156
Y. Leifels
The two predictions obtained under these conditions are presented in Fig. 12.4
together with the experimental results. The parameters which describe the data best
are obtained by fitting a linear interpolation between the two predictions. The resulting power-law coefficient is γ = 0.75 ± 0.10. The corresponding v 2 ratio is shown
as black line in Fig.12.4. In comparison with the FOPI-LAND data, the statistical
accuracy of the ASY-EOS experiments represents an improvement by a factor of 2. A
systematic uncertainty arose from occasional malfunction of the electronic circuits
for the time measurement with LAND. It prohibits extending the data evaluation
into the region of large transverse momenta. For this reason this analysis is restricted
to p t < 0.7 GeV/c. Another uncertainty is related to the lower energy threshold for
neutron detection. The necessary corrections and the methods used for estimating
the remaining errors are described in detail in [22].
With all corrections and errors included, the acceptance-integrated elliptic flow
values lead to a power-law coefficient γ = 0.72 ± 0.19. The corresponding slope
value is L = 72 ± 13 MeV. Changing the absolute value of the symmetry energy at
ground state nuclear matter density in the simulations to a lower value, E sym (ρ 0 ) =
31MeV, results in a lower γ -value γ = 0.68 ± 0.19. This is still within the error bar
of the above result.
This result is displayed in Fig. 12.5 (right panel) where the symmetry energy
is shown as a function of reduced density ρ/ρ 0 together with various microscopic
model predictions [23]. The experimental data are represented as colored bands. The
results of the FOPI-LAND experiment are shown in yellow and the one of the ASYExperiment in orange. For completeness the calculations from [23] for the EOS of
symmetric matter are shown in the left panel of Fig. 12.5 together with the experimental constraint from the FOPI collaboration [17] utilizing elliptic flow of protons
and light charged particles in Au+Au collisions between 0.25 and 1.5 GeV/nucleon.
-20
0
20
40
60
0
0.5
1
1.5
2
2.5
ρ/ρ 0
E
bind (MeV)
DBHF (BonnA)
BHF AV 18 +3-BF
var AV 18 +3-BF
NL3
DD-TW
ChPT
Sk hard
Sk soft
0
50
100
0 0.5 1 1.5 2 2.5 3
ρ/ρ 0
E
sym (MeV)
SKM*
SkLya
DBHF
varAV 18 + δv + 3-BF
NL3
DD-TW
DD-ρδ
ChPT
Fig. 12.5 Left panel: Constraints from experimental data of the FOPI collaboration as presented in
[17] (yellow area) are shown together with predictions of microscopic model calculations employing
different methods and different interactions [23]. Right panel: Result of the ASY-EOS experiment
(orange area) and the FOPI-LAND analysis (yellow area) together with theoretical predictions for
E sym (ρ) using different microscopic approaches in addition to Skyrme interactions. The calculations
are taken from [23]
Y. Leifels
The two predictions obtained under these conditions are presented in Fig. 12.4
together with the experimental results. The parameters which describe the data best
are obtained by fitting a linear interpolation between the two predictions. The resulting power-law coefficient is γ = 0.75 ± 0.10. The corresponding v 2 ratio is shown
as black line in Fig.12.4. In comparison with the FOPI-LAND data, the statistical
accuracy of the ASY-EOS experiments represents an improvement by a factor of 2. A
systematic uncertainty arose from occasional malfunction of the electronic circuits
for the time measurement with LAND. It prohibits extending the data evaluation
into the region of large transverse momenta. For this reason this analysis is restricted
to p t < 0.7 GeV/c. Another uncertainty is related to the lower energy threshold for
neutron detection. The necessary corrections and the methods used for estimating
the remaining errors are described in detail in [22].
With all corrections and errors included, the acceptance-integrated elliptic flow
values lead to a power-law coefficient γ = 0.72 ± 0.19. The corresponding slope
value is L = 72 ± 13 MeV. Changing the absolute value of the symmetry energy at
ground state nuclear matter density in the simulations to a lower value, E sym (ρ 0 ) =
31MeV, results in a lower γ -value γ = 0.68 ± 0.19. This is still within the error bar
of the above result.
This result is displayed in Fig. 12.5 (right panel) where the symmetry energy
is shown as a function of reduced density ρ/ρ 0 together with various microscopic
model predictions [23]. The experimental data are represented as colored bands. The
results of the FOPI-LAND experiment are shown in yellow and the one of the ASYExperiment in orange. For completeness the calculations from [23] for the EOS of
symmetric matter are shown in the left panel of Fig. 12.5 together with the experimental constraint from the FOPI collaboration [17] utilizing elliptic flow of protons
and light charged particles in Au+Au collisions between 0.25 and 1.5 GeV/nucleon.
-20
0
20
40
60
0
0.5
1
1.5
2
2.5
ρ/ρ 0
E
bind (MeV)
DBHF (BonnA)
BHF AV 18 +3-BF
var AV 18 +3-BF
NL3
DD-TW
ChPT
Sk hard
Sk soft
0
50
100
0 0.5 1 1.5 2 2.5 3
ρ/ρ 0
E
sym (MeV)
SKM*
SkLya
DBHF
varAV 18 + δv + 3-BF
NL3
DD-TW
DD-ρδ
ChPT
Fig. 12.5 Left panel: Constraints from experimental data of the FOPI collaboration as presented in
[17] (yellow area) are shown together with predictions of microscopic model calculations employing
different methods and different interactions [23]. Right panel: Result of the ASY-EOS experiment
(orange area) and the FOPI-LAND analysis (yellow area) together with theoretical predictions for
E sym (ρ) using different microscopic approaches in addition to Skyrme interactions. The calculations
are taken from [23]