Experimental study of asymmetric nuclear matter
EOS from heavy-ion reactions with RIBF-SPiRIT
Tadaaki Isobe
RIKEN, Nishina Center
Workshop at the Tomonaga Center for the History of the Universe (TCHoU)
March 29, 2024
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Nuclear matter : many body system of nucleon• Equation of State describes the relationship ofthermodynamical quantity  EoS of ideal gas:PV=nRT• Phase of diagram because of interaction between themolecules.

• Nuclear liquid drop model• 1st order description of nuclear mass is succeeded. (BetheWeizsäcker Mass formula)Asymmetric nuclear matter EOS: Symmetry Energy term of nuclear EOS• Equation of state of nuclear matter can be reconstructed by using the differential
thermodynamic identity:

𝐸𝐸 𝑇𝑇, 𝜌𝜌, 𝛿𝛿 = 𝐸𝐸 𝑇𝑇, 𝜌𝜌, 𝛿𝛿 = 0 + 𝐸𝐸𝑠𝑠𝑠𝑠𝑠𝑠 (𝑇𝑇, 𝜌𝜌)𝛿𝛿 2 + 𝑂𝑂(𝛿𝛿 4 )𝛿𝛿 = (𝜌𝜌𝑛𝑛 − 𝜌𝜌𝑝𝑝 )/𝜌𝜌

• The asymmetric term of nuclear EOS depends on δ
• Important term especially for astrophysics• Neutron star structure (T~0)• Solar mass star with the radius of ~10km.

• Supernovae process (T~ O(10) MeV)
• Neutron star merger/Gravitational wave

Visualization of a NS merger andthe gravitational waves
3Gravitational wave from neutron star merger
Tidal deformation depends on nuclear EoS
A. Bauswein, S. Goriely, and H.-T. Janka,APJ, 773, 21 (2013)

Soft  Easy to be deformed

Stiff  Small deformation

Λ<800 (90% confidence)
GW170817 PRL 119 161101
Hotokezaka et. al (2016)

Nuclear EoS is important also for the r-process nuclear
synthesis in neutron star merger

Fujibayashi APJ 2023
Dynamicalejecta

Post-merger
ejectaBinary NSPrompt BH formation

5Nuclear EoS is important also for the r-process nuclear
synthesis in neutron star merger

https://en.wikipedia.org/wiki/Nucleosynthesis

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Asymmetric nuclear matter EOS: Symmetry Energy term of nuclear EOS
𝐸𝐸 𝑇𝑇, 𝜌𝜌, 𝛿𝛿 = 𝐸𝐸 𝑇𝑇, 𝜌𝜌, 𝛿𝛿 = 0 + 𝐸𝐸𝑠𝑠𝑠𝑠𝑠𝑠 (𝑇𝑇, 𝜌𝜌)𝛿𝛿 2 + 𝑂𝑂(𝛿𝛿 4 )𝛿𝛿 = (𝜌𝜌𝑛𝑛 − 𝜌𝜌𝑝𝑝 )/𝜌𝜌

arXiv:1303.0064

Slope at ρ=ρ0 :L

stiff

softSoft

Stiff

Easier to be Harder to becompressed compressedSymmetry Energy

Parameter L is often referred to compare the SE as it canbe obtained both from Astrophysics and nuclear physics.

Dohi et al., Astro. Jour., 923:64, 2021

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Terrestrial experimental study of high dense matter nuclear symmetry energy
 Heavy Ion Collision (HIC)Sn+Sn @300MeV/u

Central density as a function of time.
Au+Au collisions, PRC87 067601

1.8ρ0

2.2ρ0

2.8ρ0

• Unique way to realize high dense matter in laboratory.
• Quite challenging to extract the information of high dense matter symmetry energy since
we need the help of transport model.
• Mixture of equilibrium and non-equilibrium state.

8Experimental observables from heavy ion collision to constrain
the symmetry energy• No direct observables, but contains the information of symmetry energy• Symmetry energy  appeared as pressure difference between neutron
and proton

Stiff symmetry energy (large L) lower ρn/ρp in higher dense region
 lower n/p in high ρSoft symmetry energy (small L) larger ρn/ρp in higher dense region
 larger n/p in high ρρ0=2.5×1014 g/cm39

Experimental observables from heavy ion collision to constrain
the symmetry energy• No direct observables, but contains the information of symmetry energy• Symmetry energy  appeared as pressure difference between neutronand proton

Stiff symmetry energy (large L) lower ρn/ρp in higher dense region
 lower n/p, lower π-/π+

soft
soft

stiff

stiff

n/p

π-/π+10%
10Soft symmetry energy (small L) larger ρn/ρp in higher dense region
 larger n/p, higher π-/π+10SPiRIT experiment: neutron rich Sn+Sn collision
beam line+TPC+trigger+neutron detector

RIBF-BigRIPS Making neutron rich beam

Chamber in SAMURAI magnet B=0.5T
Beam Tracker
Sn RI beam

STQ
Sn target
MWPC typeTime Proj.
Chamber
12k channel

11SPiRIT experiment: neutron rich Sn+Sn collision
beam line+TPC+trigger+neutron detector

RIBF-BigRIPS Making neutron rich beam

Chamber in SAMURAI magnet B=0.5T
Beam Tracker

5 sec./frame. Movie for ~2.5 hour.

Sn RI beam

STQ
Sn target
MWPC typeTime Proj.
Chamber
12k channel

12Sn+Sn Collision event display with TPC
MilestonesCollision
on target

1frame : 1collision“Participants”pnnpb“Spectators”

Low Znuclei

270MeV Sn beam

VetoMultiplicity
Trigger Array

1 pixel: 1 pad13

Charged particle measurement with Time Projection Chamber
Measure all of particles produced in a HIC
Particle ID based on rigidity-dE/dx (dE/dx ∝ Z2)
Rigidity  particle momentum

6Li
3He

7Li

4He

6He

tπEstee et al., PRL 126 (2021) 162701

π+pd14

Result on pion multiplicity: pion ratioLarge discrepancy among theoretical models

Size of error bar
corresponds to thedifference between
Soft and stiff EoS.

Jhang et al., PLB 813 (2021) 136016• Numerical calculation of HIC dynamics by using transport theory.
• Predictions with same EoS are supposed to be same Larger discrepancy than experimental result.
• Different assumptions regarding the mean field potentials for ∆ baryons and pions can influence the pion
15multiplicities.

High-momentum pion data: reduce the influence from theassumption for ∆/pion mean field potential• Sensitivity to the isospin dependence of mean field dominates at high-pT.

dcQMD• Neutron rich systemshows more sensitivity
at high-pT.

• Calculation
underestimate at low-pT.
Coulomb effect and/ornon-resonant pion
production.

42<L<117

16Estee et al., PRL 126 (2021) 162701

Compilation of experimentally determined symmetry energy
arXiv:2106.10119

Fitting only withlow density data

• Fitting with phenomenological formula: S0=(33.3±1.3) MeV,
L= (59.6±22.1) MeV• suggests a radius for a 1.4 solar mass neutron star of 13.1±0.6 km

17Extra observable: p/d/t dN/dy• Fundamental spectra to check the transport model.
• EoS dependence appears in triton production.
• Triton easily produced in neutron rich matter.

• Data favor L =46MeV rather than L =108MeV.

SLy4 (L=46MeV)
SLy4 (L=108MeV)

Kaneko et al., PLB 822 (2021) 136681

18Difference from Relativistic HIC• Many body system composed of nucleons.
• Cluster state such as deuterium and alphaexists.
• x100 Longer collision time of ~O(10fm).
• Less charged particles.
• Track finding is simpler.
• Worse reaction plane resolution.

Sn132 + p reaction• Possible to measure neutron productionand its flow.
• Possible to identify spectator and tomeasure its kinematics.
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Measurement of spectator for event characterization• Spectator would be useful for event characterization.
• According to AMD calculation:

thetaTarget

Kicked!

• It looks difficult to measure impact parameter through themeasurement of spectator fragment.
• Spectator information may deduce the reaction plane angle
more preciously.
• σ(∆ϕ) w/ participants: 1rad• σ(∆ϕ) w/ spectator: 0.7 rad

Beam∆phi: phi(RP) – phi(spectator)of largest Z particle

theta of largest Z particle

Xe136+Sn124
AMD, SLy4, b=8fm

σ~0.7radianradian20

Summary• Symmetry energy term of nuclear EoS is essential to understand the property ofneutron star.
• Heavy RI collision experiment was conducted at RIKEN-RIBF to give constraint on
EoS for high dense regime.
• Spirit experiment• Charged pion and hydrogen production was measured.

• Delta baryon potential in dense matter is necessary to study pion production inHIC.  next step
• Proton/neutron measurement  next step for momentum dependence of U inmatter.
• I am curious the universality of physics among the different hierarchy: nuclear
matter and quark matter.
• Exiotic hadron  Exiotic nuclei• Halo state, Borromean, Strong E/B field …

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