158
Y. Leifels
using the IQMD model [16]. For
197 Au + Au collisions at 400 MeV/u the forceweighted density, defined by the authors, is spread over a broad density regime
extending from 0.8< ρ/ρ 0 < 1.6.
The derivative of DE R F(ρ) for the neutron-proton ratio peaks at a higher value,
1.4 to 1.5ρ 0 . This observation gives rise to the expectation that with sufficient isotope
separation one would be able not only to constraint the slope of the symmetry energy
but also its curvature.
12.3 Conclusions and Outlook
The symmetry energy at supra-saturation densities can be effectively probed with
the elliptic flow ratio of neutrons and charged particles. The ASY-EOS collaboration
measured data for Au+Au collisions at 400A MeV, and a slope for the of L = 72 ± 13
for the density dependence of the symmetry energy could be deduced from the v 2
ratio of neutrons and charged particles. According to model predictions, similar
observables might also be sensitive not only to the slope of the symmetry energy
but also to its curvature at high densities. Hence, it would be interesting to measure
n and light charged particle flow also at higher energies and for different systems.
In collisions of Sn-isotopes one could investigate the evolution of the v 2 ratio as a
function of N/Z of the colliding system.
How the sensitivity of the various observables to the symmetry energy develops
with rising beam energy and larger densities is by no means obvious and more
calculations using different models and prescriptions need to be performed. Particle
production is predicted to be most sensitive to modifications in the neutron/proton
density close to threshold. Kaon production below and close to threshold (E thr,N N =
1.6 GeV has proven to be sensitive to the density reached in the course of the collision.
It has been shown in particular that Kaon yields are robust observables to constrain
the iso-scalar EOS [24]. At sub-threshold energies Kaons are produced in the central
high-density region and, because they are not re-absorbed by the surrounding nuclear
matter, they are true messengers of the dense overlap zone. The production ratio
(K
+
/K
0 ) is predicted to be sensitive to the symmetry energy and, therefore, may
be an interesting observable accessing densities beyond twice saturation density.
An experiment studying Au+Au reactions at 1.25A GeV was performed by the
HADES collaboration. The HADES detector setup allows not only for measuring
charged Kaons but also reconstructing K
0 by their decay into charged pions with
high accuracy. Sufficient statistic was accumulated and the data have been published
and compared to predictions of transport models. However, the sensitivity to the
symmetry energy has not yet been tested.
Symmetry effects are very small, because the contribution of the symmetry energy
enters with a factor δ
2 into the equation of the state of nuclear matter. Since δ is rather
small even for the most neutron-rich stable isotopes it is evident that those studies
have to be extended to radioactive beams with enhanced neutron-proton asymmetry. Experimental facilities, e.g., RIKEN/RIBF, MSU/FRIB, GANIL/SPIRAL2 are
Y. Leifels
using the IQMD model [16]. For
197 Au + Au collisions at 400 MeV/u the forceweighted density, defined by the authors, is spread over a broad density regime
extending from 0.8< ρ/ρ 0 < 1.6.
The derivative of DE R F(ρ) for the neutron-proton ratio peaks at a higher value,
1.4 to 1.5ρ 0 . This observation gives rise to the expectation that with sufficient isotope
separation one would be able not only to constraint the slope of the symmetry energy
but also its curvature.
12.3 Conclusions and Outlook
The symmetry energy at supra-saturation densities can be effectively probed with
the elliptic flow ratio of neutrons and charged particles. The ASY-EOS collaboration
measured data for Au+Au collisions at 400A MeV, and a slope for the of L = 72 ± 13
for the density dependence of the symmetry energy could be deduced from the v 2
ratio of neutrons and charged particles. According to model predictions, similar
observables might also be sensitive not only to the slope of the symmetry energy
but also to its curvature at high densities. Hence, it would be interesting to measure
n and light charged particle flow also at higher energies and for different systems.
In collisions of Sn-isotopes one could investigate the evolution of the v 2 ratio as a
function of N/Z of the colliding system.
How the sensitivity of the various observables to the symmetry energy develops
with rising beam energy and larger densities is by no means obvious and more
calculations using different models and prescriptions need to be performed. Particle
production is predicted to be most sensitive to modifications in the neutron/proton
density close to threshold. Kaon production below and close to threshold (E thr,N N =
1.6 GeV has proven to be sensitive to the density reached in the course of the collision.
It has been shown in particular that Kaon yields are robust observables to constrain
the iso-scalar EOS [24]. At sub-threshold energies Kaons are produced in the central
high-density region and, because they are not re-absorbed by the surrounding nuclear
matter, they are true messengers of the dense overlap zone. The production ratio
(K
+
/K
0 ) is predicted to be sensitive to the symmetry energy and, therefore, may
be an interesting observable accessing densities beyond twice saturation density.
An experiment studying Au+Au reactions at 1.25A GeV was performed by the
HADES collaboration. The HADES detector setup allows not only for measuring
charged Kaons but also reconstructing K
0 by their decay into charged pions with
high accuracy. Sufficient statistic was accumulated and the data have been published
and compared to predictions of transport models. However, the sensitivity to the
symmetry energy has not yet been tested.
Symmetry effects are very small, because the contribution of the symmetry energy
enters with a factor δ
2 into the equation of the state of nuclear matter. Since δ is rather
small even for the most neutron-rich stable isotopes it is evident that those studies
have to be extended to radioactive beams with enhanced neutron-proton asymmetry. Experimental facilities, e.g., RIKEN/RIBF, MSU/FRIB, GANIL/SPIRAL2 are