142
C. Hartnack et al.
lead to an intermediate
− which decays only by
−
→ nπ
− and thus does not
influence the π
− yield, a rescattering of a π
+ —yielding a
+ —will reproduce a π
+
with a probability of only one third. Thus the π
+ yield will be penalized when passing
neutron dominated matter. This effect even is enhanced by the Pauli blocking of the
delta decay: the high density of neutrons will add a penalty to the the
+
→ nπ
+
channel and reduce the π
+ yield even more. The Pauli blocking also acts on the
channel
−
→ nπ
− , but since there is no concurrent channel, this will only delay
the decay of the delta, but it does not change the π
− yield. This effect can be seen
when disabeling it: a calculation without Pauli blocking of the delta decay (black
dotted line) yields even smaller ratios.
11.2.2 Dependence of the Ratio on the Incident Energy
How to disentangle these effects? The FOPI collaboration had shown that the isospin
ratios in central collisions decrease when increasing the incident energy. Additionally
at these energies the isospin ratios could be explained by IQMD (and other models) without any assumption on the density dependence of the asymmetry potential. Figure 11.4 presents the same analysis as in Fig. 11.3 but for now for Au
(1200 AMeV)+Au. Indeed, for central collisions we see smaller values of the isospin
ratios and the differences due to the equation of state of asymmetric matter vanish
completely. However, the effect of the neutron skin becomes very prominent at
peripheral collisions while the influence of the Pauli blocking in the delta decay disappears as well. Here we get a very good handle to test the neutron skin from π
−
/π
+
ratios at high energies: from comparison of central and very peripheral collisions we
may estimate the thickness of the neutron skin. A more detailed investigation of that
procedure is presented in [16], where more refined parametrizations of the neutron
skin are studied and applied to different nuclei like
48 Ca or
208 Pb. Once the question
of the neutron skin is fixed at higher energies, one may attack the other effects at low
energies.
11.3 Influence of the Neutron Skin on Other Observables
Since standard IQMD calculations were done without any neutron skin it should
now be investigated whether this feature influences other variables, knowing that
standard IQMD was already very successful in describing many physical observables
including the dynamics of charged particles [6] and the production of strangeness
[10]. Therefore, we will analyze the influence of the neutron skin on variables related
to stopping and transverse pressure, to transverse and elliptic flow and to strangeness
production. It should also be noted that the absolute total pion yield (see, e.g., Fig.
11.1) is not affected by the neutron skin. The rescattering of pions in neutron rich
matter only changes their isospin flavors. We will compare dynamical observables
C. Hartnack et al.
lead to an intermediate
− which decays only by
−
→ nπ
− and thus does not
influence the π
− yield, a rescattering of a π
+ —yielding a
+ —will reproduce a π
+
with a probability of only one third. Thus the π
+ yield will be penalized when passing
neutron dominated matter. This effect even is enhanced by the Pauli blocking of the
delta decay: the high density of neutrons will add a penalty to the the
+
→ nπ
+
channel and reduce the π
+ yield even more. The Pauli blocking also acts on the
channel
−
→ nπ
− , but since there is no concurrent channel, this will only delay
the decay of the delta, but it does not change the π
− yield. This effect can be seen
when disabeling it: a calculation without Pauli blocking of the delta decay (black
dotted line) yields even smaller ratios.
11.2.2 Dependence of the Ratio on the Incident Energy
How to disentangle these effects? The FOPI collaboration had shown that the isospin
ratios in central collisions decrease when increasing the incident energy. Additionally
at these energies the isospin ratios could be explained by IQMD (and other models) without any assumption on the density dependence of the asymmetry potential. Figure 11.4 presents the same analysis as in Fig. 11.3 but for now for Au
(1200 AMeV)+Au. Indeed, for central collisions we see smaller values of the isospin
ratios and the differences due to the equation of state of asymmetric matter vanish
completely. However, the effect of the neutron skin becomes very prominent at
peripheral collisions while the influence of the Pauli blocking in the delta decay disappears as well. Here we get a very good handle to test the neutron skin from π
−
/π
+
ratios at high energies: from comparison of central and very peripheral collisions we
may estimate the thickness of the neutron skin. A more detailed investigation of that
procedure is presented in [16], where more refined parametrizations of the neutron
skin are studied and applied to different nuclei like
48 Ca or
208 Pb. Once the question
of the neutron skin is fixed at higher energies, one may attack the other effects at low
energies.
11.3 Influence of the Neutron Skin on Other Observables
Since standard IQMD calculations were done without any neutron skin it should
now be investigated whether this feature influences other variables, knowing that
standard IQMD was already very successful in describing many physical observables
including the dynamics of charged particles [6] and the production of strangeness
[10]. Therefore, we will analyze the influence of the neutron skin on variables related
to stopping and transverse pressure, to transverse and elliptic flow and to strangeness
production. It should also be noted that the absolute total pion yield (see, e.g., Fig.
11.1) is not affected by the neutron skin. The rescattering of pions in neutron rich
matter only changes their isospin flavors. We will compare dynamical observables