152
Y. Leifels
try energy in isospin-asymmetric systems. The FOPI collaboration has measured a
multitude of flow observables in many different collisions systems [15] in the energy
regime between 200 and 2000 MeV/nucleon with FOPI setup at SIS18@GSI.
12.2 Neutron and Charged Particle Elliptic Flow
The strengths of collective flows in heavy-ion collisions are determined by a Fourier
expansion of the azimuthal distributions of particles around the reaction plane:
dσ (y)
dφ
= C(1 + 2v 1 (y) cos φ + 2v 2 (y) cos 2φ.....)
(12.1)
The side flow of particles is characterized by the coefficient v 1 and the elliptic
flow by v 2 . The value of v 2 around mid-rapidity is negative at incident beam energies
between 0.2 and 6 GeV/nucleon which signifies that matter is squeezed out perpendicular to the reaction plane. Elliptic flow at those energies is known to be sensitive
to the stiffness of the symmetric part of the nuclear equation of state. In Fig. 12.1
data of (negative) elliptic flow of protons is shown for mid-central Au+Au collisions
at 400 MeV/nucleon (left panel) and 1.2 GeV/nucleon (right panel). The bell-shaped
experimental data are compared to IQMD predictions [16] employing a soft (SM) and
hard (HM) density dependence of the nuclear matter equation of state. The particles
within IQMD are interacting via a momentum dependent interaction which has been
deduced from experimental data on proton scattering off nuclei [16]. A momentum
dependent interaction is needed to describe the energy dependence of flow and pion
-0.05
0
0.05
0.1
-0.5
0
0.5
Y
0
-v
2
Au+Au 400 MeV/u, protons
u t0 >0.4
HM
SM
-0.05
0
0.05
0.1
-0.5
0
0.5
Y
0
-v
2
Au+Au 1.2 GeV/u, protons
HM
SM
Fig. 12.1 The elliptic flow v 2 measured with the FOPI setup in semi-central Au+Au collisions
as function of normalized rapidity Y 0 = y/y p , where y is the particle rapidity in the center-ofmass system and y p the rapidity of the projectile. The initial target-projectile rapidity gap always
extends from Y 0 = −1 to Y 0 = 1. The experimental data (shown as block points) are compared to
IQMD predictions [16] employing a soft EOS (denoted as red line) and a hard EOS (blue line). The
calculations have been performed using a momentum dependent interaction. Data and calculations
are taken from [15, 17]
Y. Leifels
try energy in isospin-asymmetric systems. The FOPI collaboration has measured a
multitude of flow observables in many different collisions systems [15] in the energy
regime between 200 and 2000 MeV/nucleon with FOPI setup at SIS18@GSI.
12.2 Neutron and Charged Particle Elliptic Flow
The strengths of collective flows in heavy-ion collisions are determined by a Fourier
expansion of the azimuthal distributions of particles around the reaction plane:
dσ (y)
dφ
= C(1 + 2v 1 (y) cos φ + 2v 2 (y) cos 2φ.....)
(12.1)
The side flow of particles is characterized by the coefficient v 1 and the elliptic
flow by v 2 . The value of v 2 around mid-rapidity is negative at incident beam energies
between 0.2 and 6 GeV/nucleon which signifies that matter is squeezed out perpendicular to the reaction plane. Elliptic flow at those energies is known to be sensitive
to the stiffness of the symmetric part of the nuclear equation of state. In Fig. 12.1
data of (negative) elliptic flow of protons is shown for mid-central Au+Au collisions
at 400 MeV/nucleon (left panel) and 1.2 GeV/nucleon (right panel). The bell-shaped
experimental data are compared to IQMD predictions [16] employing a soft (SM) and
hard (HM) density dependence of the nuclear matter equation of state. The particles
within IQMD are interacting via a momentum dependent interaction which has been
deduced from experimental data on proton scattering off nuclei [16]. A momentum
dependent interaction is needed to describe the energy dependence of flow and pion
-0.05
0
0.05
0.1
-0.5
0
0.5
Y
0
-v
2
Au+Au 400 MeV/u, protons
u t0 >0.4
HM
SM
-0.05
0
0.05
0.1
-0.5
0
0.5
Y
0
-v
2
Au+Au 1.2 GeV/u, protons
HM
SM
Fig. 12.1 The elliptic flow v 2 measured with the FOPI setup in semi-central Au+Au collisions
as function of normalized rapidity Y 0 = y/y p , where y is the particle rapidity in the center-ofmass system and y p the rapidity of the projectile. The initial target-projectile rapidity gap always
extends from Y 0 = −1 to Y 0 = 1. The experimental data (shown as block points) are compared to
IQMD predictions [16] employing a soft EOS (denoted as red line) and a hard EOS (blue line). The
calculations have been performed using a momentum dependent interaction. Data and calculations
are taken from [15, 17]