Natsumi Ikeno (Tottori University)
Neutron-proton dynamics and
pion production in heavy-ion collisions
by the AMD+JAM approach
A. Ono (Tohoku Univ.), Y. Nara (Akita International Univ.),
A. Ohnishi (YITP)
NN2018-13th International Conference on Nucleus-Nucleus Collisions
December 4(Tue.)-8(Sat.), 2018 in Omiya, Saitama, Japan
Symmetry energy and Heavy-ion collision
2
Symmetry energy
soft / stiff
Nucleon
N/Z
Pion
p-/p+
D Particle
D-/D++
(D ↔ Np)(Nucleon dynamics) (NN ↔ ND)
Interest:
High density r ~ 2r0
asy-stiff
asy-soft
(N/Z) system
Simple expectation :
p- production
p+ production
B. A. Li, PRL 88 (2002) 192701
⇒ p-/p+ ratio is related to some kind of (N/Z)2 ratio which is supposed to be
sensitive to the symmetry energy at high densities.
Formation in NN collisions
Clear difference of N/Z in
high density due to different S(r)
Pion and Symmetry energy
➢ Pion calculations by some models
3
(N/Z)2 system
✓ Model predictions do not agree
- S(r) dependence is different
✓ Relation p-/p+ (N/Z)2 does not hold
⇒We need more complete understanding of the relation between pion and
symmetry energy
➢ Pion ratio in Au+Au collisions
Theory vs. Experimental Data- B. A. Li, PRL 88 (2002) 192701 : IBUU
- Z. Xiao, B. A. Li, L. W. Chen, G.-C. Yong, and
M. Zhang, PRL102 (2009) 062502 : IBUU04
- Z. Q. Feng and G. M. Jin, PLB 683 (2010)
140 : ImIQMD
- J. Hong and P. Danielewicz , PRC90 (2014)
024605 : pBUU
- W-M. Guo, G.-C Yong and W. Zuo, PRC90
(2014) 044605
... etc.
E/A =400 MeV
Exp. Data
Contents of this talk
➢ Pion production based on AMD+JAM calculation
We like to understand mechanism how pions are produced
reflecting the dynamics of neutrons and protons
4
Symmetry energy
soft / stiff
Nucleon
N/Z
Pion
p-/p+
? D Particle
D-/D++?
(NN ↔ ND) (D ↔ Np)(Nucleon dynamics)
N. Ikeno, A. Ono, Y. Nara, A. Ohnishi,
PRC93 (2016) 044612, PRC97 (2018) 069902(E)
✓ Some effects: Cluster correlation, Pauli blocking
• Experiment @ RIKEN/RIBF
SpRIT project: 132Sn+124Sn, 108Sn+112Sn
Talk by G. Jhang at NuSYM2018
5
N N → N N
N N → N D
N D → N N
D → N p N p → D ... etc.
➢ Coupled equations for 𝑓a(𝐫, 𝐩, t) (a = N, D , p)
➢ Our model: JAM coupled with AMD
Transport model
IN[𝑓N, 𝑓D, p] :collision term
Perturbative treatment of pion and D particle production ：D and pion productions are rare
• Nucleon 𝑓N ：Zeroth order equation
• D particle 𝑓D and pion 𝑓p ：First order equation
Solved by
AMD
Solved by
JAMfor given 𝑓N
(0)
6
➢AMD (Antisymmetrized Molecular Dynamics)A. Ono, H. Horiuchi, T. Maruyama, and A. Ohnishi, PTP87 (1992) 1185
• AMD wave function at a time t for an event
Transport model (AMD)
• Turn on/off Cluster correlation
N1 + B1 + N2 + B2 -> C1 + C2
- With Cluster
N1, N2: Colliding nucleons
B1, B2: Spectator nucleons/clusters
C1, C2: N, (2N), (3N), (4N) (up to a cluster)
N1 + N2 -> N1 + N2
- Without Cluster
N1, N2 : Colliding nucleons
Solve the time evolution of the wave packet centroids Z ✓ Effective interaction
Skyrme force
Transport model (AMD+JAM)
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➢ JAM (Jet AA Microscopic transport model)Y. Nara, N. Otuka, A. Ohnishi, K. Niita, S. Chiba, PRC61 (2000) 024901
➢ Nucleon test Particles
Test particles (𝐫1, 𝐩1), (𝐫2, 𝐩2), …, (𝐫A, 𝐩A)
• generated following the Wigner function
f AMD(𝐫, 𝐩)
• sent from AMD to JAM at every 2 fm/c
with corrections for the conservation of
baryon number and charge
Test particles
• Applied to high-energy collisions (1 ～ 158 A GeV)
• Hadron-Hadron reactions are based on experimental data and the detailed balance.• No mean field (default), s-wave pion production (NN→NNp) is turned off. … etc.
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132Sn+124Sn @E/A=300 MeV, b<1
• with cluster • without cluster • JAMt=22fm/c
t=18fm/ct=18fm/c
AMD + JAM
1. with cluster (asy-soft)
2. with cluster (asy-stiff)
3. without cluster (asy-soft)
4. without cluster (asy-stiff)
5. JAM (no mean field)
asy-soft : L=46 (SLy4)
asy-stiff : L=108
Calculation set:
✓ Density maximum is different for cases with or without cluster
✓ Clear difference of N/Z ratio due to different symmetry energy
✓ Especially symmetry energy effect is weaker if there is cluster correlation
Effective interaction:
Skyrme force
➢ Dynamics of neutrons and protons
9
D resonance
Reaction rate
NN→ND
Reaction rate
ND→NN
＊D production:
＊D absorption:
＊ Numbers of
existing D and p
We study what kind of information
of neutrons and protons is carried
by D resonances.
?
NN ↔ ND
D ↔ Np
Nucleon dynamics
Symmetry energy
soft / stiff
Nucleon
N/Z
Pion
p-/p+
D resonance
D-/D++
p- production (main reaction)
p+ production (main)
Simple expectation:
D-/D++ ~ (N/Z)2
Relation between N/Z and D-/D++ Nucleon
N/Z
? D resonance
D-/D++
Simple expectation: D-/D++ ~ (N/Z)2
Nucleons in the sphere r(r) ≧r0
centered at CM.
D-/D++
(N/Z)2r
(N/Z)2r, p
(The collective radial momentum prad is subtracted)
(N/Z)2 system
(N/Z)2 system (N/Z)2
system
10
Nucleons in the sphere r(r) > r0
with high momentum
11
Final p-/p+ ratio
N(t), Z(t) : Numbers of nucleon which satisfy the conditions
➢ From nucleons to pion ratios
Representative ratios:
✓ Cluster correlation → p-/p+ up
✓ S(r) effect: 30% weaker
D-/D++ ~ (p-/p+)like
Final stage:
p-/p+ is modified from (p-/p+)like
t=20
t=20
(N/Z)2 system
w/o cluster
with cluster
Some effects on pion production
• Cluster correlation
Larger ratios, weaker dependence on Esym
12
• Pauli-blocking effect
• Pion potential effect
• Delta threshold energy (NN ->ND)
• Details of transport codes
Y . Zhang et al., PRC97 (2018) 034625, A.Ono et al., in progress (2018)
• Other unexpected effects
…. etc.
Pauli-blocking effect
13
p- production
p+ production
Pauli blocking factor (1-f) for
the final nucleon
Pauli blocking may play some important
role on the pion observables.
⇒We need to estimate
Pauli blocking factor (1-f) precisely
ex) Effect of Pauli-blocking is weaker
-> D and p numbers are larger
blocking
Methods for Pauli-blocking factor f
14
➢ Do Pauli blocking within JAM
L=2.0 fm2
Pauli blocking factor 1 - f JAM(𝐫i, 𝐩’i) calculated for Test particles {(𝐫j, 𝐩j); , j=1,2, … ,A}
(Natural prescription in AMD+JAM)
A problem is that fluctuation of f seems to be large. (Y. Zhang et al., PRC97, 034625 (2018) : Box Homework 1)
→ Blocking is less effect
N N → N D
D → N p etc.
➢ Use f of AMD for Pauli blocking
Wigner function calculated for the AMD wave function,
for t = neutron or proton, is
Pauli-blocking factor 1 - f AMD(𝐫i, 𝐩’i) for the final phase-space point (𝐫i, 𝐩’i).
(reasonable in principle)
Final p-/p+ ratio in132Sn+124Sn @E/A=300 MeV
15
with cluster
w/o cluster
✓ Pion ratios become larger in precise treatment.In particular when cluster correlation is switched on.
✓ Clear dependence on Pauli blocking
➢ Pauli blocking procedures :
4 options
: Pauli blocking factor fJAM is artificially
reduced by factor 4(1)
: Do Pauli blocking within JAM(2)
: Use Wigner function of AMD for
Pauli blockingonly for NN↔ND, D→Np is JAM
(3)
: Use Wigner function of AMD for
Pauli blocking
both for NN↔ND and D → Np
(4)
Summary
• Pion production on HIC
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Symmetry energy
soft / stiff
Nucleon
N/Z
Pion
p-/p+
D Particle
D-/D++
(NN ↔ ND) (D ↔ Np)(Nucleon dynamics)
High-r symmetry energy and Experimental data p-/p+
• Improved Pauli blocking procedure for NN<->ND, D <->Np
✓ Pion multiplicities and ratios depend on Pauli-blocking effect
✓ In the final stage, p-/p+ ratio is modified
from (p-/p+)liket=20
✓ p-/p+ and D-/D++ ratios are related to (N/Z)2
in high-r and high-p region
Future work: We need to study other treatments for pion observables
