Ⅱ-1. Nuclear Physics

RIKEN Accel. Prog. Rep. 47 (2014)

Energy dependence of π − diﬀerential cross section in 28 Si + In withbeam energies of 400, 600, and 800
M. Sako,∗1∗2 T. Murakami,∗2 Y. Ichikawa,∗2 K. Ieki,∗4 Y. Ikeda,∗4 S. Imajo,∗2 T. Isobe,∗1 S. Ebesu,∗2
M. Matsushita,∗6 J. Murata,∗4 Y. Nakai,∗1 S. Nishimura,∗1 M. Nitta,∗4 H. Sakurai,∗1∗6 R. Sameshima,∗2
E. Takada,∗3 and K. Yoshinaga∗5×103

∗1
∗2∗3
∗4
∗5
∗61/p • d 2σ /dEd Ω (mb/sr/GeV2)

Information on the nuclear equation of state (EoS)
within a broad density range is important for understanding the physics of neutron stars. However, theisospin-dependent term in EoS, i.e., the density dependence of the symmetry energy Esym (ρ) has a large
model dependence in the supra-normal density region(ρ > ρ0 , the saturation density ρ0 ∼= 0.16f m−3 ).
As a result, the relationship between the radius andthe mass of a neutron star cannot be reliably calculated. According to a transport model calculation(IBUU04),1) detailed studies of the pion yield ratio,Y(π − )/Y(π + ), in central nucleus-nucleus collisions atintermediate energies can be conducted to obtain signiﬁcant constraints on Esym (ρ) in the supra-normal
density region.
The IBUU04 predicts that the beam energy dependence of the pion yield ratio is strongly related to thebehavior of Esym (ρ) in the supra-normal density region.1) We performed a series of experiments using 400,600, and 800 MeV/nucleon 28 Si beams accelerated at
the Heavy Ion Medical Accelerator in Chiba (HIMAC)
and an In target with a compact centrality ﬁlter anda pion range counter(RC)2) .
The π + events can be clearly identiﬁed by the+π → µ+ + νµ decay after they are stopped at theRC.3) The π − events were selected using ∆Ei -∆Ej (energy deposition at each layers of RC) correlations obtained experimentally for π + events, because in-ﬂight
energy depositions are same between the π + and π −events. However, a pionic atom, which is created by
the stopped π − and surrounding nuclei, decays variousparticles and some of them hit the next counter. Next
we estimated a π − leak rate to the next counter.
The leak rate α at which the decayed particles hit
the next elements was estimated with CsI(129 Xe,π ± )X
experimental data at 90◦ for which, the statistics is
suﬃcient and the S/N ratio is large. We obtained atypical value of α, 10.83+0.81−0.59 (SYS) %. For obtaining
the production cross section of the π − , the reduction
rate by the decay in ﬂight, nuclear reaction, and multiple Coulomb scattering until the π − reaches the RC
from the production point was estimated using Geant4.
The Lorentz-invariant cross sections of the π − as°

1030°
45°
60°
75°
90 °
120

1400 MeV/nucleon

101600 MeV/nucleon

101800 MeV/nucleon

050100150
E mid (MeV)

200Fig. 1. Lorentz-invariant cross sections of the π − as afunction of kinematic energy in the mid-rapidity frame(Emid ) for In(28 Si,π ± )X reaction with 400(top part),
600(middle part) and 800(bottom part) MeV/nucleon
beam with statistical errors.

a function of the kinematic energy of the π − in a mid
rapidity frame Emid (the CM frame of NN) were shownat Figure 1. Further analysis of the π − and eﬀorts toﬁx the systematic uncertainties are in progress.
References
1) B. A. Li, G. C. Yong, and W. Zuo, Phys. Rev. C 71,
014608 (2005).
2) T. Murakami et al., Nucl. Phys. A 834, 593c (2010)(NN2009 proceedings).
3) M. Sako et al., RIKEN Accel. Prog. Rep. 46,(2013).

RIKEN Nishina Center
Department of Physics, Kyoto University, Kyoto
Department of Accelerator and Medical Physics, NIRS
Department of Physics, Rikkyo University, Tokyo
Department of Physics, Tokyo University of Science
Department of Physics, University of Tokyo- 31 -