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Constraining the symmetry energy with heavy-ion collisions and Bayesian analysis

by Pierre Morfouace

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When 2017-12-05
from 11:30 am à 12:30 pm
Where Salle 105
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Present efforts to constrain the symmetry energy S(ρ) have focused on the first two coef-
ficients S 0 and L in the Taylor expansion of S(ρ) around the saturation density ρ 0 and many
of these analyses result in a positively correlated constraints on S 0 and L. In addition to the
density dependence of the symmetry energy, the momentum-dependent potentials for neutrons
and protons at energies well away from the Fermi surface cause both to behave as if their inertial
masses are effectively 70% of the vacuum values. This effective mass describes the non-locality
both in space and in time of the nuclear effective interactions and the Pauli exchange. This
similarity in effective masses may not be true in neutron-rich matter because of the momentum
dependence of the symmetry potential in nucleonic matter. Today the sign of the effective-mass
splitting ∆m ∗ np = m ∗ n − m ∗ p and the dependences of the mass splitting on density ρ and on the
asymmetry δ remain poorly constrained. This is an important parameter in dense neutron-rich
regions within neutron stars, core-collapse supernovas, and nuclear collisions. There differences
in the momentum-dependent symmetry potentials may cause neutron and proton effective masses
to differ significantly.
To investigate this effect, measurement of the energy spectra of neutrons, protons, and
charged particles emitted in 112 Sn+ 112 Sn and 124 Sn+ 124 Sn collisions at E beam /A = 120 MeV
has been measured by the HiRA array. The double neutron to proton ratio DR n/p was con-
structed in order to cancel out the efficiency effect [1]. This double ratio was compared to model
with very different values of the neutron and proton effective masses.
The single neutron to proton ratio R n/p should be more sensitive to the isovector effective
mass. However in order to be able to use this ratio, one has to carefully correct for the detec-
tion efficiency for neutrons and the light charged particles especially at high energies where the
efficiency of detecting the full energy of the particle decreases because of multiple scattering and
nuclear reactions occurring in the detector material. In my presentation, I will show particle
energy spectrum that has been corrected from such an effect [2]. Comparions to the ImQMD
transport model code [3] is performed in a Bayesian analyses approach in order to constrain four
parameters of the equation of state: S 0 and L related to the density dependence of the symmetry
energy and the isoscalar effective mass m ∗ s and the nucleon effective mass splitting ∆m ∗ np related
to the momentum dependence of the symmetry potential. I will show that these data provide
significant constraints on the symmetry energy at slightly below half saturation density in a
region that have few experimental constraints.
This research is supported by the National Science Foundation under Grant No. PHY-
1565546. We acknowledge the computational resources provided by the Austin Advance Com-
puter Center and the Institute for Cyber-Enabled Research at Michigan State University.
1. D. D. S. Coupland et al. Phys. Rev. C 94, 011601(R) (2016).
2. P. Morfouace et al. Nucl. Instr. and Meth. in Phys. Res. A 848 45-53 (2017)
3. Y. Zhang et al. Phys. Lett. B 732 186-190 (2014)

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