Ⅱ-1. Nuclear Physics

RIKEN Accel. Prog. Rep. 52 (2019)

Recent results of collective flow for SπRIT-TPC experiment∗2∗3∗4∗5∗6∗7∗82π/N dN/d( φ - Ψ)

(b)

1.03

(c)

1.15

1.02

1.1

1.01

1.05

1.1

1.05

11

1

0.95

0.99

0.95

0.9

0.98

0.9

0.97

0.85

0.85

Since the distribution of Ψ was distorted due to a rectangular shape of SπRIT-TPC, it was corrected applying
a re-centering and a shifting method.6) The azimuthal
angle distributions with respect to Ψ were plotted forprotons measured with 132 Sn + 124 Sn in Fig. 1. In theseplots, Ψ was determined with all light fragments excluding itself to avoid auto correlation. Red lines showsﬁtting results with a formula

∗1(a)

1.15

2π/N dN/d( φ - Ψ)

The SAMURAI Pion-Reconstruction and Ion-TrackerTime-Projection Chamber (SπRIT-TPC)1) project aims
to constrain a nuclear equation of state (EoS) at suprasaturation density using heavy ion collisions. TheSπRIT-TPC was designed to measure π − /π + production ratio depending on isospin asymmetry. Since thepions are expected to be produced through the ∆ resonance formation, π − /π + ratio is related to some kindof nuetron-to-proton squared ratio which is then supposed to be sensitive to the symmetry energy at highdensities.3)
Additionally, measurements of collective ﬂow with
proton and neutron are proposed as a useful probe2) tonuclear EOS, because neutrons are repelled from dense
region as a result of the repulsive isospin symmetry potential with increase of density, while protons are opposite.
The ﬁrst experiment had been performed in April 2016with 132 Sn and 108 Sn beams at 270 MeV/nucleon on112
Sn and 124 Sn targets at SAMURAI in RIBF. Neutrons were detected by NeuLAND4) covering the midrapidity region. In this paper, recent results of the collective ﬂow for proton and neutron will be discussed.
A track reconstruction was done using SπRITROOT
software and particle identiﬁcation ability is discussed
in Ref. 5).
An orientation angle of reaction plane, Ψ was determined with summing up a transverse momentum of lightcharged fragments, p, d, t, 3 He, and 4 He event by event,as following.
()() ∑N−→cos ϕk
Q cos Ψ(1)ωk
Q ==sin ϕk
Q sin Ψk=1
{1 if rapidity in the center of mass > 0ωk =−1 otherwise

2π/N dN/d( φ - Ψ)

M. Kurata-Nishimura,∗1 J. Barney,∗2,∗1 G. Cerizza,∗2,∗1 J. Estee,∗2,∗1 B. Hong,∗3 T. Isobe,∗1 G. Jhang,∗2,∗1M. Kaneko,∗4,∗1 H. S. Lee,∗7 J. W. Lee,∗3,∗1 J. Łukasik,∗5 W. G. Lynch,∗2 A. B. McIntosh,∗8 T. Murakami,∗4,∗1P. Pawłowski,∗5,∗1 H. Sakurai,∗1 C. Santamaria,∗2,∗1 R. Shane,∗2 D. Suzuki,∗1 M. B. Tsang,∗2and S. J. Yennello∗8 for SπRIT Collaboration

RIKEN Nishina Center
NSCL and Dept. of Phys. & Ast., Michigan State University
Department of Physics, Korea University
Department of Physics, Kyoto University
IFJ PAN
Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University
Rare Isotope Science Project, Institute for Basic Science
Cyclotron Institute, Texas A&M University- 37 -0.8−30.8−2−10123∆ (φ - Ψ)−3−2−10123∆ (φ - Ψ)−3−2−10123∆ (φ - Ψ)

Fig. 1. Azimuthal angle distributions of proton with respectto Ψ . The rapidity coverages in the center of massare (a) target-rapidity: −4.0 ∼ −0.06, (b) mid-rapidity:−0.06 ∼ 0.06, and (c) Beam-rapidity: 0.06 ∼ 4.0). Redlines indicate fitting with Eq. (2).

2π dN
= 1 + 2v1 cos(ϕ) + 2v2 cos(2ϕ) + ...
N dϕ

(2)

The negative and positive v1 were observed in the target (a) and beam rapidity region (c), which is the evidence of directed ﬂow. The negative v2 was observedin the mid rapidity region (b), which indicates out-ofplane elliptic ﬂow of protons. The strength of v1 and v2
are needed to be corrected with a reaction plane resolution to compare between 132 Sn + 124 Sn and 108 Sn +112
Sn collisions. Neutron’s collective ﬂow was also observed within a limited acceptance. Simulation and further analysis are necessary to extract EoS information.
Addition to neutron to proton ratio, 3 H to 3 He analysis
is ongoing, which is expected to serve in resolving ambiguities caused by the eﬀective-mass splitting between
neutrons and proton.
This work is supported by the U.S. Department of Energy under Grant Nos. DE-SC0004835, DE-SC0014530,DE-NA0002923, US National Science Foundation Grant
No. PHY-1565546, the Japanese MEXT KAKENHI(Grant-in-Aid for Scientiﬁc Research on Innovative Areas) grant No. 24105004, and the Polish National Science Center (NCN), under contract Nos. UMO- 2013/09/B/ST2/04064 and UMO-2013/10/M/ST2/00624.
References

1) R. Shane et al., Nucl. Instrum. Methods Phys. Res. A
784, 513 (2015).
2) B. -A. Li et al., Phys. Rev. Lett. 85, 4221 (2000).
3) N. Ikeno et al., Phys. Rev. C 97, 069902 (2018).
4) NeuLAND Technical Design Report, http://www.
fair-center.eu/fileadmin/fair/experiments/NUSTAR/
Pdf/TDRs/NeuLAND-TDR-Web.pdf, accessed: 2016/01/21.
5) M. Kaneko et al., in this report.
6) J. -Y. Ollitrault et al., Nucl. Phys. A 638, 195c (1998).