomb potential In JAM, reaction thresholds are the same as in free space. Therefore AMD+JAM assumes U (N) τ 1 +U (N) τ 2 = U (N) τ 3 +U ( ) τ 4, U ( ) τ 1 = U (N) τ 3 +U (π) τ 4 for τ 1 (+τ 2 ) = τ 3 + τ 4 This is satisfied in case U (N, ) τ = U (r) + τu sym (r), U (π) τ = τu sym (r) c.f. pbuu : Hong and Danielewicz, PRC 9 (14) 246. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 2 / 34

33 Difference choices of potential Our choice Another choice V asy ( ) = 3V asy (n) V asy ( ) = V asy (n) V asy ( + ) = V asy (p) V asy ( ++ ) = 3V asy (p) V asy ( ) = V asy (n) V asy ( ) = 1 3 V asy(n) V asy ( + ) = 1 3 V asy(p) V asy ( ++ ) = V asy (p) c.f. Bao-An Li, PRC92 () Different choices of potential Different thresholds for production Different π /π + ratios Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

34 Transport code comparison J. Xu et al., PRC93 (16) x (fm) t= fm/c / BLOB z (fm) GIBUU-RMF GIBUU-Skyrme IBL IBUU pbuu RBUU RVUU SMF x (fm) t= fm/c AMD z (fm) IQMD-BNU IQMD CoMD ImQMD-CIAE IQMD-IMP IQMD-SINAP TuQMD UrQMD Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

35 Transport code comparison: Transverse flow Au + Au, b = 7 fm d<p x /A>/dy red (MeV/c) B-Full: black squares D-Full: red triangles BLOB GIBUU-RMF GIBUU-Skyrme IBL IBUU pbuu RBUU RVUU SMF AMD IQMD-BNU IQMD CoMD ImQMD-CIAE IQMD-IMP IQMD-SINAP TuQMD UrQMD E/A = 4 MeV E/A = MeV Uncertainties in the flow parameter:about 3% ( MeV), about 13% (4 MeV) Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

36 Transport code comparison: NN collisions and Pauli blocking attempted collisions B-Full b = 7 fm successful collisions 1.. dn coll /d s ( 4 GeV -1 ) B-Cascade b = 7 fm D-Full b = 7 fm Pauli Blocking factor... BLOB GIBUU-RMF GIBUU-Skyrme IBL IBUU pbuu RBUU RVUU SMF s (GeV) s (GeV) Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

37 Transport code comparison: NN collisions and Pauli blocking attempted collisions B-Full b = 7 fm successful collisions 1.. dn coll /d s ( 4 GeV -1 ) B-Cascade b = 7 fm D-Full b = 7 fm Pauli Blocking factor... AMD IQMD-BNU IQMD CoMD ImQMD-CIAE IQMD-IMP IQMD-SINAP TuQMD UrQMD s (GeV) s (GeV) Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

38 Box simulations What is the origin of the divergence of the number of NN collisions? Due to the difference of the realized states, and/or Due to the difference of the procedure for NN collisions. Let s do Box Simulations. We still had large divergence. ( 3%) Simple initialization (T = Fermi) No mean field σ N N = 4 mb Turn off Pauli blocking Many codes fixed an issue of the Bertsch prescription. Much better agreement! (a few %) Next (1) Pauli blocking Next (2) with mean field Next (3) π and in the box Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM 16 3 / 34

39 The Bertsch prescription Bertsch and Das Gupta, Phys. Rep. 16 (1988) 189. Many codes use the prescription described in this article. However, there are a few points that must be corrected implicitly. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

40 Problem of the Bertsch prescription Bertsch prescription (nonrelativistic version) Two nucleons may collide when the relative distance is minimum during a time step, 2 r v < v 2 t, and when the minimum distance is r 2 (r v) 2 /v 2 < σ/π, where r and v are the relative coordinate and velocity, respectively, at the current time t. Then the same pair of two particles can collide more than once, as in the second example. By the collision, the momenta are changed from the blue to the red arrows. After the collision, the particles are moving away from each other (r v > ), so they will not collide again. After the collision (red arrows), the particles are again approaching to each other (r v < ) and the distance is r < σ/π, so they will collide again at a later time. Several collisions occur spuriously when two nucleons come into the scattering distance. Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

41 Box simulations What is the origin of the divergence of the number of NN collisions? Due to the difference of the realized states, and/or Due to the difference of the procedure for NN collisions. Let s do Box Simulations. We still had large divergence. ( 3%) Simple initialization (T = Fermi) No mean field σ N N = 4 mb Turn off Pauli blocking Many codes fixed an issue of the Bertsch prescription. Much better agreement! (a few %) Next (1) Pauli blocking Next (2) with mean field Next (3) π and in the box Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34

42 Summary Clusters and pions are produced from the same collisions at several hundred MeV/nucleon. AMD with clusters Combining JAM with AMD to predict pions. If the cluster correlation is strong,... Strong influence on the symmetry-energy observables such as the n/p ratio and the π /π + ratio (c.f. Ikeno s talk). The expansion dynamics is simple so that some information at an early time may be directly seen in the final observables. Transport code comparison is going on. TODO: Very recent progresses in box simulations. Threshold in medium for production Box pion simulation by JAM Condition for cluster correlations in medium Akira Ono (Department of Physics, Tohoku University) Production of clusters and pions in heavy-ion collisions NPCSM / 34