114
J. Aichelin et al.
9.4 Results
It is very challenging to develop an approach which propagates clusters and baryons
consistently and no satisfying approaches have been developed so far. Therefore, in
the PHQMD approach we propagate baryons and mesons only and define a consistent theoretical method which allows to identify clusters consisting of the propagated
nucleons. In our approach clusters are formed by the same nucleon–nucleon interaction which is active during the entire heavy-ion reaction. We call this dynamical
cluster formation in contradistinction to models where fragments are created instantaneously at a given time like in coalescence models. In this article we identify the
cluster by either the SACA [22, 23] or the MST algorithm [7]. The former is based on
the idea of Dorso and Randrup [24] that the most bound configuration of nucleons
and clusters, identified after the violent phase of the reaction, has a large overlap
with the final distribution of clusters and free nucleons. The ALADIN collaboration
has measured the cluster formation at beam energies between 600 AMeV and 1000
AMeV [25, 26], the largest beam energies for which cluster studies have been performed. Therefore, we use these data to study the dependence of the cluster formation
on the nuclear equation of state. One of the key results of the ALADIN collaboration
is the “rise and fall” of the multiplicity of intermediate mass clusters 3 ≤ Z ≤ 30
emitted in forward direction. This multiplicity is presented as a function of the sum
of all forward emitted bound charges, Z bound 2 which can be expressed with help of
the function:
Z bound 2 =
i
Z i (Z i − (1 + )),
with (0 < < < 1). One obtains a distribution which is for Au projectiles almost independent of the beam energy in the interval 600AMeV ≤ E beam ≤ 1000 AMeV and
also independent of the target size. We note, that in the original publication [25]
the intermediate mass cluster multiplicity has been overestimated due to misidentified, mostly Z = 3, clusters which were in reality two α particles. Later, with an
improved apparatus, this has been realized for smaller systems. A re-measurement
for the Au+Au system has shown that the multiplicity of intermediate mass clusters
is about 15 % lower than published in [25] . The corrected rise and fall curve for
Au+Au reactions has been published in [27] and will be used for the comparison in
our study. Figure 9.4 displays this rise and fall curve and the experimental results are
compared with the results for three EOS: S (left), SM (middle), and H (right).
We see a very different result for the three equations of state. Whereas the hard
equation of state agrees quite nicely with the data, the soft and soft momentum
dependent interaction give a quite different result. It is evident that a soft equation
of state makes the nuclei quite unstable, especially in semiperipheral and peripheral
interactions where Z bound 2 is large. Although the excitation energy of the projectile
and target remnants is small there the perturbation, caused by the interaction between
projectile and target, is sufficient to create instabilities.
J. Aichelin et al.
9.4 Results
It is very challenging to develop an approach which propagates clusters and baryons
consistently and no satisfying approaches have been developed so far. Therefore, in
the PHQMD approach we propagate baryons and mesons only and define a consistent theoretical method which allows to identify clusters consisting of the propagated
nucleons. In our approach clusters are formed by the same nucleon–nucleon interaction which is active during the entire heavy-ion reaction. We call this dynamical
cluster formation in contradistinction to models where fragments are created instantaneously at a given time like in coalescence models. In this article we identify the
cluster by either the SACA [22, 23] or the MST algorithm [7]. The former is based on
the idea of Dorso and Randrup [24] that the most bound configuration of nucleons
and clusters, identified after the violent phase of the reaction, has a large overlap
with the final distribution of clusters and free nucleons. The ALADIN collaboration
has measured the cluster formation at beam energies between 600 AMeV and 1000
AMeV [25, 26], the largest beam energies for which cluster studies have been performed. Therefore, we use these data to study the dependence of the cluster formation
on the nuclear equation of state. One of the key results of the ALADIN collaboration
is the “rise and fall” of the multiplicity of intermediate mass clusters 3 ≤ Z ≤ 30
emitted in forward direction. This multiplicity is presented as a function of the sum
of all forward emitted bound charges, Z bound 2 which can be expressed with help of
the function:
Z bound 2 =
i
Z i (Z i − (1 + )),
with (0 < < < 1). One obtains a distribution which is for Au projectiles almost independent of the beam energy in the interval 600AMeV ≤ E beam ≤ 1000 AMeV and
also independent of the target size. We note, that in the original publication [25]
the intermediate mass cluster multiplicity has been overestimated due to misidentified, mostly Z = 3, clusters which were in reality two α particles. Later, with an
improved apparatus, this has been realized for smaller systems. A re-measurement
for the Au+Au system has shown that the multiplicity of intermediate mass clusters
is about 15 % lower than published in [25] . The corrected rise and fall curve for
Au+Au reactions has been published in [27] and will be used for the comparison in
our study. Figure 9.4 displays this rise and fall curve and the experimental results are
compared with the results for three EOS: S (left), SM (middle), and H (right).
We see a very different result for the three equations of state. Whereas the hard
equation of state agrees quite nicely with the data, the soft and soft momentum
dependent interaction give a quite different result. It is evident that a soft equation
of state makes the nuclei quite unstable, especially in semiperipheral and peripheral
interactions where Z bound 2 is large. Although the excitation energy of the projectile
and target remnants is small there the perturbation, caused by the interaction between
projectile and target, is sufficient to create instabilities.